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#
# This file is the units database for use with GNU units, a units conversion
# program by Adrian Mariano adrianm@gnu.org
#
# Febuary 2024 Version 3.19
# last updated 16 February 2024
#
# Copyright (C) 1996-2002, 2004-2020, 2022, 2024
# Free Software Foundation, Inc
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor,
# Boston, MA 02110-1301 USA
#
############################################################################
#
# Improvements and corrections are welcome.
#
# See the end of this file for a list of items we have chosen to exclude
# or have decided are out of scope for GNU units.
#
# Fundamental constants in this file are the 2018 CODATA recommended values.
#
# Most units data was drawn from
# 1. NIST Special Publication 811, Guide for the
# Use of the International System of Units (SI).
# Barry N. Taylor. 2008
# https://www.nist.gov/pml/special-publication-811
# 2. CRC Handbook of Chemistry and Physics 70th edition
# 3. Oxford English Dictionary
# 4. Webster's New Universal Unabridged Dictionary
# 5. Units of Measure by Stephen Dresner
# 6. A Dictionary of English Weights and Measures by Ronald Zupko
# 7. British Weights and Measures by Ronald Zupko
# 8. Realm of Measure by Isaac Asimov
# 9. United States standards of weights and measures, their
# creation and creators by Arthur H. Frazier.
# 10. French weights and measures before the Revolution: a
# dictionary of provincial and local units by Ronald Zupko
# 11. Weights and Measures: their ancient origins and their
# development in Great Britain up to AD 1855 by FG Skinner
# 12. The World of Measurements by H. Arthur Klein
# 13. For Good Measure by William Johnstone
# 14. NTC's Encyclopedia of International Weights and Measures
# by William Johnstone
# 15. Sizes by John Lord
# 16. Sizesaurus by Stephen Strauss
# 17. CODATA Recommended Values of Physical Constants available at
# http://physics.nist.gov/cuu/Constants/index.html
# 18. How Many? A Dictionary of Units of Measurement. Available at
# http://www.ibiblio.org/units/
# 19. Numericana. http://www.numericana.com
# 20. UK history of measurement
# https://metrication.uk/more/timeline/
# 21. NIST Handbook 44, Specifications, Tolerances, and
# Other Technical Requirements for Weighing and Measuring
# Devices. 2011
# 22. NIST Special Publication 447, Weights and Measures Standards
# of the United States: a brief history. Lewis V. Judson.
# 1963; rev. 1976
# 23. CRC Handbook of Chemistry and Physics, 96th edition
# 24. Dictionary of Scientific Units, 6th ed. H.G. Jerrard and D.B.
# McNeill. 1992
# 25. NIST Special Publication 330, The International System of
# Units (SI). ed. Barry N. Taylor and Ambler Thompson. 2008
# https://www.nist.gov/pml/special-publication-330
# 26. BIPM Brochure, The International System of Units (SI).
# 9th ed., 2019
# https://www.bipm.org/en/publications/si-brochure/
#
###########################################################################
#
# If units you use are missing or defined incorrectly, please contact me.
# If your country's local units are missing and you are willing to supply
# them, please send me a list.
#
###########################################################################
###########################################################################
#
# Brief Philosophy of this file
#
# Most unit definitions are made in terms of integers or simple fractions of
# other definitions. The typical exceptions are when converting between two
# different unit systems, or the values of measured physical constants. In
# this file definitions are given in the most natural and revealing way in
# terms of integer factors.
#
# If you make changes be sure to run 'units --check' to check your work.
#
# The file is USA-centric, but there is some modest effort to support other
# countries. This file is now coded in UTF-8. To support environments where
# UTF-8 is not available, definitions that require this character set are
# wrapped in !utf8 directives.
#
# When a unit name is used in different countries with the different meanings
# the system should be as follows:
#
# Suppose countries ABC and XYZ both use the "foo". Then globally define
#
# ABCfoo <some value>
# XYZfoo <different value>
#
# Then, using the !locale directive, define the "foo" appropriately for each of
# the two countries with a definition like
#
# !locale ABC
# foo ABCfoo
# !endlocale
#
###########################################################################
!locale en_US
! set UNITS_ENGLISH US
!endlocale
!locale en_GB
! set UNITS_ENGLISH GB
!endlocale
!set UNITS_ENGLISH US # Default setting for English units
!set UNITS_SYSTEM default # Set a default value
!varnot UNITS_SYSTEM si emu esu gaussian gauss hlu natural natural-gauss hartree planck planck-red default
!message Unknown unit system given with -u or UNITS_SYSTEM environment variable
!message Valid systems: si, emu, esu, gauss[ian], hlu, natural, natural-gauss
!message planck, planck-red, hartree
!message Using SI
!prompt (SI)
!endvar
!var UNITS_SYSTEM si
!message SI units selected
!prompt (SI)
!endvar
###########################################################################
# #
# Primitive units. Any unit defined to contain a '!' character is a #
# primitive unit which will not be reduced any further. All units should #
# reduce to primitive units. #
# #
###########################################################################
#
# SI units
#
# On 20 May 2019, the SI was revised to define the units by fixing the
# values of physical constants that depend on those units.
#
# https://www.nist.gov/si-redefinition/
#
# The BIPM--the International Bureau of Weights and Measures--provides a
# succinct description of the new SI in its Concise Summary:
#
# https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-concise-EN.pdf
#
# The SI is the system of units in which:
#
# * the unperturbed ground state hyperfine transition frequency of the
# caesium 133 atom is delta nu_Cs = 9 192 631 770 Hz,
# * the speed of light in vacuum, c, is 299 792 458 m/s,
# * the Planck constant, h, is 6.626 070 15 * 10^-34 J s,
# * the elementary charge, e, is 1.602 176 634 * 10^-19 C,
# * the Boltzmann constant, k, is 1.380 649 * 10^-23 J/K,
# * the Avogadro constant, N_A, is 6.022 140 76 * 10^23 mol^-1,
# * the luminous efficacy of monochromatic radiation of frequency
# 540 * 10^12 Hz, K_cd, is 683 lm/W,
#
# where the hertz, joule, coulomb, lumen, and watt, with unit symbols Hz,
# J, C, lm, and W, respectively, are related to the units second, metre,
# kilogram, ampere, kelvin, mole, and candela, with unit symbols s, m, kg,
# A, K, mol, and cd, respectively, according to Hz = s^-1, J = kg m^2 s^-2,
# C = A s, lm = cd m^2 m^-2 = cd sr, and W = kg m^2 s^-3.
#
# These definitions specify the exact numerical value of each constant when
# its value is expressed in the corresponding SI unit. By fixing the exact
# numerical value the unit becomes defined, since the product of the
# numerical value and the unit has to equal the value of the constant,
# which is invariant.
#
# The defining constants have been chosen such that, when taken together,
# their units cover all of the units of the SI. In general, there is no
# one-to-one correspondence between the defining constants and the SI base
# units. Any SI unit is a product of powers of these seven constants and a
# dimensionless factor.
#
# Until 2018, the SI was defined in terms of base units and derived units.
# These categories are no longer essential in the SI, but they are maintained
# in view of their convenience and widespread use. They are arguably more
# intuitive than the new definitions. (They are also essential to the
# operation of GNU units.) The definitions of the base units, which follow
# from the definition of the SI in terms of the seven defining constants, are
# given below.
#
s ! # The second, symbol s, is the SI unit of time. It is defined
second s # by taking the fixed numerical value of the unperturbed
# ground-state hyperfine transition frequency of the
# cesium-133 atom to be 9 192 631 770 when expressed in the
# unit Hz, which is equal to 1/s.
#
# This definition is a restatement of the previous one, the
# duration of 9192631770 periods of the radiation corresponding
# to the cesium-133 transition.
nu_133Cs 9192631770 Hz # Cesium-133 transition frequency (exact)
c_SI 299792458
c 299792458 m/s # speed of light in vacuum (exact)
m ! # The metre, symbol m, is the SI unit of length. It is
meter m # defined by taking the fixed numerical value of the speed
metre m # of light in vacuum, c, to be 299 792 458 when expressed in
# units of m/s.
#
# This definition is a rewording of the previous one and is
# equivalent to defining the meter as the distance light
# travels in 1|299792458 seconds. The meter was originally
# intended to be 1e-7 of the length along a meridian from the
# equator to a pole.
h_SI 6.62607015e-34
h 6.62607015e-34 J s # Planck constant (exact)
kg ! # The kilogram, symbol kg, is the SI unit of mass. It is
kilogram kg # defined by taking the fixed numerical value of the Planck
# constant, h, to be 6.626 070 15 * 10^-34 when expressed in
# the unit J s which is equal to kg m^2 / s.
#
# One advantage of fixing h to define the kilogram is that this
# affects constants used to define the ampere. If the kg were
# defined by directly fixing the mass of something, then h
# would be subject to error.
#
# The previous definition of the kilogram was the mass of the
# international prototype kilogram. The kilogram was the last
# unit whose definition relied on reference to an artifact.
#
# It is not obvious what this new definition means, or
# intuitively how fixing Planck's constant defines the
# kilogram. To define the kilogram we need to give the mass
# of some reference in kilograms. Previously the prototype in
# France served as this reference, and it weighed exactly 1
# kg. But the reference can have any weight as long as you
# know the weight of the reference. The new definition uses
# the "mass" of a photon, or more accurately, the mass
# equivalent of the energy of a photon. The energy of a
# photon depends on its frequency. If you pick a frequency,
# f, then the energy of the photon is hf, and hence the mass
# equivalent is hf/c^2. If we reduce this expression using
# the constant defined values for h and c the result is a
# value in kilograms for the mass-equivalent of a photon of
# frequency f, which can therefore define the size of the
# kilogram.
#
# For more on the relationship between mass an Planck's
# constant:
#
# https://www.nist.gov/si-redefinition/kilogram-mass-and-plancks-constant
# This definition may still seem rather abstract: you can't
# place a "kilogram of radiation" on one side of a balance.
# Metrologists realize the kilogram using a Kibble Balance, a
# device which relates mechanical energy to electrical energy
# and can measure mass with extreme accuracy if h is known.
#
# For more on the Kibble Balance see
#
# https://www.nist.gov/si-redefinition/kilogram-kibble-balance
# https://en.wikipedia.org/wiki/Kibble_balance
k_SI 1.380649e-23
boltzmann 1.380649e-23 J/K # Boltzmann constant (exact)
k boltzmann
K ! # The kelvin, symbol K, is the SI unit of thermodynamic
kelvin K # temperature. It is defined by taking the fixed numerical
# value of the Boltzmann constant, k, to be 1.380 649 * 10^-23
# when expressed in the unit J/K, which is equal to
# kg m^2/s^2 K.
#
# The boltzmann constant establishes the relationship between
# energy and temperature. The average thermal energy carried
# by each degree of freedom is kT/2. A monatomic ideal gas
# has three degrees of freedom corresponding to the three
# spatial directions, which means its thermal energy is
# (3/2) k T.
#
# The previous definition of the kelvin was based on the
# triple point of water. The change in the definition of the
# kelvin will not have much effect on measurement practice.
# Practical temperature calibration makes use of two scales,
# the International Temperature Scale of 1990 (ITS-90), which
# covers the range of 0.65 K to 1357.77K and the Provisional
# Low Temperature Scale of 2000 (PLTS-2000), which covers the
# range of 0.9 mK to 1 K.
# https://www.bipm.org/en/committees/cc/cct/publications-cc.html
#
# The ITS-90 contains 17 reference points including things
# like the triple point of hydrogen (13.8033 K) or the
# freezing point of gold (1337.33 K), and of course the triple
# point of water. The PLTS-2000 specifies four reference
# points, all based on properties of helium-3.
#
# The redefinition of the kelvin will not affect the values of
# these reference points, which have been determined by
# primary thermometry, using thermometers that rely only on
# relationships that allow temperature to be calculated
# directly without using any unknown quantities. Examples
# include acoustic thermometers, which measure the speed of
# sound in a gas, or electronic thermometers, which measure
# tiny voltage fluctuations in resistors. Both variables
# depend directly on temperature.
e_SI 1.602176634e-19
e 1.602176634e-19 C # electron charge (exact)
A ! # The ampere, symbol A, is the SI unit of electric current.
ampere A # It is defined by taking the fixed numerical value of the
amp ampere # elementary charge, e, to be 1.602 176 634 * 10^-19 when
# expressed in the unit C, which is equal to A*s.
#
# The previous definition was the current which produces a
# force of 2e-7 N/m between two infinitely long wires a meter
# apart. This definition was difficult to realize accurately.
#
# The ampere is actually realized by establishing the volt and
# the ohm, since A = V / ohm. These measurements can be done
# using the Josephson effect and the quantum Hall effect,
# which accurately measure voltage and resistance, respectively,
# with reference to two fixed constants, the Josephson
# constant, K_J=2e/h and the von Klitzing constant, R_K=h/e^2.
# Under the previous SI system, these constants had official
# fixed values, defined in 1990. This created a situation
# where the standard values for the volt and ohm were in some
# sense outside of SI because they depended primarily on
# constants different from the ones used to define SI. After
# the revision, since e and h have exact definitions, the
# Josephson and von Klitzing constants will also have exact
# definitions that derive from SI instead of the conventional
# 1990 values.
#
# In fact we know that there is a small offset between the
# conventional values of the electrical units based on the
# conventional 1990 values and the SI values. The new
# definition, which brings the practical electrical units back
# into SI, will lead to a one time change of +0.1ppm for
# voltage values and +0.02ppm for resistance values.
#
# The previous definition resulted in fixed exact values for
# the vacuum permeability (mu0), the impedance of free space
# (Z0), the vacuum permittivity (epsilon0), and the Coulomb
# constant. With the new definition, these four values are
# subject to experimental error.
avogadro 6.02214076e23 / mol # Size of a mole (exact)
N_A avogadro
mol ! # The mole, symbol mol, is the SI unit of amount of
mole mol # substance. One mole contains exactly 6.022 140 76 * 10^23
# elementary entities. This number is the fixed numerical
# value of the Avogadro constant, N_A, when expressed in the
# unit 1/mol and is called the Avogadro number. The amount of
# substance, symbol n, of a system is a measure of the number
# of specified elementary entities. An elementary entity may
# be an atom, a molecule, an ion, an electron, any other
# particle or specified group of particles.
#
# The atomic mass unit (u) is defined as 1/12 the mass of
# carbon-12. Previously the mole was defined so that a mole
# of carbon-12 weighed exactly 12g, or N_A u = 1 g/mol
# exactly. This relationship is now an experimental,
# approximate relationship.
#
# To determine the size of the mole, researchers used spheres
# of very pure silicon-28 that weighed a kilogram. They
# measured the molar mass of Si-28 using mass spectrometry and
# used X-ray diffraction interferometry to determine the
# spacing of the silicon atoms in the sphere. Using the
# sphere's volume it was then possible to determine the number
# of silicon atoms in the sphere, and hence determine the
# Avogadro constant. The results of this experiment were used
# to define N_A, which is henceforth a fixed, unchanging
# quantity.
cd ! # The candela, symbol cd, is the SI unit of luminous intensity
candela cd # in a given direction. It is defined by taking the fixed
# numerical value of the luminous efficacy of monochromatic
# radiation of the frequency 540e12 Hz to be 683 when
# expressed in the unit lumen/watt, which is equal to
# cd sr/W, or cd sr s^3/kg m^2
#
# This definition is a rewording of the previous definition.
# Luminous intensity differs from radiant intensity (W/sr) in
# that it is adjusted for human perceptual dependence on
# wavelength. The frequency of 540e12 Hz (yellow;
# wavelength approximately 555 nm in vacuum) is where human
# perception is most efficient.
K_cd 683 lumen/W # Luminous efficiency at 540e12 Hz (exact)
# Angular Measure
#
# The radian and steradian are defined as dimensionless primitive units.
# The radian is equal to m/m and the steradian to m^2/m^2 so these units are
# dimensionless. Retaining them as named units is useful because it allows
# clarity in expressions and makes the meaning of unit definitions more clear.
# These units will reduce to 1 in conversions but not for sums of units or for
# arguments to functions.
#
radian !dimensionless # Plane angle subtended at the center of a circle by
# an arc equal in length to the radius of the
# circle.
# Dimension: LENGTH (of arc) / DISTANCE (radius)
sr !dimensionless # Solid angle which cuts off an area of the surface
steradian sr # of the sphere equal to that of a square with
# sides of length equal to the radius of the
# sphere.
# Dimension: AREA (of surface) / DISTANCE^2
# (radius^2)
#
# A primitive non-SI unit
#
bit ! # Basic unit of information (entropy). The entropy in bits
# of a random variable over a finite alphabet is defined
# to be the sum of -p(i)*log2(p(i)) over the alphabet where
# p(i) is the probability that the random variable takes
# on the value i.
#
# Currency: the primitive unit of currency is defined in currency.units.
# It is usually the US$ or the euro, but it is user selectable.
#
#
# Absolute value
#
abs(x) noerror sqrt(x^2)
###########################################################################
# #
# Prefixes (longer names must come first) #
# #
###########################################################################
quetta- 1e30 # Allegedly from "q" plus Greek "deka" (ten)
ronna- 1e27 # Allegedly from "r" plus Greek "ennea" (nine)
yotta- 1e24 # Greek or Latin "octo" (eight)
zetta- 1e21 # Latin "septem" (seven)
exa- 1e18 # Greek "hex" (six)
peta- 1e15 # Greek "pente" (five)
tera- 1e12 # Greek "teras" (monster)
giga- 1e9 # Greek "gigas" (giant)
mega- 1e6 # Greek "megas" (large)
myria- 1e4 # Not an official SI prefix
kilo- 1e3 # Greek "chilioi" (thousand)
hecto- 1e2 # Greek "hekaton" (hundred)
deca- 1e1 # Greek "deka" (ten)
deka- deca
deci- 1e-1 # Latin "decimus" (tenth)
centi- 1e-2 # Latin "centum" (hundred)
milli- 1e-3 # Latin "mille" (thousand)
micro- 1e-6 # Latin "micro" or Greek "mikros" (small)
nano- 1e-9 # Latin "nanus" or Greek "nanos" (dwarf)
pico- 1e-12 # Spanish "pico" (a bit)
femto- 1e-15 # Danish-Norwegian "femten" (fifteen)
atto- 1e-18 # Danish-Norwegian "atten" (eighteen)
zepto- 1e-21 # Latin "septem" (seven)
yocto- 1e-24 # Greek or Latin "octo" (eight)
ronto- 1e-27 # Allegedly "r" plus Latin "novum" (nine)
quecto- 1e-30 # Allegedly "q" plus Latin "decim" (ten)
quarter- 1|4
semi- 0.5
demi- 0.5
hemi- 0.5
half- 0.5
double- 2
triple- 3
treble- 3
kibi- 2^10 # In response to the improper and confusing
mebi- 2^20 # use of SI prefixes for powers of two,
gibi- 2^30 # the International Electrotechnical
tebi- 2^40 # Commission aproved these binary prefixes
pebi- 2^50 # in IEC 60027-2 Amendment 2 (1999).
exbi- 2^60
zebi- 2^70 # Zebi- and yobi- were added in the 2005 ed.,
yobi- 2^80 # later superseded by ISO/IEC 80000-13:2008.
robi- 2^90
quebi- 2^100
Ki- kibi
Mi- mebi
Gi- gibi
Ti- tebi
Pi- pebi
Ei- exbi
Zi- zebi
Yi- yobi
Ri- robi
Qi- quebi
Q- quetta
R- ronna
Y- yotta
Z- zetta
E- exa
P- peta
T- tera
G- giga
M- mega
k- kilo
h- hecto
da- deka
d- deci
c- centi
m- milli
u- micro # it should be a mu but u is easy to type
n- nano
p- pico
f- femto
a- atto
z- zepto
y- yocto
r- ronto
q- quecto
#
# Names of some numbers
#
one 1
two 2
double 2
couple 2
three 3
triple 3
four 4
quadruple 4
five 5
quintuple 5
six 6
seven 7
eight 8
nine 9
ten 10
eleven 11
twelve 12
thirteen 13
fourteen 14
fifteen 15
sixteen 16
seventeen 17
eighteen 18
nineteen 19
twenty 20
thirty 30
forty 40
fifty 50
sixty 60
seventy 70
eighty 80
ninety 90
hundred 100
thousand 1000
million 1e6
twoscore two score
threescore three score
fourscore four score
fivescore five score
sixscore six score
sevenscore seven score
eightscore eight score
ninescore nine score
tenscore ten score
twelvescore twelve score
# These number terms were described by N. Chuquet and De la Roche in the 16th
# century as being successive powers of a million. These definitions are still
# used in most European countries. The current US definitions for these
# numbers arose in the 17th century and don't make nearly as much sense. These
# numbers are listed in the CRC Concise Encyclopedia of Mathematics by Eric
# W. Weisstein.
shortbillion 1e9
shorttrillion 1e12
shortquadrillion 1e15
shortquintillion 1e18
shortsextillion 1e21
shortseptillion 1e24
shortoctillion 1e27
shortnonillion 1e30
shortnoventillion shortnonillion
shortdecillion 1e33
shortundecillion 1e36
shortduodecillion 1e39
shorttredecillion 1e42
shortquattuordecillion 1e45
shortquindecillion 1e48
shortsexdecillion 1e51
shortseptendecillion 1e54
shortoctodecillion 1e57
shortnovemdecillion 1e60
shortvigintillion 1e63
centillion 1e303
googol 1e100
longbillion million^2
longtrillion million^3
longquadrillion million^4
longquintillion million^5
longsextillion million^6
longseptillion million^7
longoctillion million^8
longnonillion million^9
longnoventillion longnonillion
longdecillion million^10
longundecillion million^11
longduodecillion million^12
longtredecillion million^13
longquattuordecillion million^14
longquindecillion million^15
longsexdecillion million^16
longseptdecillion million^17
longoctodecillion million^18
longnovemdecillion million^19
longvigintillion million^20
# These numbers fill the gaps left by the long system above.
milliard 1000 million
billiard 1000 million^2
trilliard 1000 million^3
quadrilliard 1000 million^4
quintilliard 1000 million^5
sextilliard 1000 million^6
septilliard 1000 million^7
octilliard 1000 million^8
nonilliard 1000 million^9
noventilliard nonilliard
decilliard 1000 million^10
# For consistency
longmilliard milliard
longbilliard billiard
longtrilliard trilliard
longquadrilliard quadrilliard
longquintilliard quintilliard
longsextilliard sextilliard
longseptilliard septilliard
longoctilliard octilliard
longnonilliard nonilliard
longnoventilliard noventilliard
longdecilliard decilliard
# The long centillion would be 1e600. The googolplex is another
# familiar large number equal to 10^googol. These numbers give overflows.
#
# The short system prevails in English speaking countries
#
billion shortbillion
trillion shorttrillion
quadrillion shortquadrillion
quintillion shortquintillion
sextillion shortsextillion
septillion shortseptillion
octillion shortoctillion
nonillion shortnonillion
noventillion shortnoventillion
decillion shortdecillion
undecillion shortundecillion
duodecillion shortduodecillion
tredecillion shorttredecillion
quattuordecillion shortquattuordecillion
quindecillion shortquindecillion
sexdecillion shortsexdecillion
septendecillion shortseptendecillion
octodecillion shortoctodecillion
novemdecillion shortnovemdecillion
vigintillion shortvigintillion
#
# Numbers used in India
#
lakh 1e5
crore 1e7
arab 1e9
kharab 1e11
neel 1e13
padm 1e15
shankh 1e17
#############################################################################
# #
# Derived units which can be reduced to the primitive units #
# #
#############################################################################
#
# Named SI derived units (officially accepted)
#
newton kg m / s^2 # force
N newton
pascal N/m^2 # pressure or stress
Pa pascal
joule N m # energy
J joule
watt J/s # power
W watt
coulomb A s # charge
C coulomb
volt W/A # potential difference
V volt
ohm V/A # electrical resistance
siemens A/V # electrical conductance
S siemens
farad C/V # capacitance
F farad
weber V s # magnetic flux
Wb weber
henry V s / A # inductance, also Wb/A, but needs to be
H henry # defined this way for CGS units
tesla Wb/m^2 # magnetic flux density
T tesla
hertz /s # frequency
Hz hertz
#
# Dimensions. These are here to help with dimensional analysis and
# because they will appear in the list produced by hitting '?' at the
# "You want:" prompt to tell the user the dimension of the unit.
#
LENGTH meter
AREA LENGTH^2
VOLUME LENGTH^3
MASS kilogram
AMOUNT mole
ANGLE radian
SOLID_ANGLE steradian
MONEY US$
FORCE newton
PRESSURE FORCE / AREA
STRESS FORCE / AREA
FREQUENCY hertz
WAVELENGTH LENGTH
WAVENUMBER 1/WAVELENGTH # number of waves per distance
VELOCITY DISPLACEMENT / TIME # a vector (includes direction)
SPEED DISTANCE / TIME # a scalar
ACCELERATION VELOCITY / TIME
MOMENTUM MASS VELOCITY # Also ENERGY / VELOCITY or IMPULSE
IMPULSE FORCE TIME
DISPLACEMENT LENGTH
DISTANCE LENGTH
ELONGATION LENGTH
STRAIN ELONGATION / LENGTH
ENERGY joule
POWER watt
WORK FORCE DISTANCE
DENSITY MASS / VOLUME
LINEAR_DENSITY MASS / LENGTH
SPECIFIC_ENERGY ENERGY / MASS
VISCOSITY FORCE TIME / AREA
KINEMATIC_VISCOSITY VISCOSITY / DENSITY
CURRENT ampere
CHARGE coulomb
CAPACITANCE farad
RESISTANCE ohm
CONDUCTANCE siemens
# It may be easier to understand the relationship by considering
# an object with specified dimensions and resistivity, whose
# resistance is given by the resistivity * length / area.
RESISTIVITY RESISTANCE AREA / LENGTH
CONDUCTIVITY CONDUCTANCE LENGTH / AREA
INDUCTANCE henry
E_FIELD ELECTRIC_POTENTIAL / LENGTH
B_FIELD tesla
# The D and H fields are related to the E and B fields by factors of
# epsilon and mu respectively, so their units can be found by
# multiplying/dividing by the epsilon0 and mu0. The more complex
# definitions below make it possible to use D_FIELD and E_FIELD to
# convert between SI and CGS units for these dimensions.
D_FIELD E_FIELD epsilon0 / epsilon0_SI # mu0_SI c^2 F / m
H_FIELD B_FIELD / (mu0/mu0_SI)
ELECTRIC_DIPOLE_MOMENT C m
MAGNETIC_DIPOLE_MOMENT J / T
POLARIZATION ELECTRIC_DIPOLE_MOMENT / VOLUME
MAGNETIZATION MAGNETIC_DIPOLE_MOMENT / VOLUME
ELECTRIC_POTENTIAL ENERGY / CHARGE #volt
VOLTAGE ELECTRIC_POTENTIAL
E_FLUX E_FIELD AREA
D_FLUX D_FIELD AREA
B_FLUX B_FIELD AREA
H_FLUX H_FIELD AREA
#
# units derived easily from SI units
#
gram millikg
gm gram
g gram
tonne 1000 kg
t tonne
metricton tonne
sthene tonne m / s^2
funal sthene
pieze sthene / m^2
quintal 100 kg
bar 1e5 Pa # About 1 atm
b bar
vac millibar
micron micrometer # One millionth of a meter
bicron picometer # One brbillionth of a meter
cc cm^3
are 100 m^2
a are
liter 1000 cc # The liter was defined in 1901 as the
oldliter 1.000028 dm^3 # space occupied by 1 kg of pure water at
L liter # the temperature of its maximum density
l liter # under a pressure of 1 atm. This was
# supposed to be 1000 cubic cm, but it
# was discovered that the original
# measurement was off. In 1964, the
# liter was redefined to be exactly 1000
# cubic centimeters.
Ah amp hour # Unit of charge
mho siemens # Inverse of ohm, hence ohm spelled backward
galvat ampere # Named after Luigi Galvani
angstrom 1e-10 m # Convenient for describing molecular sizes
xunit xunit_cu # Used for measuring x-ray wavelengths.
siegbahn xunit # Originally defined to be 1|3029.45 of
xunit_cu 1.00207697e-13 m # the spacing of calcite planes at 18
xunit_mo 1.00209952e-13 m # degC. It was intended to be exactly
# 1e-13 m, but was later found to be
# slightly off. Current usage is with
# reference to common x-ray lines, either
# the K-alpha 1 line of copper or the
# same line of molybdenum.
angstromstar 1.00001495 angstrom # Defined by JA Bearden in 1965 to replace
# the X unit. The wavelength of the
# tungsten K alpha1 line was defined as
# exactly 0.20901 angstrom star, with the
# value chosen to try to make the new
# unit close to the angstrom.
silicon_d220 1.920155716e-10 m # Silicon lattice spacing
siliconlattice sqrt(8) silicon_d220# Silicon lattice parameter, (a), the side
# length of the unit cell for the diamond
# centered cubic structure of silicon.
fermi 1e-15 m # Convenient for describing nuclear sizes
# Nuclear radius is from 1 to 10 fermis
barn 1e-28 m^2 # Used to measure cross section for
# particle physics collision, said to
# have originated in the phrase "big as
# a barn".
shed 1e-24 barn # Defined to be a smaller companion to the
# barn, but it's too small to be of
# much use.
brewster micron^2/N # measures stress-optical coef
diopter /m # measures reciprocal of lens focal length
fresnel 1e12 Hz # occasionally used in spectroscopy
shake 1e-8 sec
svedberg 1e-13 s # Used for measuring the sedimentation
# coefficient for centrifuging.
gamma microgram # Also used for 1e-9 tesla
lambda microliter
spat 1e12 m # Rarely used for astronomical measurements
preece 1e13 ohm m # resistivity
planck J s # action of one joule over one second
sturgeon /henry # magnetic reluctance
daraf 1/farad # elastance (farad spelled backwards)
leo 10 m/s^2
poiseuille N s / m^2 # viscosity
mayer J/g K # specific heat
mired / microK # reciprocal color temperature. The name
# abbreviates micro reciprocal degree.
crocodile megavolt # used informally in UK physics labs
metricounce 25 g
mounce metricounce
finsenunit 1e5 W/m^2 # Measures intensity of ultraviolet light
# with wavelength 296.7 nm.
fluxunit 1e-26 W/m^2 Hz # Used in radio astronomy to measure
# the energy incident on the receiving
# body across a specified frequency
# bandwidth. [12]
jansky fluxunit # K. G. Jansky identified radio waves coming
Jy jansky # from outer space in 1931.
flick W / cm^2 sr micrometer # Spectral radiance or irradiance
pfu / cm^2 sr s # particle flux unit -- Used to measure
# rate at which particles are received by
# a spacecraft as particles per solid
# angle per detector area per second. [18]
pyron cal_IT / cm^2 min # Measures heat flow from solar radiation,
# from Greek work "pyr" for fire.
katal mol/sec # Measure of the amount of a catalyst. One
kat katal # katal of catalyst enables the reaction
# to consume or produce one mol/sec.
solarluminosity 382.8e24 W # A common yardstick for comparing the
# output of different stars.
# http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
# at mean Earth-Sun distance
solarirradiance solarluminosity / (4 pi sundist^2)
solarconstant solarirradiance
TSI solarirradiance # total solar irradiance
#
# time
#
sec s
minute 60 s
min minute
hour 60 min
hr hour
day 24 hr
d day
da day
week 7 day
wk week
sennight 7 day
fortnight 14 day
blink 1e-5 day # Actual human blink takes 1|3 second
ce 1e-2 day
cron 1e6 years
watch 4 hours # time a sentry stands watch or a ship's
# crew is on duty.
bell 1|8 watch # Bell would be sounded every 30 minutes.
# French Revolutionary Time or Decimal Time. It was Proposed during
# the French Revolution. A few clocks were made, but it never caught
# on. In 1998 Swatch defined a time measurement called ".beat" and
# sold some watches that displayed time in this unit.
decimalhour 1|10 day
decimalminute 1|100 decimalhour
decimalsecond 1|100 decimalminute
beat decimalminute # Swatch Internet Time
#
# angular measure
#
circle 2 pi radian
degree 1|360 circle
deg degree
arcdeg degree
arcmin 1|60 degree
arcminute arcmin
' arcmin
arcsec 1|60 arcmin
arcsecond arcsec
" arcsec
'' "
rightangle 90 degrees
quadrant 1|4 circle
quintant 1|5 circle
sextant 1|6 circle
sign 1|12 circle # Angular extent of one sign of the zodiac
turn circle
revolution turn
rev turn
pulsatance radian / sec
gon 1|100 rightangle # measure of grade
grade gon
centesimalminute 1|100 grade
centesimalsecond 1|100 centesimalminute
milangle 1|6400 circle # Official NIST definition.
# Another choice is 1e-3 radian.
pointangle 1|32 circle # Used for reporting compass readings
centrad 0.01 radian # Used for angular deviation of light
# through a prism.
mas milli arcsec # Used by astronomers
seclongitude circle (seconds/day) # Astronomers measure longitude
# (which they call right ascension) in
# time units by dividing the equator into
# 24 hours instead of 360 degrees.
#
# Some geometric formulas
#
circlearea(r) units=[m;m^2] range=[0,) pi r^2 ; sqrt(circlearea/pi)
spherevolume(r) units=[m;m^3] range=[0,) 4|3 pi r^3 ; \
cuberoot(spherevolume/4|3 pi)
spherevol() spherevolume
square(x) range=[0,) x^2 ; sqrt(square)
#
# Solid angle measure
#
sphere 4 pi sr
squaredegree 1|180^2 pi^2 sr
squareminute 1|60^2 squaredegree
squaresecond 1|60^2 squareminute
squarearcmin squareminute
squarearcsec squaresecond
sphericalrightangle 1|8 sphere
octant 1|8 sphere
#
# Concentration measures
#
percent 0.01
% percent
mill 0.001 # Originally established by Congress in 1791
# as a unit of money equal to 0.001 dollars,
# it has come to refer to 0.001 in general.
# Used by some towns to set their property
# tax rate, and written with a symbol similar
# to the % symbol but with two 0's in the
# denominator. [18]
proof 1|200 # Alcohol content measured by volume at
# 60 degrees Fahrenheit. This is a USA
# measure. In Europe proof=percent.
ppm 1e-6
partspermillion ppm
ppb 1e-9
partsperbillion ppb # USA billion
ppt 1e-12
partspertrillion ppt # USA trillion
karat 1|24 # measure of gold purity
caratgold karat
gammil mg/l
basispoint 0.01 % # Used in finance
fine 1|1000 # Measure of gold purity
# The pH scale is used to measure the concentration of hydronium (H3O+) ions in
# a solution. A neutral solution has a pH of 7 as a result of dissociated
# water molecules.
pH(x) units=[1;mol/liter] range=(0,) 10^(-x) mol/liter ; (-log(pH liters/mol))
#
# Temperature
#
# Two types of units are defined: units for converting temperature differences
# and functions for converting absolute temperatures. Conversions for
# differences start with "deg" and conversions for absolute temperature start
# with "temp".
#
# If the temperature inside is 72 degrees Fahrenheit and you want to
# convert this to degrees Celsius then you need absolute temperature:
#
# You have: tempF(72)
# You want: tempC
# 22.222222
#
# If the temperature rose 72 degrees Fahrenheit during the chemical reaction
# then this is a temperature difference:
#
# You have: 72 degF
# You want: degC
# * 40
# / 0.025
#
TEMPERATURE kelvin
TEMPERATURE_DIFFERENCE kelvin
# In 1741 Anders Celsius introduced a temperature scale with water boiling at
# 0 degrees and freezing at 100 degrees at standard pressure. After his death
# the fixed points were reversed and the scale was called the centigrade
# scale. Due to the difficulty of accurately measuring the temperature of
# melting ice at standard pressure, the centigrade scale was replaced in 1954
# by the Celsius scale which is defined by subtracting 273.15 from the
# temperature in Kelvins. This definition differed slightly from the old
# centigrade definition, but the Kelvin scale depends on the triple point of
# water rather than a melting point, so it can be measured accurately.
tempC(x) units=[1;K] domain=[-273.15,) range=[0,) \
x K + stdtemp ; (tempC +(-stdtemp))/K
tempcelsius() tempC
degcelsius K
degC K
# Fahrenheit defined his temperature scale by setting 0 to the coldest
# temperature he could produce in his lab with a salt water solution and by
# setting 96 degrees to body heat. In Fahrenheit's words:
#
# Placing the thermometer in a mixture of sal ammoniac or sea
# salt, ice, and water a point on the scale will be found which
# is denoted as zero. A second point is obtained if the same
# mixture is used without salt. Denote this position as 30. A
# third point, designated as 96, is obtained if the thermometer
# is placed in the mouth so as to acquire the heat of a healthy
# man." (D. G. Fahrenheit, Phil. Trans. (London) 33, 78, 1724)
tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \
(x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
tempfahrenheit() tempF
degfahrenheit 5|9 degC
degF 5|9 degC
degreesrankine degF # The Rankine scale has the
degrankine degreesrankine # Fahrenheit degree, but its zero
degreerankine degF # is at absolute zero.
degR degrankine
tempR degrankine
temprankine degrankine
tempreaumur(x) units=[1;K] domain=[-218.52,) range=[0,) \
x degreaumur+stdtemp ; (tempreaumur+(-stdtemp))/degreaumur
degreaumur 10|8 degC # The Reaumur scale was used in Europe and
# particularly in France. It is defined
# to be 0 at the freezing point of water
# and 80 at the boiling point. Reaumur
# apparently selected 80 because it is
# divisible by many numbers.
degK K # "Degrees Kelvin" is forbidden usage.
tempK K # For consistency
# Gas mark is implemented below but in a terribly ugly way. There is
# a simple formula, but it requires a conditional which is not
# presently supported.
#
# The formula to convert to degrees Fahrenheit is:
#
# 25 log2(gasmark) + k_f gasmark<=1
# 25 (gasmark-1) + k_f gasmark>=1
#
# k_f = 275
#
gasmark[degR] \
.0625 634.67 \
.125 659.67 \
.25 684.67 \
.5 709.67 \
1 734.67 \
2 759.67 \
3 784.67 \
4 809.67 \
5 834.67 \
6 859.67 \
7 884.67 \
8 909.67 \
9 934.67 \
10 959.67
# The Beaufort wind force scale was developed from 1805-1807 by Sir Francis
# Beaufort to categorize wind conditions at sea. It is normally defined from
# Beaufort 0, also called "Force 0," through Beaufort 12. Beaufort numbers
# 13-17 were later defined for tropical cyclones but are rarely used. The
# original Beaufort scale was qualitative and did not relate directly to wind
# speed. In 1906, George Simpson of the British Met Office fit wind-speed
# measurements to visual Beaufort estimates made from five coastal and inland
# stations in Britain. Simpson's formula was adopted by the World Meterological
# Organization in 1946 to produce a table, known as WMO Code 1100, giving mean
# (and min/max) wind speed equivalents at a height of 10 meters for each
# Beaufort number. This is the "operational" Beaufort scale that mariners
# use. Meterological and climatic researchers typically use a "scientific"
# Beaufort scale based on more recent and comprehensive fits. See Wallbrink and
# Cook, Historical Wind Speed Equivalents Of The Beaufort Scale, 1850-1950, at
# https://icoads.noaa.gov/reclaim/pdf/Hisklim13.pdf
#
beaufort_WMO1100(B) units=[1;m/s] domain=[0,17] range=[0,) \
0.836 B^3|2 m/s; (beaufort_WMO1100 s / 0.836 m)^2|3
beaufort(B) units=[1;m/s] domain=[0,17] range=[0,) \
beaufort_WMO1100(B); ~beaufort_WMO1100(beaufort)
# Units cannot handle wind chill or heat index because they are two-variable
# functions, but they are included here for your edification. Clearly these
# equations are the result of a model fitting operation.
#
# wind chill index (WCI) a measurement of the combined cooling effect of low
# air temperature and wind on the human body. The index was first defined
# by the American Antarctic explorer Paul Siple in 1939. As currently used
# by U.S. meteorologists, the wind chill index is computed from the
# temperature T (in deg F) and wind speed V (in mi/hr) using the formula:
# WCI = 0.0817(3.71 sqrt(V) + 5.81 - 0.25V)(T - 91.4) + 91.4.
# For very low wind speeds, below 4 mi/hr, the WCI is actually higher than
# the air temperature, but for higher wind speeds it is lower than the air
# temperature.
#
# heat index (HI or HX) a measure of the combined effect of heat and
# humidity on the human body. U.S. meteorologists compute the index
# from the temperature T (in deg F) and the relative humidity H (as a
# value from 0 to 1).
# HI = -42.379 + 2.04901523 T + 1014.333127 H - 22.475541 TH
# - .00683783 T^2 - 548.1717 H^2 + 0.122874 T^2 H + 8.5282 T H^2
# - 0.0199 T^2 H^2.
#
# Physical constants
#
# Basic constants
pi 3.14159265358979323846
tau 2 pi
phi (sqrt(5)+1)/2
light c
coulombconst alpha hbar c / e^2 # Coulomb constant
k_C coulombconst # Gets overridden in CGS modes
k_C_SI alpha hbar_SI c_SI / e_SI^2
epsilon0_SI 1 / 4 pi k_C_SI # Vacuum electric permittivity
epsilon0 1 / 4 pi k_C # Also overridden in CGS modes
mu0_SI 1 / epsilon0_SI c_SI^2 # Vacuum magnetic permeability
mu0 1 / epsilon0 c^2 # Also overridden in CGS modes
Z0 4 pi k_C / c # Free space impedance
energy c^2 # Convert mass to energy
hbar h / 2 pi
hbar_SI h_SI / 2 pi
spin hbar
G_SI 6.67430e-11
G 6.67430e-11 N m^2 / kg^2 # Newtonian gravitational constant
# Physico-chemical constants
atomicmassunit_SI 1.66053906660e-27 # Unified atomic mass unit, defined as
atomicmassunit 1.66053906660e-27 kg # Unified atomic mass unit, defined as
u atomicmassunit # 1|12 of the mass of carbon 12.
amu atomicmassunit # The relationship N_A u = 1 g/mol
dalton u # is approximately, but not exactly
Da dalton # true (with the 2019 SI).
# Previously the mole was defined to
# make this relationship exact.
amu_chem 1.66026e-27 kg # 1|16 of the weighted average mass of
# the 3 naturally occuring neutral
# isotopes of oxygen
amu_phys 1.65981e-27 kg # 1|16 of the mass of a neutral
# oxygen 16 atom
gasconstant k N_A # Molar gas constant (exact)
R gasconstant
kboltzmann boltzmann
molarvolume R stdtemp / atm # Volume occupied by one mole of an
V_m molarvolume # ideal gas at STP. (exact)
loschmidt avogadro / molarvolume # Molecules per cubic meter of an
n0 loschmidt # ideal gas at STP. Loschmidt did
# work similar to Avogadro.
molarvolume_si N_A siliconlattice^3 / 8 # Volume of a mole of crystalline
# silicon. The unit cell contains 8
# silicon atoms and has a side
# length of siliconlattice.
stefanboltzmann pi^2 k^4 / 60 hbar^3 c^2 # The power per area radiated by a
sigma stefanboltzmann # blackbody at temperature T is
# given by sigma T^4. (exact)
wiendisplacement (h c/k)/4.9651142317442763 # Wien's Displacement Law gives
# the frequency at which the
# Planck spectrum has maximum
# intensity. The relation is lambda
# T = b where lambda is wavelength,
# T is temperature and b is the Wien
# displacement. This relation is
# used to determine the temperature
# of stars. The constant is the
# solution to x=5(1-exp(-x)).
# This expression has no experimental
# error, and x is defined exactly
# by the equation above, so it is
# an exact definition.
K_J90 483597.9 GHz/V # Direct measurement of the volt is difficult. Until
K_J 2e/h # recently, laboratories kept Weston cadmium cells as
# a reference, but they could drift. In 1987 the
# CGPM officially recommended the use of the
# Josephson effect as a laboratory representation of
# the volt. The Josephson effect occurs when two
# superconductors are separated by a thin insulating
# layer. A "supercurrent" flows across the insulator
# with a frequency that depends on the potential
# applied across the superconductors. This frequency
# can be very accurately measured. The Josephson
# constant K_J relates the measured frequency to the
# potential. Two values given, the conventional
# (exact) value from 1990, which was used until the
# 2019 SI revision, and the current exact value.
R_K90 25812.807 ohm # Measurement of the ohm also presents difficulties.
R_K h/e^2 # The old approach involved maintaining resistances
# that were subject to drift. The new standard is
# based on the Hall effect. When a current carrying
# ribbon is placed in a magnetic field, a potential
# difference develops across the ribbon. The ratio
# of the potential difference to the current is
# called the Hall resistance. Klaus von Klitzing
# discovered in 1980 that the Hall resistance varies
# in discrete jumps when the magnetic field is very
# large and the temperature very low. This enables
# accurate realization of the resistance h/e^2 in the
# lab. The 1990 value was an exact conventional
# value used until the SI revision in 2019. This value
# did not agree with measurements. The new value
# is exact.
# The 2019 update to SI gives exact definitions for R_K and K_J. Previously
# the electromagnetic units were realized using the 1990 conventional values
# for these constants, and as a result, the standard definitions were in some
# sense outside of SI. The revision corrects this problem. The definitions
# below give the 1990 conventional values for the electromagnetic units in
# terms of 2019 SI.
ampere90 (K_J90 R_K90 / K_J R_K) A
coulomb90 (K_J90 R_K90 / K_J R_K) C
farad90 (R_K90/R_K) F
henry90 (R_K/R_K90) H
ohm90 (R_K/R_K90) ohm
volt90 (K_J90/K_J) V
watt90 (K_J90^2 R_K90 / K_J^2 R_K) W
# Various conventional values
gravity 9.80665 m/s^2 # std acceleration of gravity (exact)
# Established by the 3rd CGPM in
# 1901. This is a nominal midrange
# value, originally based on the
# acceleration of a body at sea
# level at 45 degrees latitude.
# The value was actually determined
# by measuring at the International
# Bureau and correcting the
# measurement by a theoretical
# cofficient to get the 45 deg
# latitude sea level value.
# (Wikipedia: Standard gravity)
force gravity # use to turn masses into forces
atm 101325 Pa # Standard atmospheric pressure
atmosphere atm
Hg 13.5951 gram force / cm^3 # Standard weight of mercury (exact)
water gram force/cm^3 # Standard weight of water (exact)
waterdensity gram / cm^3 # Density of water
H2O water
wc water # water column
mach 331.46 m/s # speed of sound in dry air at STP
standardtemp 273.15 K # standard temperature
stdtemp standardtemp
normaltemp tempF(70) # for gas density, from NIST
normtemp normaltemp # Handbook 44
# Weight of mercury and water at different temperatures using the standard
# force of gravity.
Hg10C 13.5708 force gram / cm^3 # These units, when used to form
Hg20C 13.5462 force gram / cm^3 # pressure measures, are not accurate
Hg23C 13.5386 force gram / cm^3 # because of considerations of the
Hg30C 13.5217 force gram / cm^3 # revised practical temperature scale.
Hg40C 13.4973 force gram / cm^3
Hg60F 13.5574 force gram / cm^3
H2O0C 0.99987 force gram / cm^3
H2O5C 0.99999 force gram / cm^3
H2O10C 0.99973 force gram / cm^3
H2O15C 0.99913 force gram / cm^3
H2O18C 0.99862 force gram / cm^3
H2O20C 0.99823 force gram / cm^3
H2O25C 0.99707 force gram / cm^3
H2O50C 0.98807 force gram / cm^3
H2O100C 0.95838 force gram / cm^3
# Atomic constants
hartree 4.3597447222071e-18 J # Approximate electric potential energy
E_h hartree # of the hydrogen atom in its ground
# state, and approximately twice its
# ionization energy. The hartree
# energy is traditionally defined as
# coulombconst^2 m_e e^4 / hbar^2,
# but it can be measured to greater
# precision using the relationship
# hartree = 2 h c Rinfinity
# because Rinfinity is one of the
# most accurately measured physical
# constants. Because h and c are
# exact we can choose either hartree
# or Rinfinity from CODATA to use as
# the primary value without
# affecting the precision.
Rinfinity hartree / 2 h c # The wavelengths of a spectral series
R_H Rinfinity m_p / (m_e + m_p) # can be expressed as
# 1/lambda = R (1/m^2 - 1/n^2).
# where R is a number that various
# slightly from element to element.
# For hydrogen, R_H is the value,
# and for heavy elements, the value
# approaches Rinfinity, which can be
# computed from
# Rinfinity = m_e c alpha^2 / 2 h
# with loss of precision. Rinfinity
# is one of the most accurately
# measured physical constants and is
# known to higher precision than m_e
# or alpha.
alpha 7.2973525693e-3 # The fine structure constant was
# introduced to explain fine
# structure visible in spectral
# lines.
bohrradius hbar / alpha m_e c
a0 bohrradius
prout 185.5 keV # nuclear binding energy equal to 1|12
# binding energy of the deuteron
conductancequantum e^2 / pi hbar
G0 conductancequantum
magneticfluxquantum pi hbar / e
Phi0 magneticfluxquantum
# Particle radius
electronradius coulombconst e^2 / electronmass c^2 # Classical
deuteronchargeradius 2.12799e-15 m
protonchargeradius 0.8751e-15 m
# Masses of elementary particles
electronmass_SI electronmass_u atomicmassunit_SI
electronmass_u 5.48579909065e-4
electronmass 5.48579909065e-4 u
m_e electronmass
muonmass 0.1134289259 u
m_mu muonmass
taumass 1.90754 u
m_tau taumass
protonmass 1.007276466621 u
m_p protonmass
neutronmass 1.00866491595 u
m_n neutronmass
deuteronmass 2.013553212745 u # Nucleus of deuterium, one
m_d deuteronmass # proton and one neutron
alphaparticlemass 4.001506179127 u # Nucleus of He, two protons
m_alpha alphaparticlemass # and two neutrons
tritonmass 3.01550071621 u # Nucleus of H3, one proton
m_t tritonmass # and two neutrons
helionmass 3.014932247175 u # Nucleus of He3, two protons
m_h helionmass # and one neutron
# particle wavelengths: the compton wavelength of a particle is
# defined as h / m c where m is the mass of the particle.
electronwavelength h / m_e c
lambda_C electronwavelength
protonwavelength h / m_p c
lambda_C,p protonwavelength
neutronwavelength h / m_n c
lambda_C,n neutronwavelength
muonwavelength h / m_mu c
lambda_C,mu muonwavelength
# The g-factor or dimensionless magnetic moment is a quantity that
# characterizes the magnetic moment of a particle. The electron g-factor is
# one of the most precisely measured values in physics, with a relative
# uncertainty of 1.7e-13.
g_d 0.8574382338 # Deuteron g-factor
g_e -2.00231930436256 # Electron g-factor
g_h -4.255250615 # Helion g-factor
g_mu -2.0023318418 # Muon g-factor
g_n -3.82608545 # Neutron g-factor
g_p 5.5856946893 # Proton g-factor
g_t 5.957924931 # Triton g-factor
fermicoupling 1.1663787e-5 / GeV^2
# Magnetic moments (derived from the more accurate g-factors)
#
# The magnetic moment is g * mu_ref * spin where in most cases
# the reference is the nuclear magneton, and all of the particles
# except the deuteron have spin 1/2.
bohrmagneton e hbar / 2 electronmass # Reference magnetic moment for
mu_B bohrmagneton # the electron
mu_e g_e mu_B / 2 # Electron spin magnet moment
mu_mu g_mu mu_B m_e / 2 muonmass # Muon spin magnetic moment
nuclearmagneton mu_B m_e / protonmass # Convenient reference magnetic
mu_N nuclearmagneton # moment for heavy particles
mu_p g_p mu_N / 2 # Proton magnetic moment
mu_n g_n mu_N / 2 # Neutron magnetic moment
mu_d g_d mu_N # Deuteron magnetic moment, spin 1
mu_t g_t mu_N / 2 # Triton magnetic moment
mu_h g_h mu_N / 2 # Helion magnetic moment
#
# Units derived from physical constants
#
kgf kg force
technicalatmosphere kgf / cm^2
at technicalatmosphere
hyl kgf s^2 / m # Also gram-force s^2/m according to [15]
mmHg mm Hg
torr atm / 760 # The torr, named after Evangelista
# Torricelli, and is very close to the mm Hg
tor Pa # Suggested in 1913 but seldom used [24].
# Eventually renamed the Pascal. Don't
# confuse the tor with the torr.
inHg inch Hg
inH2O inch water
mmH2O mm water
eV e V # Energy acquired by a particle with charge e
electronvolt eV # when it is accelerated through 1 V
lightyear c julianyear # The 365.25 day year is specified in
ly lightyear # NIST publication 811
lightsecond c s
lightminute c min
parsec au / tan(arcsec) # Unit of length equal to distance
pc parsec # from the Sun to a point having
# heliocentric parallax of 1
# arcsec (derived from parallax
# second). A distant object with
# parallax theta will be about
# (arcsec/theta) parsecs from the
# Sun (using the approximation
# that tan(theta) = theta).
rydberg 1|2 hartree # Rydberg energy
crith 0.089885 gram # The crith is the mass of one
# liter of hydrogen at standard
# temperature and pressure.
amagat N_A / molarvolume # Used to measure gas as a number
amagatvolume mol molarvolume # density
lorentz bohrmagneton / h c # Used to measure the extent
# that the frequency of light
# is shifted by a magnetic field.
cminv h c / cm # Unit of energy used in infrared
invcm cminv # spectroscopy.
wavenumber 1/cm #
kcal_mol kcal_th / mol N_A # kcal/mol is used as a unit of
# energy by physical chemists.
#
# CGS system based on centimeter, gram and second
#
dyne cm gram / s^2 # force
dyn dyne
erg cm dyne # energy
poise gram / cm s # viscosity, honors Jean Poiseuille
P poise
rhe /poise # reciprocal viscosity
stokes cm^2 / s # kinematic viscosity
St stokes
stoke stokes
lentor stokes # old name
Gal cm / s^2 # acceleration, used in geophysics
galileo Gal # for Earth's gravitational field
# (note that "gal" is for gallon
# but "Gal" is the standard symbol
# for the gal which is evidently a
# shortened form of "galileo".)
barye dyne/cm^2 # pressure
barad barye # old name
kayser 1/cm # Proposed as a unit for wavenumber
balmer kayser # Even less common name than "kayser"
kine cm/s # velocity
bole g cm / s # momentum
pond gram force
glug gram force s^2 / cm # Mass which is accelerated at
# 1 cm/s^2 by 1 gram force
darcy centipoise cm^2 / s atm # Measures permeability to fluid flow.
# One darcy is the permeability of a
# medium that allows a flow of cc/s
# of a liquid of centipoise viscosity
# under a pressure gradient of
# atm/cm. Named for H. Darcy.
mobileohm cm / dyn s # mobile ohm, measure of mechanical
# mobility
mechanicalohm dyn s / cm # mechanical resistance
acousticalohm dyn s / cm^5 # ratio of the sound pressure of
# 1 dyn/cm^2 to a source of strength
# 1 cm^3/s
ray acousticalohm
rayl dyn s / cm^3 # Specific acoustical resistance
eotvos 1e-9 Gal/cm # Change in gravitational acceleration
# over horizontal distance
#
# Electromagnetic CGS Units
#
# For measuring electromagnetic quantities in SI, we introduce the new base
# dimension of current, define the ampere to measure current, and derive the
# other electromagnetic units from the ampere. With the CGS units one approach
# is to use the basic equations of electromagnetism to define units that
# eliminate constants from those equations. Coulomb's law has the form
#
# F = k_C q1 q2 / r^2
#
# where k_C is the Coulomb constant equal to 1|4 pi epsilon0 in SI units.
# Ampere's force law takes the form
#
# dF/dl = 2 k_A I1 I2 / r
#
# where k_A is the ampere constant. In the CGS system we force either k_C or
# k_A to 1 which then defines either a unit for charge or a unit for current.
# The other unit then becomes a derived unit. When k_C is 1 the ESU system
# results. When k_A is 1 the EMU system results. Note that these parameters
# are not independent of each other: Maxwell's equations indicate that
#
# k_C / k_A = c^2
#
# where c is the speed of light.
#
# One more choice is needed to define a complete system. Using Coulomb's law
# we define the electric field as the force per unit charge
#
# E = k_C 1 / r^2.
#
# But what about the magnetic field? It is derived from Ampere's law but we
# have the option of adding a proportionality constant, k_B, that may have
# dimensions:
#
# B = 2 k_A k_B I / r
#
# We can choose k_B = 1, which is done in the SI, ESU and EMU systems. But if
# instead we give k_B units of length/time then the magnetic field has
# the same units as the electric field. This choice leads to the Gaussian
# and Heaviside-Lorentz systems.
#
# The relations above are used to determine the dimensions, but the units are
# derived from the base units of CGS, not directly from those formulas. We
# will use the notation [unit] to refer to the dimension of the unit in
# brackets. This same process gives rise to the SI units such as the tesla,
# which is defined by
#
# [tesla] = [2 (1/4 pi c^2 epsilon0) amp / m] = [(mu0 / 2) amp / m]
#
# which gives kg / A s^2 as expected.
#
# References:
#
# Classical Electrodynamics by John David Jackson, 3rd edition.
# Cardarelli, Francois. 1999. Scientific Unit Conversion. 2nd ed. Trans.
# M.J. Shields. London: Springer-Verlag. ISBN 1-85233-043-0
#
#
# All of the CGS systems result in electromagnetic units that involve the square
# roots of the centimeter and gram. This requires a change in the primitive
# units.
#
!var UNITS_SYSTEM esu emu gaussian gauss hlu
sqrt_cm !
sqrt_centimeter sqrt_cm
+m 100 sqrt_cm^2
sqrt_g !
sqrt_gram sqrt_g
+kg kilo sqrt_g^2
!endvar
# Electrostatic CGS (ESU)
#
# This system uses the statcoulomb as the fundamental unit of charge, with
# derived units that parallel the conventional terminology but use the stat-
# prefix. The statcoulomb is derived from Coulomb's law based on the dyne
#
# dyne = statcoulomb^2 / k_C cm^2.
#
# and in the EUS system, k_C=1. The statcoulomb is also called the
# franklin or esu.
#
# The ESU system was specified by a committee report in 1873 and rarely used.
statcoulomb sqrt(dyne cm^2/k_C) # Charge such that two charges
esu statcoulomb # of 1 statC separated by 1 cm
statcoul statcoulomb # exert a force of 1 dyne
statC statcoulomb
stC statcoulomb
franklin statcoulomb
Fr franklin
!var UNITS_SYSTEM esu
!message CGS-ESU units selected
!prompt (ESU)
+coulombconst 1
+epsilon0 1 / k_C # SI relation: 1 / 4 pi k_C
+A 10 c_SI statamp
!endvar
statampere statcoulomb / s
statamp statampere
statA statampere
stA statampere
statvolt dyne cm / statamp sec
statV statvolt
stV statvolt
statfarad statamp sec / statvolt
statF statfarad
stF statfarad
cmcapacitance statfarad
stathenry statvolt sec / statamp
statH stathenry
stH stathenry
statohm statvolt / statamp
stohm statohm
statmho /statohm
stmho statmho
statweber statvolt sec
statWb statweber
stWb statweber
stattesla statWb/cm^2 # Defined by analogy with SI; rarely
statT stattesla # if ever used
stT stattesla
debye 1e-10 statC angstrom # unit of electrical dipole moment
helmholtz debye/angstrom^2 # Dipole moment per area
jar 1000 statfarad # approx capacitance of Leyden jar
# Electromagnetic CGS (EMU)
#
# The abampere is the fundamental unit of this system, with the derived units
# using the ab- prefix. The dimensions of the abampere are defined by assuming
# that k_A=1, which
#
# [dyne / cm] = [2 abampere^2 / cm]
#
# where the brackets indicate taking the dimension of the unit in base units
# and discarding any constant factors. This results in the definition from
# base CGS units of:
#
# abampere = sqrt(dyne).
#
# The abampere is also called the biot. The magnetic field unit (the gauss)
# follows from the assumption that k_B=1, which means
#
# B = 2 I / r,
#
# and hence the dimensions of the gauss are given by
#
# [gauss] = [2 abampere / cm]
#
# or rewriting in terms of the base units
#
# gauss = abampere / cm.
#
# The definition given below is different because it is in a form that
# gives a valid reduction for SI and ESU and still gives the correct
# result in EMU. (It can be derived from Faraday's law.)
#
# The EMU system was developed by Gauss and Weber and formalized as a system in
# a committee report by the British Association for the Advancement of Science
# in 1873.
abampere 10 A # Current which produces a force of
abamp abampere # 2 dyne/cm between two infinitely
aA abampere # long wires that are 1 cm apart
abA abampere
biot abampere
Bi biot
!var UNITS_SYSTEM emu
!message CGS-EMU units selected
!prompt (EMU)
+coulombconst c^2
+epsilon0 1 / k_C # SI relation: 1 / 4 pi k_C
+abampere sqrt(dyne)
+A 0.1 abamp
!endvar
abcoulomb abamp sec
abcoul abcoulomb
abC abcoulomb
abfarad abampere sec / abvolt
abF abfarad
abhenry abvolt sec / abamp
abH abhenry
abvolt dyne cm / abamp sec
abV abvolt
abohm abvolt / abamp
abmho /abohm
maxwell erg / abamp # Also called the "line"
Mx maxwell
gauss maxwell / cm^2 # The magnetic field 2 cm from a wire
Gs gauss # carrying a current of 1 abampere
oersted gauss / mu0 # From the relation H = B / mu
Oe oersted
gilbert gauss cm / mu0
Gb gilbert
Gi gilbert
unitpole 4 pi maxwell # unit magnetic pole
emu erg/gauss # "electro-magnetic unit", a measure of
# magnetic moment, often used as emu/cm^3
# to specify magnetic moment density.
# Electromagnetic CGS (Gaussian)
#
# The Gaussian system uses the statcoulomb and statamp from the ESU system
# derived by setting k_C=1, but it defines the magnetic field unit differently
# by taking k_B=c instead of k_B=1. As noted above, k_C and k_A are not
# independent. With k_C=1 we must have k_A=c^-2. This results in the magnetic
# field unit, the gauss, having dimensions give by:
#
# [gauss] = [2 (c^-2) c statamp / cm] = [statamp / c cm]
#
# We then define the gauss using base CGS units to obtain
#
# gauss = statamp / ((cm/s) cm) = statcoulomb / cm^2.
#
# Note that this definition happens to give the same result as the definition
# for the EMU system, so the definitions of the gauss are consistent.
#
# This definition gives the same dimensions for the E and B fields and was also
# known as the "symmetric system". This system was proposed by Hertz in 1888.
!var UNITS_SYSTEM gaussian gauss
!message CGS-Gaussian units selected
!prompt (Gaussian)
!endvar
!var UNITS_SYSTEM gaussian gauss natural-gauss
+coulombconst 1
+A 10 c_SI statamp
# Some SI-based definitions need re-scaling
# by factors of "c" and/or "4 pi":
+epsilon0 1 / k_C # SI relation: 1 / 4 pi k_C
+mu0 1 / epsilon0 # SI relation: 1 / epsilon0 c^2
+bohrmagneton (e hbar / 2 electronmass) / c
+magneticfluxquantum c (pi hbar / e)
+maxwell c (erg / abamp)
+weber c (J / A)
!endvar
# Electromagnetic CGS (Heaviside-Lorentz)
# The Heaviside-Lorentz system is similar to the Gaussian system, but it is
# "rationalized" so that factors of 4 pi do not appear in Maxwell's equations.
# The SI system is similarly rationalized, but the other CGS systems are not.
#
# The factor of 4 pi appears instead in Coulomb's law, so in this system
# k_C = 1 / 4 pi, which means the charge unit is defined by
#
# dyne = (1 / 4 pi) hlu_charge^2 / cm^2.
#
# Since we have the leading constant of (1 / 4pi) the numerical value of the
# charge number is larger by sqrt(4pi), which in turns means that the HLU
# charge unit is smaller by this multiple. But note that the dimensions of the
# charge unit are the same as the Gaussian system, so both systems measure
# charge with cm^(3/2) g^(1/2) / s, but the amount of charge for this dimension
# differs by a factor of sqrt(4pi) between the two systems.
#
# Ampere's law for the Heaviside-Lorentz system has the form
#
# B = 1/(2 pi c) * I/r
# The Heaviside-Lorentz system does not appear to have any named units, so we
# use "hlu" for "Heaviside-Lorentz unit" so we can define values for the basic
# units in this system.
hlu_charge statcoulomb / sqrt(4 pi)
hlu_current hlu_charge / sec
hlu_volt erg / hlu_charge
hlu_efield hlu_volt / cm
hlu_bfield sqrt(4 pi) gauss
!var UNITS_SYSTEM hlu
!message CGS-Heaviside-Lorentz Units selected
!prompt (HLU)
!endvar
!var UNITS_SYSTEM hlu natural planck planck-red
+coulombconst 1 / 4 pi
+A 10 c_SI statamp
# Some SI-based magnetism definitions
# need re-scaling by factors of "c":
+mu0 1 / epsilon0 # SI relation: 1 / epsilon0 c^2
+bohrmagneton (e hbar / 2 electronmass) / c
+magneticfluxquantum c (pi hbar / e)
+weber c (J / A)
+maxwell c (erg / abamp)
!endvar
# "Natural units" (high energy physics and cosmology)
#
# In particle physics "natural units" (which don't seem to have a more specific
# name) are defined by setting hbar = c = boltzmann = 1. In this system the
# electron volt is the only base unit. The electromagnetic units can be
# derived from the rationalized Heaviside-Lorentz units or from Gaussian units.
# The default form is the rationalized HLU derived version.
#
# The basic mechanical and thermodynamic definitions for the natural
# units are identical in both systems. These appear below. The
# natural-gauss system has additional electromagnetic redefinitions
# that appear above in the "Electromagnetic CGS (Gaussian)" Section.
# These are the Heaviside-Lorentz natural units
natural_energy eV
natural_charge e / sqrt(4 pi alpha)
natural_time hbar / natural_energy
natural_length natural_time c
natural_mass natural_energy / c^2
natural_temp natural_energy / boltzmann
natural_force natural_energy / natural_length
natural_power natural_energy / natural_time
natural_volt natural_energy / natural_charge
natural_Efield natural_volt / natural_length
natural_Bfield natural_Efield / c
natural_current natural_charge / natural_time
!var UNITS_SYSTEM natural
!message Natural units selected (Heavyside-Lorentz based)
!prompt (natural)
!endvar
!var UNITS_SYSTEM natural-gauss
!message Natural units selected (Gaussian based)
!prompt (natgauss)
!endvar
# These definitions are the same in both natural unit systems
!var UNITS_SYSTEM natural natural-gauss
+eV !
+h 2 pi
+c 1
+boltzmann 1
+m e_SI / hbar_SI c_SI eV
+kg (c_SI^2 / e_SI) eV
+s e_SI / hbar_SI eV
+K (k_SI / e_SI) eV
!endvar
#
# Planck units
#
# Planck units are a set of "natural" units based on physical constants c, G,
# hbar, boltzmann's constant, and epsilon0, often used when working with
# gravitational theory. In planck units, all quantities are dimensionless.
# Some variations are possible for exactly how the units are defined. We
# provide two variations, the rationalized planck units and the
# rationalized-reduced planck units.
#
# In both forms the units are defined by c = hbar = boltzmann = 1.
# But the choice of rationalized and reduced affects how epsilon0 and G
# are treated.
#
# In the "rationalized" units, factors of 4 pi do not appear in Maxwell's
# equation, and Coulomb's law bears a factor of 1/4 pi. See the section on
# the Heaviside-Lorentz units for more about this. The choice of rationalized
# units means that epsilon0 = 1. (In the unrationalized case, which is not
# supported, 1/(4 pi epsilon0) = 1.)
#
# The "reduced" units similarly are defined to eliminate factors of 8 pi
# from the Einstein field equations for gravitation. With reduced units
# we set 8 pi G = 1 and with the unreduced units, simply G = 1.
# Rationalized, unreduced planck units
planckmass sqrt(hbar c / G)
m_P planckmass
planckenergy planckmass c^2
E_P planckenergy
plancktime hbar / planckenergy
t_P plancktime
plancklength plancktime c
l_P plancklength
plancktemperature planckenergy / k
T_P plancktemperature
planckforce planckenergy / plancklength
planckcharge sqrt(epsilon0 hbar c)
planckcurrent planckcharge / plancktime
planckvolt planckenergy / planckcharge
planckEfield planckvolt / plancklength
planckBfield planckEfield / c
# Rationalized, reduced planck units
planckmass_red sqrt(hbar c / 8 pi G)
planckenergy_red planckmass_red c^2
plancktime_red hbar / planckenergy_red
plancklength_red plancktime_red c
plancktemperature_red planckenergy_red / k
planckforce_red planckenergy_red / plancklength_red
planckcharge_red sqrt(epsilon0 hbar c)
planckcurrent_red planckcharge_red / plancktime_red
planckvolt_red planckenergy_red / planckcharge_red
planckEfield_red planckvolt_red / plancklength_red
planckBfield_red planckEfield_red /c
!var UNITS_SYSTEM planck
!message Planck units selected
!prompt (planck)
+c 1
+h 2 pi
+G 1
+boltzmann 1
+kg sqrt(G_SI / hbar_SI c_SI)
+s c_SI^2 / hbar_SI kg
+m s / c_SI
+K k_SI / hbar_SI s
!endvar
!var UNITS_SYSTEM planck-red
!message Reduced planck units selected
!prompt (planck reduced)
+c 1
+h 2 pi
+G 1/8 pi
+boltzmann 1
+kg sqrt(8 pi G_SI / hbar_SI c_SI)
+s c_SI^2 / hbar_SI kg
+m s / c_SI
+K k_SI / hbar_SI s
!endvar
#
# Some historical electromagnetic units
#
intampere 0.999835 A # Defined as the current which in one
intamp intampere # second deposits .001118 gram of
# silver from an aqueous solution of
# silver nitrate.
intfarad 0.999505 F
intvolt 1.00033 V
intohm 1.000495 ohm # Defined as the resistance of a
# uniform column of mercury containing
# 14.4521 gram in a column 1.063 m
# long and maintained at 0 degC.
daniell 1.042 V # Meant to be electromotive force of a
# Daniell cell, but in error by .04 V
faraday N_A e mol # Charge that must flow to deposit or
faraday_phys 96521.9 C # liberate one gram equivalent of any
faraday_chem 96495.7 C # element. (The chemical and physical
faradayconst N_A e # values are off slightly from what is
# obtained by multiplying by amu_chem
# or amu_phys. These values are from
# a 1991 NIST publication.) Note that
# there is also a Faraday constant,
# which has units of C/mol.
kappline 6000 maxwell # Named by and for Gisbert Kapp
siemensunit 0.9534 ohm # Resistance of a meter long column of
# mercury with a 1 mm cross section.
#
# Printed circuit board units.
#
# Iowa State University Center for Nondestructive Evaluation
# Electrical Conductivity and Resistivity
# https://www.nde-ed.org/Physics/Materials/Physical_Chemical/Electrical.xhtml
#
# Conductivity is often expressed as a percentage of IACS. A copper wire a
# meter long with a 1 mm^2 cross section has a resistance of 1|58 ohm at
# 20 deg C. Copper density also has a standard IACS value at that temperature.
#
copperconductivity 58 siemens m / mm^2 # A wire a meter long with
IACS copperconductivity # a 1 mm^2 cross section
copperdensity 8.89 g/cm^3 # The "ounce" measures the
ouncecopper oz / ft^2 copperdensity # thickness of copper used
ozcu ouncecopper # in circuitboard fabrication
#
# Photometric units
#
LUMINOUS_INTENSITY candela
LUMINOUS_FLUX lumen
LUMINOUS_ENERGY talbot
ILLUMINANCE lux
EXITANCE lux
candle 1.02 candela # Standard unit for luminous intensity
hefnerunit 0.9 candle # in use before candela
hefnercandle hefnerunit #
violle 20.17 cd # luminous intensity of 1 cm^2 of
# platinum at its temperature of
# solidification (2045 K)
lumen cd sr # Luminous flux (luminous energy per
lm lumen # time unit)
talbot lumen s # Luminous energy
lumberg talbot # References give these values for
lumerg talbot # lumerg and lumberg both. Note that
# a paper from 1948 suggests that
# lumerg should be 1e-7 talbots so
# that lumergs/erg = talbots/joule.
# lumerg = luminous erg
lux lm/m^2 # Illuminance or exitance (luminous
lx lux # flux incident on or coming from
phot lumen / cm^2 # a surface)
ph phot #
footcandle lumen/ft^2 # Illuminance from a 1 candela source
# at a distance of one foot
metercandle lumen/m^2 # Illuminance from a 1 candela source
# at a distance of one meter
mcs metercandle s # luminous energy per area, used to
# measure photographic exposure
nox 1e-3 lux # These two units were proposed for
skot 1e-3 apostilb # measurements relating to dark adapted
# eyes.
# Luminance measures
LUMINANCE nit
nit cd/m^2 # Luminance: the intensity per projected
stilb cd / cm^2 # area of an extended luminous source.
sb stilb # (nit is from latin nitere = to shine.)
apostilb cd/pi m^2
asb apostilb
blondel apostilb # Named after a French scientist.
# Equivalent luminance measures. These units are units which measure
# the luminance of a surface with a specified exitance which obeys
# Lambert's law. (Lambert's law specifies that luminous intensity of
# a perfectly diffuse luminous surface is proportional to the cosine
# of the angle at which you view the luminous surface.)
equivalentlux cd / pi m^2 # luminance of a 1 lux surface
equivalentphot cd / pi cm^2 # luminance of a 1 phot surface
lambert cd / pi cm^2
footlambert cd / pi ft^2
# The bril is used to express "brilliance" of a source of light on a
# logarithmic scale to correspond to subjective perception. An increase of 1
# bril means doubling the luminance. A luminance of 1 lambert is defined to
# have a brilliance of 1 bril.
bril(x) units=[1;lambert] 2^(x+-100) lamberts ;log2(bril/lambert)+100
# Some luminance data from the IES Lighting Handbook, 8th ed, 1993
sunlum 1.6e9 cd/m^2 # at zenith
sunillum 100e3 lux # clear sky
sunillum_o 10e3 lux # overcast sky
sunlum_h 6e6 cd/m^2 # value at horizon
skylum 8000 cd/m^2 # average, clear sky
skylum_o 2000 cd/m^2 # average, overcast sky
moonlum 2500 cd/m^2
#
# Photographic Exposure Value
# This section by Jeff Conrad (jeff_conrad@msn.com)
#
# The Additive system of Photographic EXposure (APEX) proposed in ASA
# PH2.5-1960 was an attempt to simplify exposure determination for people who
# relied on exposure tables rather than exposure meters. Shortly thereafter,
# nearly all cameras incorporated exposure meters, so the APEX system never
# caught on, but the concept of exposure value remains in use. Though given as
# 'Ev' in ASA PH2.5-1960, it is now more commonly indicated by 'EV'. EV is
# related to exposure parameters by
#
# A^2 LS ES
# 2^EV = --- = -- = --
# t K C
#
# Where
# A = Relative aperture (f-number)
# t = Exposure time in seconds
# L = Scene luminance in cd/m2
# E = Scene illuminance in lux
# S = Arithmetic ISO speed
# K = Reflected-light meter calibration constant
# C = Incident-light meter calibration constant
#
# Strictly, an exposure value is a combination of aperture and exposure time,
# but it's also commonly used to indicate luminance (or illuminance).
# Conversion to luminance or illuminance units depends on the ISO speed and the
# meter calibration constant. Common practice is to use an ISO speed of 100.
# Calibration constants vary among camera and meter manufacturers: Canon,
# Nikon, and Sekonic use a value of 12.5 for reflected-light meters, while
# Kenko (formerly Minolta) and Pentax use a value of 14. Kenko and Sekonic use
# a value of 250 for incident-light meters with flat receptors.
#
# The values for in-camera meters apply only averaging, weighted-averaging, or
# spot metering--the multi-segment metering incorporated in most current
# cameras uses proprietary algorithms that evaluate many factors related to the
# luminance distribution of what is being metered; they are not amenable to
# simple conversions, and are usually not disclosed by the manufacturers.
s100 100 / lx s # ISO 100 speed
iso100 s100
# Reflected-light meter calibration constant with ISO 100 speed
k1250 12.5 (cd/m2) / lx s # For Canon, Nikon, and Sekonic
k1400 14 (cd/m2) / lx s # For Kenko (Minolta) and Pentax
# Incident-light meter calibration constant with ISO 100 film
c250 250 lx / lx s # flat-disc receptor
# Exposure value to scene luminance with ISO 100 imaging media
# For Kenko (Minolta) or Pentax
#ev100(x) units=[;cd/m^2] range=(0,) 2^x k1400 / s100; log2(ev100 s100/k1400)
# For Canon, Nikon, or Sekonic
ev100(x) units=[1;cd/m^2] range=(0,) 2^x k1250 / s100; log2(ev100 s100/k1250)
EV100() ev100
# Exposure value to scene illuminance with ISO 100 imaging media
iv100(x) units=[1;lx] range=(0,) 2^x c250 / s100; log2(iv100 s100 / c250)
# Other Photographic Exposure Conversions
#
# As part of APEX, ASA PH2.5-1960 proposed several logarithmic quantities
# related by
#
# Ev = Av + Tv = Bv + Sv
#
# where
# Av = log2(A^2) Aperture value
# Tv = log2(1/t) Time value
# Sv = log2(N Sx) Speed value
# Bv = log2(B S / K) Luminance ("brightness") value
# Iv = log2(I S / C) Illuminance value
#
# and
# A = Relative aperture (f-number)
# t = Exposure time in seconds
# Sx = Arithmetic ISO speed in 1/lux s
# B = luminance in cd/m2
# I = luminance in lux
# The constant N derives from the arcane relationship between arithmetic
# and logarithmic speed given in ASA PH2.5-1960. That relationship
# apparently was not obvious--so much so that it was thought necessary
# to explain it in PH2.12-1961. The constant has had several values
# over the years, usually without explanation for the changes. Although
# APEX had little impact on consumer cameras, it has seen a partial
# resurrection in the Exif standards published by the Camera & Imaging
# Products Association of Japan.
#N_apex 2^-1.75 lx s # precise value implied in ASA PH2.12-1961,
# derived from ASA PH2.5-1960.
#N_apex 0.30 lx s # rounded value in ASA PH2.5-1960,
# ASA PH2.12-1961, and ANSI PH2.7-1986
#N_apex 0.3162 lx s # value in ANSI PH2.7-1973
N_exif 1|3.125 lx s # value in Exif 2.3 (2010), making Sv(5) = 100
K_apex1961 11.4 (cd/m2) / lx s # value in ASA PH2.12-1961
K_apex1971 12.5 (cd/m2) / lx s # value in ANSI PH3.49-1971; more common
C_apex1961 224 lx / lx s # value in PH2.12-1961 (20.83 for I in
# footcandles; flat sensor?)
C_apex1971 322 lx / lx s # mean value in PH3.49-1971 (30 +/- 5 for I in
# footcandles; hemispherical sensor?)
N_speed N_exif
K_lum K_apex1971
C_illum C_apex1961
# Units for Photographic Exposure Variables
#
# Practical photography sometimes pays scant attention to units for exposure
# variables. In particular, the "speed" of the imaging medium is treated as if
# it were dimensionless when it should have units of reciprocal lux seconds;
# this practice works only because "speed" is almost invariably given in
# accordance with international standards (or similar ones used by camera
# manufacturers)--so the assumed units are invariant. In calculating
# logarithmic quantities--especially the time value Tv and the exposure value
# EV--the units for exposure time ("shutter speed") are often ignored; this
# practice works only because the units of exposure time are assumed to be in
# seconds, and the missing units that make the argument to the logarithmic
# function dimensionless are silently provided.
#
# In keeping with common practice, the definitions that follow treat "speeds"
# as dimensionless, so ISO 100 speed is given simply as '100'. When
# calculating the logarithmic APEX quantities Av and Tv, the definitions
# provide the missing units, so the times can be given with any appropriate
# units. For example, giving an exposure time of 1 minute as either '1 min' or
# '60 s' will result in Tv of -5.9068906.
#
# Exposure Value from f-number and Exposure Time
#
# Because nonlinear unit conversions only accept a single quantity,
# there is no direct conversion from f-number and exposure time to
# exposure value EV. But the EV can be obtained from a combination of
# Av and Tv. For example, the "sunny 16" rule states that correct
# exposure for a sunlit scene can achieved by using f/16 and an exposure
# time equal to the reciprocal of the ISO speed in seconds; this can be
# calculated as
#
# ~Av(16) + ~Tv(1|100 s),
#
# which gives 14.643856. These conversions may be combined with the
# ev100 conversion:
#
# ev100(~Av(16) + ~Tv(1|100 s))
#
# to yield the assumed average scene luminance of 3200 cd/m^2.
# convert relative aperture (f-number) to aperture value
Av(A) units=[1;1] domain=[-2,) range=[0.5,) 2^(A/2); 2 log2(Av)
# convert exposure time to time value
Tv(t) units=[1;s] range=(0,) 2^(-t) s; log2(s / Tv)
# convert logarithmic speed Sv in ASA PH2.5-1960 to ASA/ISO arithmetic speed;
# make arithmetic speed dimensionless
# 'Sv' conflicts with the symbol for sievert; you can uncomment this function
# definition if you don't need that symbol
#Sv(S) units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sv)
Sval(S) units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sval)
# convert luminance value Bv in ASA PH2.12-1961 to luminance
Bv(x) units=[1;cd/m^2] range=(0,) \
2^x K_lum N_speed ; log2(Bv / (K_lum N_speed))
# convert illuminance value Iv in ASA PH2.12-1961 to illuminance
Iv(x) units=[1;lx] range=(0,) \
2^x C_illum N_speed ; log2(Iv / (C_illum N_speed))
# convert ASA/ISO arithmetic speed Sx to ASA logarithmic speed in
# ASA PH2.5-1960; make arithmetic speed dimensionless
Sx(S) units=[1;1] domain=(0,) \
log2((N_speed/lx s) S); 2^Sx / (N_speed/lx s)
# convert DIN speed/ISO logarithmic speed in ISO 6:1993 to arithmetic speed
# for convenience, speed is treated here as if it were dimensionless
Sdeg(S) units=[1;1] range=(0,) 10^((S - 1) / 10) ; (1 + 10 log(Sdeg))
Sdin() Sdeg
# Numerical Aperture and f-Number of a Lens
#
# The numerical aperture (NA) is given by
#
# NA = n sin(theta)
#
# where n is the index of refraction of the medium and theta is half
# of the angle subtended by the aperture stop from a point in the image
# or object plane. For a lens in air, n = 1, and
#
# NA = 0.5 / f-number
#
# convert NA to f-number
numericalaperture(x) units=[1;1] domain=(0,1] range=[0.5,) \
0.5 / x ; 0.5 / numericalaperture
NA() numericalaperture
#
# convert f-number to itself; restrict values to those possible
fnumber(x) units=[1;1] domain=[0.5,) range=[0.5,) x ; fnumber
# Referenced Photographic Standards
#
# ASA PH-2.5-1960. USA Standard, Method for Determining (Monochrome,
# Continuous-Tone) Speed of Photographic Negative Materials.
# ASA PH2.12-1961. American Standard, General-Purpose Photographic
# Exposure Meters (photoelectric type).
# ANSI PH3.49-1971. American National Standard for general-purpose
# photographic exposure meters (photoelectric type).
# ANSI PH2.7-1973. American National Standard Photographic Exposure Guide.
# ANSI PH2.7-1986. American National Standard for Photography --
# Photographic Exposure Guide.
# CIPA DC-008-2010. Exchangeable image file format for digital still
# cameras: Exif Version 2.3
# ISO 6:1993. International Standard, Photography -- Black-and-white
# pictorial still camera negative film/process systems --
# Determination of ISO Speed.
#
# Astronomical time measurements
#
# Astronomical time measurement is a complicated matter. The length of the
# true day at a given place can be 21 seconds less than 24 hours or 30 seconds
# over 24 hours. The two main reasons for this are the varying speed of
# Earth in its elliptical orbit and the fact that the Sun moves on the ecliptic
# instead of along the celestial equator. To devise a workable system for time
# measurement, Simon Newcomb (1835-1909) used a fictitious "mean Sun".
# Consider a first fictitious Sun traveling along the ecliptic at a constant
# speed and coinciding with the true Sun at perigee and apogee. Then
# considering a second fictitious Sun traveling along the celestial equator at
# a constant speed and coinciding with the first fictitious Sun at the
# equinoxes. The second fictitious Sun is the "mean Sun". From this equations
# can be written out to determine the length of the mean day, and the tropical
# year. The length of the second was determined based on the tropical year
# from such a calculation and was officially used from 1960-1967 until atomic
# clocks replaced astronomical measurements for a standard of time. All of the
# values below give the mean time for the specified interval.
#
# See "Mathematical Astronomy Morsels" by Jean Meeus for more details
# and a description of how to compute the correction to mean time.
#
TIME second
anomalisticyear 365.2596 days # The time between successive
# perihelion passages of
# Earth.
siderealyear 365.256360417 day # The time for Earth to make
# one revolution around the Sun
# relative to the stars.
tropicalyear 365.242198781 day # The time needed for the mean Sun
# as defined above to increase
# its longitude by 360 degrees.
# Most references defined the
# tropical year as the interval
# between vernal equinoxes, but
# this is misleading. The length
# of the season changes over time
# because of the eccentricity of
# Earth's orbit. The time
# between vernal equinoxes is
# approximately 365.24237 days
# around the year 2000. See
# "Mathematical Astronomy
# Morsels" for more details.
eclipseyear 346.62 days # The line of nodes is the
# intersection of the plane of
# Earth's orbit around the Sun
# with the plane of the Moon's
# orbit around Earth. Eclipses
# can only occur when the Moon
# and Sun are close to this
# line. The line rotates and
# appearances of the Sun on the
# line of nodes occur every
# eclipse year.
saros 223 synodicmonth # The Earth, Moon and Sun appear in
# the same arrangement every
# saros, so if an eclipse occurs,
# then one saros later, a similar
# eclipse will occur. (The saros
# is close to 19 eclipse years.)
# The eclipse will occur about
# 120 degrees west of the
# preceding one because the
# saros is not an even number of
# days. After 3 saros, an
# eclipse will occur at
# approximately the same place.
solarday day # Time from noon to noon
siderealday 86164.09054 s # The sidereal day is the interval
siderealhour 1|24 siderealday # between two successive transits
siderealminute 1|60 siderealhour # of a star over the meridian,
siderealsecond 1|60 siderealminute # or the time required for
# Earth to make one rotation
# relative to the stars. Another
# way to think about it is to
# imagine looking down at the
# solar system and noting when
# Earth has made a rotation.
# The more usual solar day is the
# time required to make a
# rotation relative to the Sun,
# which means the same point on
# Earth faces the Sun again.
# Because Earth moves in its
# orbit, it has to rotate a bit
# more to face the Sun again,
# hence the solar day is slightly
# longer than the sidereal day.
# The value given here is the
# mean day length taken from
# ssd.jpl.nasa.gov/astro_par.html
# which in turn cites the
# "Explanatory Supplement to the
# Astronomical Almanac", 1992.
anomalisticmonth 27.55454977 day # Time for the Moon to travel from
# perigee to perigee
nodicalmonth 27.2122199 day # The nodes are the points where
draconicmonth nodicalmonth # an orbit crosses the ecliptic.
draconiticmonth nodicalmonth # This is the time required to
# travel from the ascending node
# to the next ascending node.
siderealmonth 27.321661 day # Time required for the Moon to
# orbit the Earth
lunarmonth 29 days + 12 hours + 44 minutes + 2.8 seconds
# Mean time between full moons.
synodicmonth lunarmonth # Full moons occur when the Sun
lunation synodicmonth # and Moon are on opposite sides
lune 1|30 lunation # of the Earth. Since the Earth
lunour 1|24 lune # moves around the Sun, the Moon
# has to move a bit further in its
# orbit to return to the full moon
# configuration.
year tropicalyear
yr year
month 1|12 year
mo month
lustrum 5 years # The Lustrum was a Roman
# purification ceremony that took
# place every five years.
# Classically educated Englishmen
# used this term.
decade 10 years
century 100 years
millennium 1000 years
millennia millennium
solaryear year
lunaryear 12 lunarmonth
calendaryear 365 day
commonyear 365 day
leapyear 366 day
# The Julian year is The length of an average year over a 4-year cycle in the
# Julian calendar. The calendar was proposed by Julius Caesar in 46 BCE and
# took effect the following year. It has a normal year of 365 days and a leap
# year of 366 days every four years. Though this calendar was used in
# Europe for more than 1600 years, it drifts from the topical year by
# about 1 day every 128 years, which became noticeable over its period
# of use.
# This growing discrepancy between the seasons and the calendar was perhaps
# confusing but was also of concern to the Catholic Church because it led to a
# shift in the date of Easter. To correct this discrepancy, Pope Gregory XIII
# introduced the more accurate Gregorian calendar in 1582. The Gregorian year
# is the length of an average year over a 400-year cycle in the Gregorian
# calendar. Every year that is exactly divisible by four is a
# leap year, except for years that are exactly divisible by 100, unless these
# centurial years are exactly divisible by 400. This calendar was adopted by
# many Catholic countries when it was proclaimed, but was not adopted by many
# other countries until much later; Britain and the British Empire, including
# what is now the eastern part of the United States, adopted it in 1752. See
# https://en.wikipedia.org/wiki/List_of_adoption_dates_of_the_Gregorian_calendar_by_country
# for additional details.
julianyear 365.25 days
gregorianyear 365.2425 days
islamicyear 354 day # A year of 12 lunar months. They
islamicleapyear 355 day # began counting on July 16, AD 622
# when Muhammad emigrated to Medina
# (the year of the Hegira). They need
# 11 leap days in 30 years to stay in
# sync with the lunar year which is a
# bit longer than the 29.5 days of the
# average month. The months do not
# keep to the same seasons, but
# regress through the seasons every
# 32.5 years.
islamicmonth 1|12 islamicyear # They have 29 day and 30 day months.
# The Hebrew year is also based on lunar months, but synchronized to the solar
# calendar. The months vary irregularly between 29 and 30 days in length, and
# the years likewise vary. The regular year is 353, 354, or 355 days long. To
# keep up with the solar calendar, a leap month of 30 days is inserted every
# 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years of a 19 year cycle. This
# gives leap years that last 383, 384, or 385 days.
#
# Planetary data from JPL's planet fact sheets. Each planet has its
# own sheet at https://nssdc.gsfc.nasa.gov/planetary/factsheet/<name>fact.html
# The source for data on the fact sheets is described at
# https://nssdc.gsfc.nasa.gov/planetary/factsheet/fact_notes.html
# and they also indicate that the values listed are not "official" values:
# there is no single set of agreed upon values.
# Sidereal days. The sidereal day is the time required for a planet to make a
# revolution relative to the stars. This is the default day value.
mercuryday mercuryday_sidereal
venusday venusday_sidereal
earthday earthday_sidereal
marsday marsday_sidereal
jupiterday jupiterday_sidereal
saturnday saturnday_sidereal
uranusday uranusday_sidereal
neptuneday neptuneday_sidereal
plutoday plutoday_sidereal
mercuryday_sidereal 1407.6 hr # Mercury is in a 3:2 resonance lock
# where it makes 3 rotations per 2 orbits
# so 3 sidereal days = 2 years
venusday_sidereal 5832.6 hr # Retrograde
earthday_sidereal siderealday
marsday_sidereal 24.6229 hr
jupiterday_sidereal 9.9250 hr
saturnday_sidereal 10.656 hr
uranusday_sidereal 17.24 hr # Retrograde
neptuneday_sidereal 16.11 hr
plutoday_sidereal 153.2928 hr # Retrograde
# In astronomy, an object's rotation is "prograde" if it rotates in
# the same direction as the primary object it orbits. Prograde
# rotation is the more common case: in Earth's solar system, Mercury,
# Earth, Mars, Jupiter, Saturn, and Neptune have prograde rotation.
# When an object rotates opposite the direction of its primary object,
# the object's rotation is "retrograde". Venus, Uranus, and Pluto have
# retrograde rotation.
#
# The solar (or synodic) day is the time from noon to noon on a planet. This
# is different from the sidereal day because the planet has moved in its orbit,
# so (if its rotation is prograde) it needs additional rotation to return to
# the same orientation relative to the Sun. In one orbital period (a year),
# this amounts to one additional complete rotation, so the number of sidereal
# days in a year is one greater than the number of solar days.
#
# If the planet's rotation is retrograde, less rotation is needed to return to
# the same orientation relative to the Sun, and the number of sidereal days in
# a year is one fewer than the number of solar days.
#
# The solar day can be computed from the sidereal day in the typical prograde
# case by:
# solar_day = sidereal_day year / (year - sidereal_day)
# If the planet's rotation is retrograde like Venus then the formula is
# solar_day = sidereal_day year / (year + sidereal_day)
# If the sidereal day and year are the same length then the same face of the
# planet faces the Sun and there is no solar day.
mercuryday_solar 4222.6 hr
venusday_solar 2802.0 hr
earthday_solar 24 hr
marsday_solar 24.6597 hr
jupiterday_solar 9.9259 hr
saturnday_solar 10.656 hr
uranusday_solar 17.24 hr
neptuneday_solar 16.11 hr
plutoday_solar 153.2820 hr
# Sidereal years
mercuryyear 87.969 day
venusyear 224.701 day
earthyear siderealyear
marsyear 686.980 day
jupiteryear 4332.589 day
saturnyear 10759.22 day
uranusyear 30685.4 day
neptuneyear 60189 day
plutoyear 90560 day
# Equatorial radii for the planets from JPL fact sheets
mercuryradius 2440.5 km
venusradius 6051.8 km
earthradius 6378.137 km
marsradius 3396.2 km
jupiterradius 71492 km # 1 bar level
saturnradius 60268 km # 1 bar level
uranusradius 25559 km # 1 bar level
neptuneradius 24764 km # 1 bar level
plutoradius 1188 km
# Volumetric mean radii
mercuryradius_mean 2440.5 km
venusradius_mean 6051.8 km
earthradius_mean 6371 km
marsradius_mean 3389.5 km
jupiterradius_mean 69911 km
saturnradius_mean 58232 km
uranusradius_mean 25362 km
neptuneradius_mean 24622 km
plutoradius_mean 1188 km
# Polar radii
mercuryradius_polar 2438.3 km
venusradius_polar 6051.8 km
marsradius_polar 3376.2 km
jupiterradius_polar 66854 km
saturnradius_polar 54364 km
uranusradius_polar 24973 km
neptuneradius_polar 24341 km
plutoradius_polar 1188 km
mercurysundist_min 46.000 Gm
mercurysundist_max 69.818 Gm
venussundist_min 107.480 Gm
venussundist_max 108.941 Gm
earthsundist_min sundist_min
earthsundist_max sundist_max
marssundist_min 206.650 Gm
marssundist_max 249.261 Gm
jupitersundist_min 740.595 Gm
jupitersundist_max 816.363 Gm
saturnsundist_min 1357.554 Gm
saturnsundist_max 1506.527 Gm
uranussundist_min 2732.696 Gm
uranussundist_max 3001.390 Gm
neptunesundist_min 4471.050 Gm
neptunesundist_max 4558.857 Gm
plutosundist_min 4434.987 Gm
plutosundist_max 7304.326 Gm
sundist 1.0000010178 au # mean Earth-Sun distance
moondist 384400 km # mean Earth-Moon distance
sundist_near 147.095 Gm # Earth-Sun distance at perihelion
sundist_min sundist_near
sundist_far 152.100 Gm # Earth-Sun distance at aphelion
sundist_max sundist_far
# The Earth-Moon distances at perigee and apogee are different for every
# lunation. The values here are the extremes for 1500-2500 according to
# Jean Meeus's Astronomical Algorithms (1991, 332).
moondist_min 356371 km # minimum distance at perigee 1500-2500
moondist_max 406720 km # maximum distance at apogee 1500-2500
# Objects on Earth are charted relative to a perfect ellipsoid whose
# dimensions are specified by different organizations. The ellipsoid is
# specified by an equatorial radius and a flattening value which defines the
# polar radius.
earthflattening IERS_earthflattening
earthradius_equatorial IERS_earthradius_equatorial
earthradius_polar (1-earthflattening) earthradius_equatorial
# The World Geodetic System maintains a standard, WGS84, which is used by the
# the GPS system. This system uses a conventional ellipsoid that was fixed in
# 1984 and has remained constant so that data collected at different times is
# referenced to the same ellipsoid. https://epsg.io/4326
WGS84_earthflattening 1|298.257223563
WGS84_earthradius_equatorial 6378137 m
WGS84_earthradius_polar (1-WGS84_earthflattening) WGS84_earthradius_equatorial
# The International Earth Rotation Service (IERS) attempts to
# maintain an accurate model of Earth, with updates to maintain the highest
# possible accuracy, even though this makes it more difficult to relate geodetic
# measurements made at different times.
# IERS Conventions, Chapter 1, General definitions and numerical standards (16 November 2017)
# https://iers-conventions.obspm.fr/content/chapter1/icc1.pdf
IERS_earthflattening 1|298.25642
IERS_earthradius_equatorial 6378136.6 m
IERS_earthradius_polar (1-IERS_earthflattening) IERS_earthradius_equatorial
landarea 148.847e6 km^2
oceanarea 361.254e6 km^2
moonradius 1738 km # mean value
sunradius 6.96e8 m
# Many astronomical values can be measured most accurately in a system of units
# using the astronomical unit and the mass of the Sun as base units. The
# uncertainty in the gravitational constant makes conversion to SI units
# significantly less accurate.
# The astronomical unit was defined to be the length of the of the semimajor
# axis of a massless object with the same year as Earth. With such a
# definition in force, and with the mass of the Sun set equal to one, Kepler's
# third law can be used to solve for the value of the gravitational constant.
# Kepler's third law says that (2 pi / T)^2 a^3 = G M where T is the orbital
# period, a is the size of the semimajor axis, G is the gravitational constant
# and M is the mass. With M = 1 and T and a chosen for Earth's orbit, we
# find sqrt(G) = (2 pi / T) sqrt(AU^3). This constant is called the Gaussian
# gravitational constant, apparently because Gauss originally did the
# calculations. However, when the original calculation was done, the value
# for the length of Earth's year was inaccurate. The value used is called
# the Gaussian year. Changing the astronomical unit to bring it into
# agreement with more accurate values for the year would have invalidated a
# lot of previous work, so instead the astronomical unit has been kept equal
# to this original value. This is accomplished by using a standard value for
# the Gaussian gravitational constant. This constant is called k.
gauss_k 0.01720209895 # This beast has dimensions of
# au^(3|2) / day and is exact.
gaussianyear (2 pi / gauss_k) days # Year that corresponds to the Gaussian
# gravitational constant. This is a
# fictional year, and doesn't
# correspond to any celestial event.
astronomicalunit 149597870700 m # IAU definition from 2012, exact
au astronomicalunit # ephemeris for the above described
# astronomical unit. (See the NASA
# site listed above.)
GMsun 132712440041.279419 km^3 / s^2 # heliocentric gravitational constant
solarmass GMsun/G # is known more accurately than G.
sunmass solarmass # Estimated from DE440
# The following are masses for planetary systems, not just the planet itself,
# except for the case of Earth, where the Moon is excluded. Masses are
# relative to G because they are known much more accurately than G.
#
# See https://ssd.jpl.nasa.gov/astro_par.html. Values are from
# the DE440 Ephemeris: https://ssd.jpl.nasa.gov/doc/Park.2021.AJ.DE440.pdf
mercurymass 22031.868551 km^3 / s^2 G
venusmass 324858.592000 km^3 / s^2 G
marsmass 42828.375816 km^3 / s^2 G
jupitermass 126712764.100000 km^3 / s^2 G
saturnmass 37940584.841800 km^3 / s^2 G
uranusmass 5794556.400000 km^3 / s^2 G
neptunemass 6836527.100580 km^3 / s^2 G
plutomass 975.500000 km^3 / s^2 G
ceresmass 62.62890 km^3 / s^2 G
vestamass 17.288245 km^3 / s^2 G
earthmass 398600.435507 km^3 / s^2 G # Earth alone
moonmass 4902.800118 km^3 / s^2 G
moonearthmassratio moonmass/earthmass
earthmoonmass earthmass+moonmass
moongravity 1.62 m/s^2
# Earth gravity values at the equator and poles. These values are
# obtained from the WGS84 model.
gravity_equatorial 9.7803263359 m / s^2
gravity_polar 9.8321849378 m / s^2
# The Hubble constant gives the speed at which distance galaxies are moving
# away from Earth according to v = H0*d, where H0 is the hubble constant
# and d is the distance to the galaxy.
hubble 70 km/s/Mpc # approximate
H0 hubble
# Parallax is the angular difference between the topocentric (on Earth's
# surface) and geocentric (at Earth's center) direction toward a celestial body
# when the body is at a given altitude. When the body is on the horizon, the
# parallax is the horizontal parallax; when the body is on the horizon and the
# observer is on the equator, the parallax is the equatorial horizontal
# parallax. When the body is at zenith, the parallax is zero.
lunarparallax asin(earthradius_equatorial / moondist) # Moon equatorial
moonhp lunarparallax # horizontal parallax
# at mean distance
# Light from celestial objects is attenuated by passage through Earth's
# atmosphere. A body near the horizon passes through much more air than an
# object at zenith, and is consequently less bright. Air mass is the ratio of
# the length of the optical path at a given altitude (angle above the horizon)
# to the length at zenith. Air mass at zenith is by definition unity; at the
# horizon, air mass is approximately 38, though the latter value can vary
# considerably with atmospheric conditions. The general formula is # E = E0
# exp(-c X), where E0 is the value outside Earth's atmosphere, E is the value
# seen by an observer, X is the air mass and c is the extinction coefficient.
# A common value for c in reasonably clear air is 0.21, but values can be
# considerably greater in urban areas. Apparent altitude is that perceived by
# an observer; it includes the effect of atmospheric refraction. There is no
# shortage of formulas for air mass
# (https://en.wikipedia.org/wiki/Air_mass_(astronomy)); all are subject to
# variations in local atmospheric conditions. The formula used here is simple
# and is in good agreement with rigorously calculated values under standard
# conditions.
#
# Extraterrestrial illuminance or luminance of an object at a given altitude
# determined with vmag() or SB_xxx() below can be multiplied by
# atm_transmission() or atm_transmissionz() to estimate the terrestrial value.
#
# Kasten and Young (1989) air mass formula. alt is apparent altitude
# Reference:
# Kasten, F., and A.T. Young. 1989. "Revised Optical Air Mass Tables
# and Approximation Formula." Applied Optics. Vol. 28, 4735-4738.
# Bibcode:1989ApOpt..28.4735K. doi:10.1364/AO.28.004735.
airmass(alt) units=[degree;1] domain=[0,90] noerror \
1 / (sin(alt) + 0.50572 (alt / degree + 6.07995)^-1.6364)
# zenith is apparent zenith angle (zenith = 90 deg - alt)
airmassz(zenith) units=[degree;1] domain=[0,90] noerror \
1 / (cos(zenith) + 0.50572 (96.07995 - zenith / degree)^-1.6364)
# For reasonably clear air at sea level; values may need adjustment for
# elevation and local atmospheric conditions
# for scotopic vision (510 nm), appropriate for the dark-adapted eye
# extinction_coeff 0.26
# for photopic vision, appropriate for observing brighter objects such
# as the full moon
extinction_coeff 0.21
atm_transmission(alt) units=[degree;1] domain=[0,90] noerror \
exp(-extinction_coeff airmass(alt))
# in terms of zenith angle (zenith = 90 deg - alt)
atm_transmissionz(zenith) units=[degree;1] domain=[0,90] noerror \
exp(-extinction_coeff airmassz(zenith))
# Moon and Sun data at mean distances
moonvmag -12.74 # Moon apparent visual magnitude at mean distance
sunvmag -26.74 # Sun apparent visual magnitude at mean distance
moonsd asin(moonradius / moondist) # Moon angular semidiameter at mean distance
sunsd asin(sunradius / sundist) # Sun angular semidiameter at mean distance
# Visual magnitude of star or other celestial object. The system of stellar
# magnitudes, developed in ancient Greece, assigned magnitudes from 1
# (brightest) to 6 (faintest visible to the naked eye). In 1856, British
# astronomer Norman Pogson made the system precise, with a magnitude 1 object
# 100 times as bright as a magnitude 6 object, and each magnitude differing
# from the next by a constant ratio; the ratio, sometimes known as Pogson's
# ratio, is thus 100^0.2, or approximately 2.5119. The logarithm of 100^0.2 is
# 0.4, hence the common use of powers of 10 and base-10 logarithms.
#
# Reference:
# Allen, C.W. 1976. Astrophysical Quantities, 3rd ed. 1973, reprinted
# with corrections, 1976. London: Athlone.
#
# The function argument is the (dimensionless) visual magnitude; reference
# illuminance of 2.54e-6 lx is from Allen (2000, 21), and is for outside
# Earth's atmosphere. Illuminance values can be adjusted to terrestrial values
# by multiplying by one of the atm_transmission functions above.
# Illuminance from apparent visual magnitude
vmag(mag) units=[1;lx] domain=[,] range=(0,] \
2.54e-6 lx 10^(-0.4 mag); -2.5 log(vmag / (2.54e-6 lx))
# Surface brightness of a celestial object of a given visual magnitude
# is a logarithmic measure of the luminance the object would have if its
# light were emitted by an object of specified solid angle; it is
# expressed in magnitudes per solid angle. Surface brightness can be
# obtained from the visual magnitude by
# S = m + 2.5 log(pi pi k a b),
# where k is the phase (fraction illuminated), a is the equatorial
# radius, and b is the polar radius. For 100% illumination (e.g., full
# moon), this is often simplified to
# S = m + 2.5 log(pi k s^2),
# where s is the object's angular semidiameter; the units of s determine
# the units of solid angle. The visual magnitude and semidiameter must
# be appropriate for the object's distance; for other than 100%
# illumination, the visual magnitude must be appropriate for the phase.
# Luminance values are for outside Earth's atmosphere; they can be
# adjusted to terrestrial values by multiplying by one of the atm_transmission
# functions above.
# luminance from surface brightness in magnitudes per square degree
SB_degree(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
vmag(sb) / squaredegree ; \
~vmag(SB_degree squaredegree)
# luminance from surface brightness in magnitudes per square minute
SB_minute(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
vmag(sb) / squareminute ; \
~vmag(SB_minute squareminute)
# luminance from surface brightness in magnitudes per square second
SB_second(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
vmag(sb) / squaresecond ; \
~vmag(SB_second squaresecond)
# luminance from surface brightness in magnitudes per steradian
SB_sr(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
vmag(sb) / sr ; \
~vmag(SB_sr sr)
SB() SB_second
SB_sec() SB_second
SB_min() SB_minute
SB_deg() SB_degree
# The brightness of one tenth-magnitude star per square degree outside
# Earth's atmosphere; often used for night sky brightness.
S10 SB_degree(10)
# Examples for magnitude and surface brightness functions
# Sun illuminance from visual magnitude
# You have: sunvmag
# You want:
# Definition: -26.74 = -26.74
# You have: vmag(sunvmag)
# You want: lx
# * 126134.45
# / 7.9280482e-06
#
# Moon surface brightness from visual magnitude and semidiameter at 100%
# illumination (full moon):
# You have: moonvmag
# You want:
# Definition: -12.74 = -12.74
# You have: moonsd
# You want: arcsec
# * 932.59484
# / 0.001072277
# You have: moonvmag + 2.5 log(pi 932.59484^2)
# You want:
# Definition: 3.3513397
#
# Similar example with specific data obtained from another source (JPL
# Horizons, https://ssd.jpl.nasa.gov/horizons.cgi); semidiameter is in
# arcseconds
#
# You have: -12.9 + 2.5 log(pi 2023.201|2^2)
# You want:
# Definition: 3.3679199
# You have: SB_second(-12.9 + 2.5 log(pi 2023.201|2^2))
# You want:
# Definition: 4858.6547 cd / m^2
#
# If surface brightness is provided by another source (e.g., Horizons),
# it can simply be used directly:
# You have: SB_second(3.3679199)
# You want: cd/m^2
# * 4858.6546
# / 0.0002058183
# The illuminance and luminance values are extraterrestrial (outside
# Earth's atmosphere). The values at Earth's surface are less than these
# because of atmospheric extinction. For example, in the last example
# above, if the Moon were at an altitude of 55 degrees, the terrestrial
# luminance could be calculated with
# You have: SB_second(3.3679199)
# You want: cd/m^2
# * 4858.6546
# / 0.0002058183
# You have: _ atm_transmission(55 deg)
# You want: cd/m^2
# * 3760.6356
# / 0.0002659125
# If desired, photographic exposure can be determined with EV100(),
# leading to acceptable combinations of aperture and exposure time.
# For the example above, but with the Moon at 10 degrees,
# You have: SB_second(3.3679199) atm_transmission(10 deg)
# You want: EV100
# 13.553962
#
# The Hartree system of atomic units, derived from fundamental units
# of mass (of the electron), action (Planck's constant), charge, and
# the Coulomb constant. This system is used in the fields of physical
# chemistry and condensed matter physics.
#
# Fundamental units
atomicmass electronmass
atomiccharge e
atomicaction hbar
atomicenergy hartree
# Derived units
atomicvelocity sqrt(atomicenergy / atomicmass)
atomictime atomicaction / atomicenergy
atomiclength atomicvelocity atomictime
atomicforce atomicenergy / atomiclength
atomicmomentum atomicenergy / atomicvelocity
atomiccurrent atomiccharge / atomictime
atomicpotential atomicenergy / atomiccharge # electrical potential
atomicvolt atomicpotential
atomicEfield atomicpotential / atomiclength
atomicBfield atomicEfield / atomicvelocity
atomictemperature atomicenergy / boltzmann
#
# In Hartree units, m_e = hbar = e = coulombconst = bohrradius = alpha*c = 1
#
!var UNITS_SYSTEM hartree
!message Hartree units selected
!prompt (hartree)
+hartree 1
+kg 1/electronmass_SI
+K k_SI / hbar_SI s
+m alpha c_SI electronmass_SI / hbar_SI
+s alpha c_SI m
+A 1 / s e_SI
!endvar
#
# These thermal units treat entropy as charge, from [5]
#
thermalcoulomb J/K # entropy
thermalampere W/K # entropy flow
thermalfarad J/K^2
thermalohm K^2/W # thermal resistance
fourier thermalohm
thermalhenry J K^2/W^2 # thermal inductance
thermalvolt K # thermal potential difference
#
# United States units
#
# linear measure
# The US Metric Law of 1866 legalized the metric system in the USA and
# defined the meter in terms of the British system with the exact
# 1 meter = 39.37 inches. On April 5, 1893 Thomas Corwin Mendenhall,
# Superintendent of Weights and Measures, decided, in what has become
# known as the "Mendenhall Order" that the meter and kilogram would be the
# fundamental standards in the USA. The definition from 1866 was turned
# around to give an exact definition of the yard as 3600|3937 meters This
# definition was used until July of 1959 when the definition was changed
# to bring the US and other English-speaking countries into agreement; the
# Canadian value of 1 yard = 0.9144 meter (exactly) was chosen because it
# was approximately halfway between the British and US values; it had the
# added advantage of making 1 inch = 25.4 mm (exactly). Since 1959, the
# "international" foot has been exactly 0.3048 meters. At the same time,
# it was decided that any data expressed in feet derived from geodetic
# surveys within the US would continue to use the old definition and call
# the old unit the "survey foot."
#
# Until 1 January 2023, the US continued to define the statute
# mile, furlong, chain, rod, link, and fathom in terms of the US survey
# foot. Since then, use of the US survey foot has been officially
# deprecated, with its use limited to historical and legacy applications.
# These units are now defined in terms of the international foot.
#
# Sources:
# NIST Special Publication 447, Sects. 5, 7, and 8.
# NIST Handbook 44, 2024 ed., Appendix C.
# Canadian Journal of Physics, 1959, 37:(1) 84, 10.1139/p59-014.
inch 2.54 cm # Exact, international inch (1959)
in inch
foot 12 inch
feet foot
ft foot
yard 3 ft
yd yard
mile 5280 ft # The mile was enlarged from 5000 ft
# to this number in order to make
# it an even number of furlongs.
# (The Roman mile is 5000 romanfeet.)
line 1|12 inch # Also defined as '.1 in' or as '1e-8 Wb'
rod 16.5 ft
pole rod
perch rod
furlong 40 rod # From "furrow long"
statutemile mile
league 3 mile # Intended to be an hour's walk
# surveyor's measure
# The US survey foot is officially deprecated as of 1 January 2023
US 1200|3937 m/ft # These four values will convert
US- US # international measures to
survey- US # US Survey measures
geodetic- US
int 3937|1200 ft/m # Convert US Survey measures to
int- int # international measures
# values based on the US survey foot are deprecated as of 1 January 2023
surveyorschain 66 surveyft
surveychain surveyorschain
surveyorspole 1|4 surveyorschain
surveyorslink 1|100 surveyorschain
USacre 10 surveychain^2
USacrefoot USacre surveyfoot
chain 66 ft
link 1|100 chain
ch chain
intacre 10 chain^2 # Acre based on international ft
intacrefoot acre foot
acrefoot intacrefoot
acre intacre
ac acre
section mile^2
township 36 section
homestead 160 acre # Area of land granted by the 1862 Homestead
# Act of the United States Congress
gunterschain surveyorschain
engineerschain 100 ft
engineerslink 1|100 engineerschain
ramsdenschain engineerschain
ramsdenslink engineerslink
gurleychain 33 feet # Andrew Ellicott chain is the
gurleylink 1|50 gurleychain # same length
wingchain 66 feet # Chain from 1664, introduced by
winglink 1|80 wingchain # Vincent Wing, also found in a
# 33 foot length with 40 links.
# early US length standards
# The US has had four standards for the yard: one by Troughton of London
# (1815); bronze yard #11 (1856); the Mendhall yard (1893), consistent
# with the definition of the meter in the metric joint resolution of
# Congress in 1866, but defining the yard in terms of the meter; and the
# international yard (1959), which standardized definitions for Australia,
# Canada, New Zealand, South Africa, the UK, and the US.
# Sources: Pat Naughtin (2009), Which Inch?:
# https://metricationmatters.org/docs/WhichInch.pdf,
# Lewis E. Barbrow and Lewis V. Judson (1976). NBS Special
# Publication 447, Weights and Measures Standards of the United States: A
# Brief History.
troughtonyard 914.42190 mm
bronzeyard11 914.39980 mm
mendenhallyard surveyyard
internationalyard yard
# nautical measure
fathom 6 ft # Originally defined as the distance from
# fingertip to fingertip with arms fully
# extended.
nauticalmile 1852 m # Supposed to be one minute of latitude at
# the equator. That value is about 1855 m.
# Early estimates of Earth's circumference
# were a bit off. The value of 1852 m was
# made the international standard in 1929.
# The US did not accept this value until
# 1954. The UK switched in 1970.
# The cable is used for depth in water and has a wide range of definitions
intcable 1|10 nauticalmile # international cable
uscable 120 fathom # value after 1 January 2023
surveycable 120 USfathom # value before 1 January 2023
UScable surveycable
cableslength cable
cablelength cable
navycablelength cable
brcable 1|10 brnauticalmile
admiraltycable brcable
marineleague 3 nauticalmile
geographicalmile brnauticalmile
knot nauticalmile / hr
click km # US military slang
klick click
# Avoirdupois weight
pound 0.45359237 kg # Exact, International Pound (1959)
lb pound # From the Latin libra
grain 1|7000 pound # The grain is the same in all three
# weight systems. It was originally
# defined as the weight of a barley
# corn taken from the middle of the
# ear.
ounce 1|16 pound
oz ounce
dram 1|16 ounce
dr dram
ushundredweight 100 pounds
cwt hundredweight
shorthundredweight ushundredweight
uston shortton
shortton 2000 lb
quarterweight 1|4 uston
shortquarterweight 1|4 shortton
shortquarter shortquarterweight
# Troy Weight. In 1828 the troy pound was made the first United States
# standard weight. It was to be used to regulate coinage.
troypound 5760 grain
troyounce 1|12 troypound
ozt troyounce
pennyweight 1|20 troyounce # Abbreviated "d" in reference to a
dwt pennyweight # Frankish coin called the "denier"
# minted in the late 700's. There
# were 240 deniers to the pound.
assayton mg ton / troyounce # mg / assayton = troyounce / ton
usassayton mg uston / troyounce
brassayton mg brton / troyounce
fineounce troyounce # A troy ounce of 99.5% pure gold
# Some other jewelers units
metriccarat 0.2 gram # Defined in 1907
metricgrain 50 mg
carat metriccarat
ct carat
jewelerspoint 1|100 carat
silversmithpoint 1|4000 inch
momme 3.75 grams # Traditional Japanese unit based
# on the chinese mace. It is used for
# pearls in modern times and also for
# silk density. The definition here
# was adopted in 1891.
# Apothecaries' weight
appound troypound
apounce troyounce
apdram 1|8 apounce
apscruple 1|3 apdram
# Liquid measure
usgallon 231 in^3 # US liquid measure is derived from
gal gallon # the British wine gallon of 1707.
quart 1|4 gallon # See the "winegallon" entry below
pint 1|2 quart # more historical information.
gill 1|4 pint
usquart 1|4 usgallon
uspint 1|2 usquart
usgill 1|4 uspint
usfluidounce 1|16 uspint
fluiddram 1|8 usfloz
minimvolume 1|60 fluiddram
qt quart
pt pint
floz fluidounce
usfloz usfluidounce
fldr fluiddram
liquidbarrel 31.5 usgallon
usbeerbarrel 2 beerkegs
beerkeg 15.5 usgallon # Various among brewers
ponykeg 1|2 beerkeg
winekeg 12 usgallon
petroleumbarrel 42 usgallon # Originated in Pennsylvania oil
barrel petroleumbarrel # fields, from the winetierce
bbl barrel
ushogshead 2 liquidbarrel
usfirkin 9 usgallon
# Dry measures: The Winchester Bushel was defined by William III in 1702 and
# legally adopted in the US in 1836.
usbushel 2150.42 in^3 # Volume of 8 inch cylinder with 18.5
bu bushel # inch diameter (rounded)
peck 1|4 bushel
uspeck 1|4 usbushel
brpeck 1|4 brbushel
pk peck
drygallon 1|2 uspeck
dryquart 1|4 drygallon
drypint 1|2 dryquart
drybarrel 7056 in^3 # Used in US for fruits, vegetables,
# and other dry commodities except for
# cranberries.
cranberrybarrel 5826 in^3 # US cranberry barrel
heapedbushel 1.278 usbushel# The following explanation for this
# value was provided by Wendy Krieger
# <os2fan2@yahoo.com> based on
# guesswork. The cylindrical vessel is
# 18.5 inches in diameter and 1|2 inch
# thick. A heaped bushel includes the
# contents of this cylinder plus a heap
# on top. The heap is a cone 19.5
# inches in diameter and 6 inches
# high. With these values, the volume
# of the bushel is 684.5 pi in^3 and
# the heap occupies 190.125 pi in^3.
# Therefore, the heaped bushel is
# 874.625|684.5 bushels. This value is
# approximately 1.2777575 and it rounds
# to the value listed for the size of
# the heaped bushel. Sometimes the
# heaped bushel is reported as 1.25
# bushels. This same explanation gives
# that value if the heap is taken to
# have an 18.5 inch diameter.
# Grain measures. The bushel as it is used by farmers in the USA is actually
# a measure of mass which varies for different commodities. Canada uses the
# same bushel masses for most commodities, but not for oats.
wheatbushel 60 lb
soybeanbushel 60 lb
cornbushel 56 lb
ryebushel 56 lb
barleybushel 48 lb
oatbushel 32 lb
ricebushel 45 lb
canada_oatbushel 34 lb
# Wine and Spirits measure
ponyvolume 1 usfloz
jigger 1.5 usfloz # Can vary between 1 and 2 usfloz
shot jigger # Sometimes 1 usfloz
eushot 25 ml # EU standard spirits measure
fifth 1|5 usgallon
winebottle 750 ml # US industry standard, 1979
winesplit 1|4 winebottle
magnum 1.5 liter # Standardized in 1979, but given
# as 2 qt in some references
metrictenth 375 ml
metricfifth 750 ml
metricquart 1 liter
# Old British bottle size
reputedquart 1|6 brgallon
reputedpint 1|2 reputedquart
brwinebottle reputedquart # Very close to 1|5 winegallon
# French champagne bottle sizes
split 200 ml
jeroboam 2 magnum
rehoboam 3 magnum
methuselah 4 magnum
imperialbottle 4 magnum
salmanazar 6 magnum
balthazar 8 magnum
nebuchadnezzar 10 magnum
solomon 12 magnum
melchior 12 magnum
sovereign 17.5 magnum
primat 18 magnum
goliath 18 magnum
melchizedek 20 magnum
midas 20 magnum
# The wine glass doesn't seem to have an official standard, but the same value
# is suggested by several sources in the US.
wineglass 150 mL
# In the UK, serving size offerings legally mandated by The Weights and
# Measures (Specified Quantities) (Unwrapped Bread and Intoxicating
# Liquor) Order 2011, effective 1st October 2011. The quantities--not
# the names--are mandated. Lawful size offerings are these or multiples
# thereof, but other sizes can be provided at the express request of a
# buyer.
smallwineglass 125 mL
mediumwineglass 175 mL
# Values vary considerably among countries and even more so in practice. The
# "standard" US value gives 5 glasses per standard 750 ml bottle. Old practice
# in the UK was 125 ml per glass, or 6 glasses per bottle. Some sources suggest
# a more recent common value of 250 ml per glass, or 3 glasses per
# bottle; as a multiple of 125 ml, this would be a lawful serving size offering.
#
# The value refers to the size of the serving, not the total volume of the
# glass, which is typically not filled above the height of its greatest
# diameter.
#
# A unit of alcohol is a specified amount of pure ethyl alcohol, expressed as a
# mass or volumetric equivalent. Many countries use the same concept but use
# different terms. "Alcohol unit" is used officially in the UK; the US, Canada,
# and Australia use "standard drink." Values vary considerably among
# countries. The UK value of 8 g is nominally the amount of alcohol that a
# typical adult can metabolize in one hour.
alcoholunitus 14 g / ethanoldensity
alcoholunitca 13.6 g / ethanoldensity
alcoholunituk 8 g / ethanoldensity
alcoholunitau 10 g / ethanoldensity
# Common serving sizes have roughly equivalent amounts of alcohol, as
# illustrated by US examples for wine (12% Alcohol By Volume), beer (5% ABV),
# and spirits (80 proof).
#
# alcoholunitus / 12% = 147.8 mL, close to the "standard" serving of 150 mL.
# alcoholunitus / 5% = 11.995346 floz, close to a standard 12 floz bottle or can
# alcoholunitus / 80 proof = 1.4994182 floz, close to a standard "shot" or jigger
# https://www.rethinkingdrinking.niaaa.nih.gov/
# https://www.cdc.gov/alcohol/faqs.htm
# https://www.canada.ca/en/health-canada/services/substance-use/alcohol/low-risk-alcohol-drinking-guidelines
# https://www.drinkaware.co.uk/
# https://www.drinkaware.co.uk/facts/alcoholic-drinks-and-units
# https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/545937/UK_CMOs__report.pdf
# https://adf.org.au/reducing-risk/alcohol/alcohol-guidelines/
# https://www.health.gov.au/topics/alcohol/about-alcohol/standard-drinks-guide
# https://en.wikipedia.org/wiki/Unit_of_alcohol
# https://en.wikipedia.org/wiki/Standard_drink
# Coffee
#
# The recommended ratio of coffee to water. Values vary considerably;
# one is from the Specialty Coffee Association of America: Brewing Best Practices
# https://sca.coffee/research/protocols-best-practices
coffeeratio 55 g/L # +/- 10%
# other recommendations are more loose, e.g.,
# http://www.ncausa.org/About-Coffee/How-to-Brew-Coffee
#
# Water is "hard" if it contains various minerals, especially calcium
# carbonate.
#
clarkdegree grains/brgallon # Content by weigh of calcium carbonate
gpg grains/usgallon # Divide by water's density to convert to
# a dimensionless concentration measure
#
# Shoe measures
#
shoeiron 1|48 inch # Used to measure leather in soles
shoeounce 1|64 inch # Used to measure non-sole shoe leather
# USA shoe sizes. These express the length of the shoe or the length
# of the "last", the form that the shoe is made on. But note that
# this only captures the length. It appears that widths change 1/4
# inch for each letter within the same size, and if you change the
# length by half a size then the width changes between 1/8 inch and
# 1/4 inch. But this may not be standard. If you know better, please
# contact me.
shoesize_delta 1|3 inch # USA shoe sizes differ by this amount
shoe_men0 8.25 inch
shoe_women0 (7+11|12) inch
shoe_boys0 (3+11|12) inch
shoe_girls0 (3+7|12) inch
shoesize_men(n) units=[1;inch] shoe_men0 + n shoesize_delta ; \
(shoesize_men+(-shoe_men0))/shoesize_delta
shoesize_women(n) units=[1;inch] shoe_women0 + n shoesize_delta ; \
(shoesize_women+(-shoe_women0))/shoesize_delta
shoesize_boys(n) units=[1;inch] shoe_boys0 + n shoesize_delta ; \
(shoesize_boys+(-shoe_boys0))/shoesize_delta
shoesize_girls(n) units=[1;inch] shoe_girls0 + n shoesize_delta ; \
(shoesize_girls+(-shoe_girls0))/shoesize_delta
# European shoe size. According to
# http://www.shoeline.com/footnotes/shoeterm.shtml
# shoe sizes in Europe are measured with Paris points which simply measure
# the length of the shoe.
europeshoesize 2|3 cm
#
# USA slang units
#
buck US$
fin 5 US$
sawbuck 10 US$
usgrand 1000 US$
greenback US$
key kg # usually of marijuana, 60's
lid 1 oz # Another 60's weed unit
footballfield usfootballfield
usfootballfield 100 yards
canadafootballfield 110 yards # And 65 yards wide
marathon 26 miles + 385 yards
#
# British
#
# The length measure in the UK was defined by a bronze bar manufactured in
# 1844. Various conversions were sanctioned for convenience at different
# times, which makes conversions before 1963 a confusing matter. Apparently
# previous conversions were never explicitly revoked. Four different
# conversion factors appear below. Multiply them times an imperial length
# units as desired. The Weights and Measures Act of 1963 switched the UK away
# from their bronze standard and onto a definition of the yard in terms of the
# meter. This happened after an international agreement in 1959 to align the
# world's measurement systems.
UK UKlength_SJJ
UK- UK
british- UK
UKlength_B 0.9143992 meter / yard # Benoit found the yard to be
# 0.9143992 m at a weights and
# measures conference around
# 1896. Legally sanctioned
# in 1898.
UKlength_SJJ 0.91439841 meter / yard # In 1922, Seers, Jolly and
# Johnson found the yard to be
# 0.91439841 meters.
# Used starting in the 1930's.
UKlength_K meter / 39.37079 inch # In 1816 Kater found this ratio
# for the meter and inch. This
# value was used as the legal
# conversion ratio when the
# metric system was legalized
# for contract in 1864.
UKlength_C meter / 1.09362311 yard # In 1866 Clarke found the meter
# to be 1.09362311 yards. This
# conversion was legalized
# around 1878.
brnauticalmile 6080 ft # Used until 1970 when the UK
brknot brnauticalmile / hr # switched to the international
admiraltymile brnauticalmile # nautical mile.
admiraltyknot brknot
seamile 6000 ft
shackle 15 fathoms # Adopted 1949 by British navy
# British Imperial weight is mostly the same as US weight. A few extra
# units are added here.
clove 7 lb
stone 14 lb
tod 28 lb
brquarterweight 1|4 brhundredweight
brhundredweight 8 stone
longhundredweight brhundredweight
longton 20 brhundredweight
brton longton
# British Imperial volume measures
brminim 1|60 brdram
brscruple 1|3 brdram
fluidscruple brscruple
brdram 1|8 brfloz
brfluidounce 1|20 brpint
brfloz brfluidounce
brgill 1|4 brpint
brpint 1|2 brquart
brquart 1|4 brgallon
brgallon 4.54609 l # The British Imperial gallon was
# defined in 1824 to be the volume of
# water which weighed 10 pounds at 62
# deg F with a pressure of 30 inHg.
# It was also defined as 277.274 in^3,
# Which is slightly in error. In
# 1963 it was defined to be the volume
# occupied by 10 pounds of distilled
# water of density 0.998859 g/ml weighed
# in air of density 0.001217 g/ml
# against weights of density 8.136 g/ml.
# This gives a value of approximately
# 4.5459645 liters, but the old liter
# was in force at this time. In 1976
# the definition was changed to exactly
# 4.54609 liters using the new
# definition of the liter (1 dm^3).
brbarrel 36 brgallon # Used for beer
brbushel 8 brgallon
brheapedbushel 1.278 brbushel
brquarter 8 brbushel
brchaldron 36 brbushel
# Obscure British volume measures. These units are generally traditional
# measures whose definitions have fluctuated over the years. Often they
# depended on the quantity being measured. They are given here in terms of
# British Imperial measures. For example, the puncheon may have historically
# been defined relative to the wine gallon or beer gallon or ale gallon
# rather than the British Imperial gallon.
bag 4 brbushel
bucket 4 brgallon
kilderkin 2 brfirkin
last 40 brbushel
noggin brgill
pottle 0.5 brgallon
pin 4.5 brgallon
puncheon 72 brgallon
seam 8 brbushel
coomb 4 brbushel
boll 6 brbushel
firlot 1|4 boll
brfirkin 9 brgallon # Used for ale and beer
cran 37.5 brgallon # measures herring, about 750 fish
brwinehogshead 52.5 brgallon # This value is approximately equal
brhogshead brwinehogshead # to the old wine hogshead of 63
# wine gallons. This adjustment
# is listed in the OED and in
# "The Weights and Measures of
# England" by R. D. Connor
brbeerhogshead 54 brgallon
brbeerbutt 2 brbeerhogshead
registerton 100 ft^3 # Used for internal capacity of ships
shippington 40 ft^3 # Used for ship's cargo freight or timber
brshippington 42 ft^3 #
freightton shippington # Both register ton and shipping ton derive
# from the "tun cask" of wine.
displacementton 35 ft^3 # Approximate volume of a longton weight of
# sea water. Measures water displaced by
# ships.
waterton 224 brgallon
strike 70.5 l # 16th century unit, sometimes
# defined as .5, 2, or 4 bushels
# depending on the location. It
# probably doesn't make a lot of
# sense to define in terms of imperial
# bushels. Zupko gives a value of
# 2 Winchester grain bushels or about
# 70.5 liters.
amber 4 brbushel# Used for dry and liquid capacity [18]
# British volume measures with "imperial"
imperialminim brminim
imperialscruple brscruple
imperialdram brdram
imperialfluidounce brfluidounce
imperialfloz brfloz
imperialgill brgill
imperialpint brpint
imperialquart brquart
imperialgallon brgallon
imperialbarrel brbarrel
imperialbushel brbushel
imperialheapedbushel brheapedbushel
imperialquarter brquarter
imperialchaldron brchaldron
imperialwinehogshead brwinehogshead
imperialhogshead brhogshead
imperialbeerhogshead brbeerhogshead
imperialbeerbutt brbeerbutt
imperialfirkin brfirkin
# obscure British lengths
barleycorn 1|3 UKinch # Given in Realm of Measure as the
# difference between successive shoe sizes
nail 1|16 UKyard # Originally the width of the thumbnail,
# or 1|16 ft. This took on the general
# meaning of 1|16 and settled on the
# nail of a yard or 1|16 yards as its
# final value. [12]
UKpole 16.5 UKft # This was 15 Saxon feet, the Saxon
rope 20 UKft # foot (aka northern foot) being longer
englishell 45 UKinch
flemishell 27 UKinch
ell englishell # supposed to be measure from elbow to
# fingertips
span 9 UKinch # supposed to be distance from thumb
# to pinky with full hand extension
goad 4.5 UKft # used for cloth, possibly named after the
# stick used for prodding animals.
# misc obscure British units
hide 120 acre # English unit of land area dating to the 7th
# century, originally the amount of land
# that a single plowman could cultivate,
# which varied from 60-180 acres regionally.
# Standardized at Normon conquest.
virgate 1|4 hide
nook 1|2 virgate
rood furlong rod # Area of a strip a rod by a furlong
englishcarat troyounce/151.5 # Originally intended to be 4 grain
# but this value ended up being
# used in the London diamond market
mancus 2 oz
mast 2.5 lb
nailkeg 100 lbs
basebox 31360 in^2 # Used in metal plating
# alternate spellings
gramme gram
litre liter
dioptre diopter
sulphur sulfur
#
# Units derived the human body (may not be very accurate)
#
geometricpace 5 ft # distance between points where the same
# foot hits the ground
pace 2.5 ft # distance between points where alternate
# feet touch the ground
USmilitarypace 30 in # United States official military pace
USdoubletimepace 36 in # United States official doubletime pace
fingerbreadth 7|8 in # The finger is defined as either the width
fingerlength 4.5 in # or length of the finger
finger fingerbreadth
palmwidth hand # The palm is a unit defined as either the width
palmlength 8 in # or the length of the hand
hand 4 inch # width of hand
shaftment 6 inch # Distance from tip of outstretched thumb to the
# opposite side of the palm of the hand. The
# ending -ment is from the old English word
# for hand. [18]
smoot 5 ft + 7 in # Created as part of an MIT fraternity prank.
# In 1958 Oliver Smoot was used to measure
# the length of the Harvard Bridge, which was
# marked off in Smoot lengths. These
# markings have been maintained on the bridge
# since then and repainted by subsequent
# incoming fraternity members. During a
# bridge renovation the new sidewalk was
# scored every Smoot rather than at the
# customary 6 ft spacing.
tomcruise 5 ft + 7.75 in # Height of Tom Cruise
#
# Cooking measures
#
# Common abbreviations
tbl tablespoon
tbsp tablespoon
tblsp tablespoon
Tb tablespoon
tsp teaspoon
saltspoon 1|4 tsp
# US measures
uscup 8 usfloz
ustablespoon 1|16 uscup
usteaspoon 1|3 ustablespoon
ustbl ustablespoon
ustbsp ustablespoon
ustblsp ustablespoon
ustsp usteaspoon
metriccup 250 ml
stickbutter 1|4 lb # Butter in the USA is sold in one
# pound packages that contain four
# individually wrapped pieces. The
# pieces are marked into tablespoons,
# making it possible to measure out
# butter by volume by slicing the
# butter.
legalcup 240 ml # The cup used on nutrition labeling
legaltablespoon 1|16 legalcup
legaltbsp legaltablespoon
# Scoop size. Ice cream scoops in the US are marked with numbers
# indicating the number of scoops required to fill a US quart.
scoop(n) units=[1;cup] domain=[4,100] range=[0.04,1] \
32 usfloz / n ; 32 usfloz / scoop
# US can sizes.
number1can 10 usfloz
number2can 19 usfloz
number2.5can 3.5 uscups
number3can 4 uscups
number5can 7 uscups
number10can 105 usfloz
# British measures
brcup 1|2 brpint
brteacup 1|3 brpint
brtablespoon 15 ml # Also 5|8 brfloz, approx 17.7 ml
brteaspoon 1|3 brtablespoon # Also 1|4 brtablespoon
brdessertspoon 2 brteaspoon
dessertspoon brdessertspoon
dsp dessertspoon
brtsp brteaspoon
brtbl brtablespoon
brtbsp brtablespoon
brtblsp brtablespoon
# Australian
australiatablespoon 20 ml
austbl australiatablespoon
austbsp australiatablespoon
austblsp australiatablespoon
australiateaspoon 1|4 australiatablespoon
austsp australiateaspoon
# Italian
etto 100 g # Used for buying items like meat and
etti etto # cheese.
# Chinese
catty 0.5 kg
oldcatty 4|3 lbs # Before metric conversion.
tael 1|16 oldcatty # Should the tael be defined both ways?
mace 0.1 tael
oldpicul 100 oldcatty
picul 100 catty # Chinese usage
# Indian
seer 14400 grain # British Colonial standard
ser seer
maund 40 seer
pakistanseer 1 kg
pakistanmaund 40 pakistanseer
chittak 1|16 seer
tola 1|5 chittak
ollock 1|4 liter # Is this right?
# Japanese
japancup 200 ml
# densities of cooking ingredients from The Cake Bible by Rose Levy Beranbaum
# so you can convert '2 cups sugar' to grams, for example, or in the other
# direction grams could be converted to 'cup flour_scooped'.
butter 8 oz/uscup
butter_clarified 6.8 oz/uscup
cocoa_butter 9 oz/uscup
shortening 6.75 oz/uscup # vegetable shortening
oil 7.5 oz/uscup
cakeflour_sifted 3.5 oz/uscup # The density of flour depends on the
cakeflour_spooned 4 oz/uscup # measuring method. "Scooped", or
cakeflour_scooped 4.5 oz/uscup # "dip and sweep" refers to dipping a
flour_sifted 4 oz/uscup # measure into a bin, and then sweeping
flour_spooned 4.25 oz/uscup # the excess off the top. "Spooned"
flour_scooped 5 oz/uscup # means to lightly spoon into a measure
breadflour_sifted 4.25 oz/uscup # and then sweep the top. Sifted means
breadflour_spooned 4.5 oz/uscup # sifting the flour directly into a
breadflour_scooped 5.5 oz/uscup # measure and then sweeping the top.
cornstarch 120 grams/uscup
dutchcocoa_sifted 75 g/uscup # These are for Dutch processed cocoa
dutchcocoa_spooned 92 g/uscup
dutchcocoa_scooped 95 g/uscup
cocoa_sifted 75 g/uscup # These are for nonalkalized cocoa
cocoa_spooned 82 g/uscup
cocoa_scooped 95 g/uscup
heavycream 232 g/uscup
milk 242 g/uscup
sourcream 242 g/uscup
molasses 11.25 oz/uscup
cornsyrup 11.5 oz/uscup
honey 11.75 oz/uscup
sugar 200 g/uscup
powdered_sugar 4 oz/uscup
brownsugar_light 217 g/uscup # packed
brownsugar_dark 239 g/uscup
baking_powder 4.6 grams / ustsp
salt 6 g / ustsp
koshersalt 2.8 g / ustsp # Diamond Crystal kosher salt
koshersalt_morton 4.8 g / ustsp # Morton kosher salt
# Values are from the nutrition info
# on the packages
# Egg weights and volumes for a USA large egg
egg 50 grams # without shell
eggwhite 30 grams
eggyolk 18.6 grams
eggvolume 3 ustablespoons + 1|2 ustsp
eggwhitevolume 2 ustablespoons
eggyolkvolume 3.5 ustsp
# Alcohol density
ethanoldensity 0.7893 g/cm^3 # From CRC Handbook, 91st Edition
alcoholdensity ethanoldensity
#
# Density measures. Density has traditionally been measured on a variety of
# bizarre nonlinear scales.
#
# Density of a sugar syrup is frequently measured in candy making procedures.
# In the USA the boiling point of the syrup is measured. Some recipes instead
# specify the density using degrees Baume. Conversion between degrees Baume
# and the boiling point measure has proved elusive. This table appeared in one
# text, and provides a fragmentary relationship to the concentration.
#
# temp(C) conc (%)
# 100 30
# 101 40
# 102 50
# 103 60
# 106 70
# 112 80
# 123 90
# 140 95
# 151 97
# 160 98.2
# 166 99.5
# 171 99.6
#
# The best source identified to date came from "Boiling point elevation of
# technical sugarcane solutions and its use in automatic pan boiling" by
# Michael Saska. International Sugar Journal, 2002, 104, 1247, pp 500-507.
#
# But I'm using equation (3) which is credited to Starzak and Peacock,
# "Water activity coefficient in aqueous solutions of sucrose--A comprehensive
# data analysis. Zuckerindustrie, 122, 380-387. (I couldn't find this
# document.)
#
# Note that the range of validity is uncertain, but answers are in agreement
# with the above table all the way to 99.6.
#
# The original equation has a parameter for the boiling point of water, which
# of course varies with altitude. It also includes various other model
# parameters. The input is the molar concentration of sucrose in the solution,
# (moles sucrose) / (total moles).
#
# Bsp 3797.06 degC
# Csp 226.28 degC
# QQ -17638 J/mol
# asp -1.0038
# bsp -0.24653
# tbw 100 degC # boiling point of water
# sugar_bpe_orig(x) ((1-QQ/R Bsp * x^2 (1+asp x + bsp x^2) (tbw + Csp) \
# /(tbw+stdtemp)) / (1+(tbw + Csp)/Bsp *ln(1-x))-1) * (tbw + Csp)
#
# To convert mass concentration (brix) to molar concentration
#
# sc(x) (x / 342.3) / (( x/342.3) + (100-x)/18.02); \
# 100 sc 342.3|18.02 / (sc (342.3|18.02-1)+1)
#
# Here is a simplified version of this equation where the temperature of boiling
# water has been fixed at 100 degrees Celsius and the argument is now the
# concentration (brix).
#
# sugar_bpe(x) ((1+ 0.48851085 * sc(x)^2 (1+ -1.0038 sc(x) + -0.24653 sc(x)^2)) \
# / (1+0.08592964 ln(1-sc(x)))-1) 326.28 K
#
#
# The formula is not invertible, so to implement it in units we unfortunately
# must turn it into a table.
# This table gives the boiling point elevation as a function of the sugar syrup
# concentration expressed as a percentage.
sugar_conc_bpe[K] \
0 0.0000 5 0.0788 10 0.1690 15 0.2729 20 0.3936 25 0.5351 \
30 0.7027 35 0.9036 40 1.1475 42 1.2599 44 1.3825 46 1.5165 \
48 1.6634 50 1.8249 52 2.0031 54 2.2005 56 2.4200 58 2.6651 \
60 2.9400 61 3.0902 62 3.2499 63 3.4198 64 3.6010 65 3.7944 \
66 4.0012 67 4.2227 68 4.4603 69 4.7156 70 4.9905 71 5.2870 \
72 5.6075 73 5.9546 74 6.3316 75 6.7417 76 7.1892 77 7.6786 \
78.0 8.2155 79.0 8.8061 80.0 9.4578 80.5 9.8092 81.0 10.1793 \
81.5 10.5693 82.0 10.9807 82.5 11.4152 83.0 11.8743 83.5 12.3601 \
84.0 12.8744 84.5 13.4197 85.0 13.9982 85.5 14.6128 86.0 15.2663 \
86.5 15.9620 87.0 16.7033 87.5 17.4943 88.0 18.3391 88.5 19.2424 \
89.0 20.2092 89.5 21.2452 90.0 22.3564 90.5 23.5493 91.0 24.8309 \
91.5 26.2086 92.0 27.6903 92.5 29.2839 93.0 30.9972 93.5 32.8374 \
94.0 34.8104 94.5 36.9195 95.0 39.1636 95.5 41.5348 96.0 44.0142 \
96.5 46.5668 97.0 49.1350 97.5 51.6347 98.0 53.9681 98.1 54.4091 \
98.2 54.8423 98.3 55.2692 98.4 55.6928 98.5 56.1174 98.6 56.5497 \
98.7 56.9999 98.8 57.4828 98.9 58.0206 99.0 58.6455 99.1 59.4062 \
99.2 60.3763 99.3 61.6706 99.4 63.4751 99.5 66.1062 99.6 70.1448 \
99.7 76.7867
# Using the brix table we can use this to produce a mapping from boiling point
# to density which makes all of the units interconvertible. Because the brix
# table stops at 95 this approach works up to a boiling point elevation of 39 K
# or a boiling point of 139 C / 282 F, which is the "soft crack" stage in candy
# making. The "hard crack" stage continues up to 310 F.
# Boiling point elevation
sugar_bpe(T) units=[K;g/cm^3] domain=[0,39.1636] range=[0.99717,1.5144619] \
brix(~sugar_conc_bpe(T)); sugar_conc_bpe(~brix(sugar_bpe))
# Absolute boiling point (produces an absolute temperature)
sugar_bp(T) units=[K;g/cm^3] domain=[373.15,412.3136] \
range=[0.99717,1.5144619] \
brix(~sugar_conc_bpe(T-tempC(100))) ;\
sugar_conc_bpe(~brix(sugar_bp))+tempC(100)
# In practice dealing with the absolute temperature is annoying because it is
# not possible to convert to a nested function, so you're stuck retyping the
# absolute temperature in Kelvins to convert to celsius or Fahrenheit. To
# prevent this we supply definitions that build in the temperature conversion
# and produce results in the Fahrenheit and Celsius scales. So using these
# measures, to convert 46 degrees Baume to a Fahrenheit boiling point:
#
# You have: baume(45)
# You want: sugar_bpF
# 239.05647
#
sugar_bpF(T) units=[1;g/cm^3] domain=[212,282.49448] range=[0.99717,1.5144619]\
brix(~sugar_conc_bpe(tempF(T)+-tempC(100))) ;\
~tempF(sugar_conc_bpe(~brix(sugar_bpF))+tempC(100))
sugar_bpC(T) units=[1;g/cm^3] domain=[100,139.1636] range=[0.99717,1.5144619]\
brix(~sugar_conc_bpe(tempC(T)+-tempC(100))) ;\
~tempC(sugar_conc_bpe(~brix(sugar_bpC))+tempC(100))
# Degrees Baume is used in European recipes to specify the density of a sugar
# syrup. An entirely different definition is used for densities below
# 1 g/cm^3. An arbitrary constant appears in the definition. This value is
# equal to 145 in the US, but was according to [], the old scale used in
# Holland had a value of 144, and the new scale or Gerlach scale used 146.78.
baumeconst 145 # US value
baume(d) units=[1;g/cm^3] domain=[0,145) range=[1,) \
(baumeconst/(baumeconst+-d)) g/cm^3 ; \
(baume+((-g)/cm^3)) baumeconst / baume
# It's not clear if this value was ever used with negative degrees.
twaddell(x) units=[1;g/cm^3] domain=[-200,) range=[0,) \
(1 + 0.005 x) g / cm^3 ; \
200 (twaddell / (g/cm^3) +- 1)
# The degree quevenne is a unit for measuring the density of milk.
# Similarly it's unclear if negative values were allowed here.
quevenne(x) units=[1;g/cm^3] domain=[-1000,) range=[0,) \
(1 + 0.001 x) g / cm^3 ; \
1000 (quevenne / (g/cm^3) +- 1)
# Degrees brix measures sugar concentration by weigh as a percentage, so a
# solution that is 3 degrees brix is 3% sugar by weight. This unit was named
# after Adolf Brix who invented a hydrometer that read this percentage
# directly. This data is from Table 114 of NIST Circular 440, "Polarimetry,
# Saccharimetry and the Sugars". It gives apparent specific gravity at 20
# degrees Celsius of various sugar concentrations. As rendered below this
# data is converted to apparent density at 20 degrees Celsius using the
# density figure for water given in the same NIST reference. They use the
# word "apparent" to refer to measurements being made in air with brass
# weights rather than vacuum.
brix[0.99717g/cm^3]\
0 1.00000 1 1.00390 2 1.00780 3 1.01173 4 1.01569 5 1.01968 \
6 1.02369 7 1.02773 8 1.03180 9 1.03590 10 1.04003 11 1.04418 \
12 1.04837 13 1.05259 14 1.05683 15 1.06111 16 1.06542 17 1.06976 \
18 1.07413 19 1.07853 20 1.08297 21 1.08744 22 1.09194 23 1.09647 \
24 1.10104 25 1.10564 26 1.11027 27 1.11493 28 1.11963 29 1.12436 \
30 1.12913 31 1.13394 32 1.13877 33 1.14364 34 1.14855 35 1.15350 \
36 1.15847 37 1.16349 38 1.16853 39 1.17362 40 1.17874 41 1.18390 \
42 1.18910 43 1.19434 44 1.19961 45 1.20491 46 1.21026 47 1.21564 \
48 1.22106 49 1.22652 50 1.23202 51 1.23756 52 1.24313 53 1.24874 \
54 1.25439 55 1.26007 56 1.26580 57 1.27156 58 1.27736 59 1.28320 \
60 1.28909 61 1.29498 62 1.30093 63 1.30694 64 1.31297 65 1.31905 \
66 1.32516 67 1.33129 68 1.33748 69 1.34371 70 1.34997 71 1.35627 \
72 1.36261 73 1.36900 74 1.37541 75 1.38187 76 1.38835 77 1.39489 \
78 1.40146 79 1.40806 80 1.41471 81 1.42138 82 1.42810 83 1.43486 \
84 1.44165 85 1.44848 86 1.45535 87 1.46225 88 1.46919 89 1.47616 \
90 1.48317 91 1.49022 92 1.49730 93 1.50442 94 1.51157 95 1.51876
# Density measure invented by the American Petroleum Institute. Lighter
# petroleum products are more valuable, and they get a higher API degree.
#
# The intervals of range and domain should be open rather than closed.
#
apidegree(x) units=[1;g/cm^3] domain=[-131.5,) range=[0,) \
141.5 g/cm^3 / (x+131.5) ; \
141.5 (g/cm^3) / apidegree + (-131.5)
#
# Average densities of various woods (dried)
# Data from The Wood Database https://www.wood-database.com
#
# North American Hardwoods
wood_cherry 35 lb/ft^3
wood_redoak 44 lb/ft^3
wood_whiteoak 47 lb/ft^3
wood_blackwalnut 38 lb/ft^3
wood_walnut wood_blackwalnut
wood_birch 43 lb/ft^3
wood_hardmaple 44 lb/ft^3
wood_bigleafmaple 34 lb/ft^3
wood_boxeldermaple 30 lb/ft^3
wood_redmaple 38 lb/ft^3
wood_silvermaple 33 lb/ft^3
wood_stripedmaple 32 lb/ft^3
wood_softmaple (wood_bigleafmaple \
+ wood_boxeldermaple \
+ wood_redmaple \
+ wood_silvermaple \
+ wood_stripedmaple) / 5
wood_poplar 29 lb/ft^3
wood_beech 45 lb/ft^3
# North American Softwoods
wood_jeffreypine 28 lb/ft^3
wood_ocotepine 44 lb/ft^3
wood_ponderosapine 28 lb/ft^3
wood_loblollypine 35 lb/ft^3
wood_longleafpine 41 lb/ft^3
wood_shortleafpine 35 lb/ft^3
wood_slashpine 41 lb/ft^3
wood_yellowpine (wood_loblollypine \
+ wood_longleafpine \
+ wood_shortleafpine \
+ wood_slashpine) / 4
wood_redpine 34 lb/ft^3
wood_easternwhitepine 25 lb/ft^3
wood_westernwhitepine 27 lb/ft^3
wood_whitepine (wood_easternwhitepine + wood_westernwhitepine) / 2
wood_douglasfir 32 lb/ft^3
wood_blackspruce 28 lb/ft^3
wood_engelmannspruce 24 lb/ft^3
wood_redspruce 27 lb/ft^3
wood_sitkaspruce 27 lb/ft^3
wood_whitespruce 27 lb/ft^3
wood_spruce (wood_blackspruce \
+ wood_engelmannspruce \
+ wood_redspruce \
+ wood_sitkaspruce \
+ wood_whitespruce) / 5
# Other woods
wood_basswood 26 lb/ft^3
wood_balsa 9 lb/ft^3
wood_ebony_gaboon 60 lb/ft^3
wood_ebony_macassar 70 lb/ft^3
wood_mahogany 37 lb/ft^3 # True (Honduran) mahogany,
# Swietenia macrophylla
wood_teak 41 lb/ft^3
wood_rosewood_brazilian 52 lb/ft^3
wood_rosewood_honduran 64 lb/ft^3
wood_rosewood_indian 52 lb/ft^3
wood_cocobolo 69 lb/ft^3
wood_bubinga 56 lb/ft^3
wood_zebrawood 50 lb/ft^3
wood_koa 38 lb/ft^3
wood_snakewood 75.7 lb/ft^3
wood_lignumvitae 78.5 lb/ft^3
wood_blackwood 79.3 lb/ft^3
wood_blackironwood 84.5 lb/ft^3 # Krugiodendron ferreum, listed
# in database as the heaviest wood
#
# Modulus of elasticity of selected woods.
# Data from The Wood Database https://www.wood-database.com
#
# North American Hardwoods
wood_mod_beech 1.720e6 lbf/in^2
wood_mod_birchyellow 2.010e6 lbf/in^2
wood_mod_birch wood_mod_birchyellow
wood_mod_cherry 1.490e6 lbf/in^2
wood_mod_hardmaple 1.830e6 lbf/in^2
wood_mod_bigleafmaple 1.450e6 lbf/in^2
wood_mod_boxeldermaple 1.050e6 lbf/in^2
wood_mod_redmaple 1.640e6 lbf/in^2
wood_mod_silvermaple 1.140e6 lbf/in^2
wood_mod_softmaple (wood_mod_bigleafmaple \
+ wood_mod_boxeldermaple \
+ wood_mod_redmaple \
+ wood_mod_silvermaple) / 4
wood_mod_redoak 1.761e6 lbf/in^2
wood_mod_whiteoak 1.762e6 lbf/in^2
wood_mod_poplar 1.580e6 lbf/in^2
wood_mod_blackwalnut 1.680e6 lbf/in^2
wood_mod_walnut wood_mod_blackwalnut
# North American Softwoods
wood_mod_jeffreypine 1.240e6 lbf/in^2
wood_mod_ocotepine 2.209e6 lbf/in^2
wood_mod_ponderosapine 1.290e6 lbf/in^2
wood_mod_loblollypine 1.790e6 lbf/in^2
wood_mod_longleafpine 1.980e6 lbf/in^2
wood_mod_shortleafpine 1.750e6 lbf/in^2
wood_mod_slashpine 1.980e6 lbf/in^2
wood_mod_yellowpine (wood_mod_loblollypine \
+ wood_mod_longleafpine \
+ wood_mod_shortleafpine \
+ wood_mod_slashpine) / 4
wood_mod_redpine 1.630e6 lbf/in^2
wood_mod_easternwhitepine 1.240e6 lbf/in^2
wood_mod_westernwhitepine 1.460e6 lbf/in^2
wood_mod_whitepine (wood_mod_easternwhitepine + \
wood_mod_westernwhitepine) / 2
wood_mod_douglasfir 1.765e6 lbf/in^2
wood_mod_blackspruce 1.523e6 lbf/in^2
wood_mod_englemannspruce 1.369e6 lbf/in^2
wood_mod_redspruce 1.560e6 lbf/in^2
wood_mod_sitkaspruce 1.600e6 lbf/in^2
wood_mod_whitespruce 1.315e6 lbf/in^2
wood_mod_spruce (wood_mod_blackspruce \
+ wood_mod_englemannspruce \
+ wood_mod_redspruce + wood_mod_sitkaspruce \
+ wood_mod_whitespruce) / 5
# Other woods
wood_mod_balsa 0.538e6 lbf/in^2
wood_mod_basswood 1.460e6 lbf/in^2
wood_mod_blackwood 2.603e6 lbf/in^2 # African, Dalbergia melanoxylon
wood_mod_bubinga 2.670e6 lbf/in^2
wood_mod_cocobolo 2.712e6 lbf/in^2
wood_mod_ebony_gaboon 2.449e6 lbf/in^2
wood_mod_ebony_macassar 2.515e6 lbf/in^2
wood_mod_blackironwood 2.966e6 lbf/in^2 # Krugiodendron ferreum
wood_mod_koa 1.503e6 lbf/in^2
wood_mod_lignumvitae 2.043e6 lbf/in^2
wood_mod_mahogany 1.458e6 lbf/in^2 # True (Honduran) mahogany,
# Swietenia macrophylla
wood_mod_rosewood_brazilian 2.020e6 lbf/in^2
wood_mod_rosewood_honduran 3.190e6 lbf/in^2
wood_mod_rosewood_indian 1.668e6 lbf/in^2
wood_mod_snakewood 3.364e6 lbf/in^2
wood_mod_teak 1.781e6 lbf/in^2
wood_mod_zebrawood 2.374e6 lbf/in^2
#
# Area of countries and other regions. This is the "total area" which
# includes land and water areas within international boundaries and
# coastlines. Data from January, 2019.
#
# except as noted, sources are
# https://en.wikipedia.org/wiki/List_of_countries_and_dependencies_by_area
# US Central Intelligence Agency: The World Factbook
# https://www.cia.gov/the-world-factbook/
area_russia 17098246 km^2
area_antarctica 14000000 km^2
# area_canada is covered below as sum of province and territory areas
area_china 9596961 km^2
# area_unitedstates is covered below as sum of state areas
# includes only the 50 states and District of Columbia
area_us area_unitedstates
area_brazil 8515767 km^2
area_australia 7692024 km^2
# area_europeanunion is covered below as sum of member areas
area_india 3287263 km^2
area_argentina 2780400 km^2
area_kazakhstan 2724900 km^2
area_algeria 2381741 km^2
area_drcongo 2344858 km^2
area_greenland 2166086 km^2
area_saudiarabia 2149690 km^2
area_mexico 1964375 km^2
area_indonesia 1910931 km^2
area_sudan 1861484 km^2
area_libya 1759540 km^2
area_iran 1648195 km^2
area_mongolia 1564110 km^2
area_peru 1285216 km^2
area_chad 1284000 km^2
area_niger 1267000 km^2
area_angola 1246700 km^2
area_mali 1240192 km^2
area_southafrica 1221037 km^2
area_colombia 1141748 km^2
area_ethiopia 1104300 km^2
area_bolivia 1098581 km^2
area_mauritania 1030700 km^2
area_egypt 1002450 km^2
area_tanzania 945087 km^2
area_nigeria 923768 km^2
area_venezuela 916445 km^2
area_pakistan 881912 km^2
area_namibia 825615 km^2
area_mozambique 801590 km^2
area_turkey 783562 km^2
area_chile 756102 km^2
area_zambia 752612 km^2
area_myanmar 676578 km^2
area_burma area_myanmar
area_afghanistan 652230 km^2
area_southsudan 644329 km^2
area_france 640679 km^2
area_somalia 637657 km^2
area_centralafrica 622984 km^2
area_ukraine 603500 km^2
area_crimea 27000 km^2 # occupied by Russia; included in
# (Encyclopedia Britannica)
area_madagascar 587041 km^2
area_botswana 581730 km^2
area_kenya 580367 km^2
area_yemen 527968 km^2
area_thailand 513120 km^2
area_spain 505992 km^2
area_turkmenistan 488100 km^2
area_cameroon 475422 km^2
area_papuanewguinea 462840 km^2
area_sweden 450295 km^2
area_uzbekistan 447400 km^2
area_morocco 446550 km^2
area_iraq 438317 km^2
area_paraguay 406752 km^2
area_zimbabwe 390757 km^2
area_japan 377973 km^2
area_germany 357114 km^2
area_congorepublic 342000 km^2
area_finland 338424 km^2
area_vietnam 331212 km^2
area_malaysia 330803 km^2
area_norway 323802 km^2
area_ivorycoast 322463 km^2
area_poland 312696 km^2
area_oman 309500 km^2
area_italy 301339 km^2
area_philippines 300000 km^2
area_ecuador 276841 km^2
area_burkinafaso 274222 km^2
area_newzealand 270467 km^2
area_gabon 267668 km^2
area_westernsahara 266000 km^2
area_guinea 245857 km^2
# area_unitedkingdom is covered below
area_uganda 241550 km^2
area_ghana 238533 km^2
area_romania 238397 km^2
area_laos 236800 km^2
area_guyana 214969 km^2
area_belarus 207600 km^2
area_kyrgyzstan 199951 km^2
area_senegal 196722 km^2
area_syria 185180 km^2
area_golanheights 1150 km^2 # occupied by Israel; included in
# Syria (Encyclopedia Britannica)
area_cambodia 181035 km^2
area_uruguay 176215 km^2
area_somaliland 176120 km^2
area_suriname 163820 km^2
area_tunisia 163610 km^2
area_bangladesh 147570 km^2
area_nepal 147181 km^2
area_tajikistan 143100 km^2
area_greece 131990 km^2
area_nicaragua 130373 km^2
area_northkorea 120540 km^2
area_malawi 118484 km^2
area_eritrea 117600 km^2
area_benin 114763 km^2
area_honduras 112492 km^2
area_liberia 111369 km^2
area_bulgaria 110879 km^2
area_cuba 109884 km^2
area_guatemala 108889 km^2
area_iceland 103000 km^2
area_southkorea 100210 km^2
area_hungary 93028 km^2
area_portugal 92090 km^2
area_jordan 89342 km^2
area_serbia 88361 km^2
area_azerbaijan 86600 km^2
area_austria 83871 km^2
area_uae 83600 km^2
area_czechia 78865 km^2
area_czechrepublic area_czechia
area_panama 75417 km^2
area_sierraleone 71740 km^2
area_ireland 70273 km^2
area_georgia 69700 km^2
area_srilanka 65610 km^2
area_lithuania 65300 km^2
area_latvia 64559 km^2
area_togo 56785 km^2
area_croatia 56594 km^2
area_bosnia 51209 km^2
area_costarica 51100 km^2
area_slovakia 49037 km^2
area_dominicanrepublic 48671 km^2
area_estonia 45227 km^2
area_denmark 43094 km^2
area_netherlands 41850 km^2
area_switzerland 41284 km^2
area_bhutan 38394 km^2
area_taiwan 36193 km^2
area_guineabissau 36125 km^2
area_moldova 33846 km^2
area_belgium 30528 km^2
area_lesotho 30355 km^2
area_armenia 29743 km^2
area_solomonislands 28896 km^2
area_albania 28748 km^2
area_equitorialguinea 28051 km^2
area_burundi 27834 km^2
area_haiti 27750 km^2
area_rwanda 26338 km^2
area_northmacedonia 25713 km^2
area_djibouti 23200 km^2
area_belize 22966 km^2
area_elsalvador 21041 km^2
area_israel 20770 km^2
area_slovenia 20273 km^2
area_fiji 18272 km^2
area_kuwait 17818 km^2
area_eswatini 17364 km^2
area_easttimor 14919 km^2
area_bahamas 13943 km^2
area_montenegro 13812 km^2
area_vanatu 12189 km^2
area_qatar 11586 km^2
area_gambia 11295 km^2
area_jamaica 10991 km^2
area_kosovo 10887 km^2
area_lebanon 10452 km^2
area_cyprus 9251 km^2
area_puertorico 9104 km^2 # United States territory; not included
# in United States area
area_westbank 5860 km^2 # (CIA World Factbook)
area_hongkong 2755 km^2
area_luxembourg 2586 km^2
area_singapore 716 km^2
area_gazastrip 360 km^2 # (CIA World Factbook)
area_malta 316 km^2 # smallest EU country
area_liechtenstein 160 km^2
area_monaco 2.02 km^2
area_vaticancity 0.44 km^2
# Members as of 1 Feb 2020
area_europeanunion area_austria + area_belgium + area_bulgaria \
+ area_croatia + area_cyprus + area_czechia + area_denmark \
+ area_estonia + area_finland + area_france + area_germany \
+ area_greece + area_hungary + area_ireland + area_italy \
+ area_latvia + area_lithuania + area_luxembourg \
+ area_malta + area_netherlands + area_poland \
+ area_portugal + area_romania + area_slovakia \
+ area_slovenia + area_spain + area_sweden
area_eu area_europeanunion
#
# Areas of the individual US states
#
# https://en.wikipedia.org/wiki/List_of_U.S._states_and_territories_by_area
#
# United States Summary: 2010, Population and Housing Unit Counts, Table 18, p. 41
# Issued September 2012
area_alaska 1723336.8 km^2
area_texas 695661.6 km^2
area_california 423967.4 km^2
area_montana 380831.1 km^2
area_newmexico 314917.4 km^2
area_arizona 295233.5 km^2
area_nevada 286379.7 km^2
area_colorado 269601.4 km^2
area_oregon 254799.2 km^2
area_wyoming 253334.5 km^2
area_michigan 250486.8 km^2
area_minnesota 225162.8 km^2
area_utah 219881.9 km^2
area_idaho 216442.6 km^2
area_kansas 213100.0 km^2
area_nebraska 200329.9 km^2
area_southdakota 199728.7 km^2
area_washington 184660.8 km^2
area_northdakota 183107.8 km^2
area_oklahoma 181037.2 km^2
area_missouri 180540.3 km^2
area_florida 170311.7 km^2
area_wisconsin 169634.8 km^2
area_georgia_us 153910.4 km^2
area_illinois 149995.4 km^2
area_iowa 145745.9 km^2
area_newyork 141296.7 km^2
area_northcarolina 139391.0 km^2
area_arkansas 137731.8 km^2
area_alabama 135767.4 km^2
area_louisiana 135658.7 km^2
area_mississippi 125437.7 km^2
area_pennsylvania 119280.2 km^2
area_ohio 116097.7 km^2
area_virginia 110786.6 km^2
area_tennessee 109153.1 km^2
area_kentucky 104655.7 km^2
area_indiana 94326.2 km^2
area_maine 91633.1 km^2
area_southcarolina 82932.7 km^2
area_westvirginia 62755.5 km^2
area_maryland 32131.2 km^2
area_hawaii 28313.0 km^2
area_massachusetts 27335.7 km^2
area_vermont 24906.3 km^2
area_newhampshire 24214.2 km^2
area_newjersey 22591.4 km^2
area_connecticut 14357.4 km^2
area_delaware 6445.8 km^2
area_rhodeisland 4001.2 km^2
area_districtofcolumbia 177.0 km^2
area_unitedstates area_alabama + area_alaska + area_arizona \
+ area_arkansas + area_california + area_colorado \
+ area_connecticut + area_delaware \
+ area_districtofcolumbia + area_florida \
+ area_georgia_us + area_hawaii + area_idaho \
+ area_illinois + area_indiana + area_iowa \
+ area_kansas + area_kentucky + area_louisiana \
+ area_maine + area_maryland + area_massachusetts \
+ area_michigan + area_minnesota + area_mississippi \
+ area_missouri + area_montana + area_nebraska \
+ area_nevada + area_newhampshire + area_newjersey \
+ area_newmexico + area_newyork + area_northcarolina \
+ area_northdakota + area_ohio + area_oklahoma \
+ area_oregon + area_pennsylvania + area_rhodeisland \
+ area_southcarolina + area_southdakota \
+ area_tennessee + area_texas + area_utah \
+ area_vermont + area_virginia + area_washington \
+ area_westvirginia + area_wisconsin + area_wyoming
# Total area of Canadian province and territories
#
# Statistics Canada, "Land and freshwater area, by province and territory",
# 2016-10-07:
#
# https://www150.statcan.gc.ca/n1/pub/11-402-x/2012000/chap/geo/tbl/tbl06-eng.htm
area_ontario 1076395 km^2 # confederated 1867-Jul-01
area_quebec 1542056 km^2 # confederated 1867-Jul-01
area_novascotia 55284 km^2 # confederated 1867-Jul-01
area_newbrunswick 72908 km^2 # confederated 1867-Jul-01
area_canada_original area_ontario + area_quebec + area_novascotia \
+ area_newbrunswick
area_manitoba 647797 km^2 # confederated 1870-Jul-15
area_britishcolumbia 944735 km^2 # confederated 1871-Jul-20
area_princeedwardisland 5660 km^2 # confederated 1873-Jul-01
area_canada_additional area_manitoba + area_britishcolumbia \
+ area_princeedwardisland
area_alberta 661848 km^2 # confederated 1905-Sep-01
area_saskatchewan 651036 km^2 # confederated 1905-Sep-01
area_newfoundlandandlabrador 405212 km^2 # confederated 1949-Mar-31
area_canada_recent area_alberta + area_saskatchewan \
+ area_newfoundlandandlabrador
area_canada_provinces area_canada_original + area_canada_additional \
+ area_canada_recent
area_northwestterritories 1346106 km^2 # NT confederated 1870-Jul-15
area_yukon 482443 km^2 # YT confederated 1898-Jun-13
area_nunavut 2093190 km^2 # NU confederated 1999-Apr-01
area_canada_territories area_northwestterritories + area_yukon \
+ area_nunavut
area_canada area_canada_provinces + area_canada_territories
# area-uk-countries.units - UK country (/province) total areas
# https://en.wikipedia.org/wiki/Countries_of_the_United_Kingdom#Statistics
# GB is official UK country code for some purposes but internally is a Kingdom
#
# areas from A Beginners Guide to UK Geography 2019 v1.0, Office for National Statistics
# England: country; 0927-Jul-12 united; 1603-Mar-24 union of crowns
area_england 132947.76 km^2
#
# Wales: 1282 conquered; 1535 union; principality until 2011
area_wales 21224.48 km^2
#
# England and Wales: nation; 1535 union
area_englandwales area_england + area_wales
#
# Scotland: country; ~900 united; 1603-Mar-24 union of crowns
area_scotland 80226.36 km^2
#
# Great Britain: kingdom; excludes NI;
# 1707 Treaty and Acts of Union: union of parliaments
area_greatbritain area_england + area_wales + area_scotland
area_gb area_greatbritain
#
# Northern Ireland: province; Ireland: 1177 Henry II lordship;
# 1542 Henry VIII kingdom; 1652 Cromwell commonwealth;
# 1691 William III kingdom; 1800 Acts of Union: UK of GB & Ireland;
# 1921 Irish Free State independent of UK
area_northernireland 14133.38 km^2
#
# United Kingdom of GB & NI: 1800 Acts of Union: UK of GB & Ireland;
# 1921 Irish Free State independent of UK
area_unitedkingdom area_greatbritain + area_northernireland
area_uk area_unitedkingdom
#
# Units derived from imperial system
#
ouncedal oz ft / s^2 # force which accelerates an ounce
# at 1 ft/s^2
poundal lb ft / s^2 # same thing for a pound
tondal longton ft / s^2 # and for a ton
pdl poundal
osi ounce force / inch^2 # used in aviation
psi pound force / inch^2
psia psi # absolute pressure
# Note that gauge pressure can be given
# using the gaugepressure() and
# psig() nonlinear unit definitions
tsi ton force / inch^2
reyn psi sec
slug lbf s^2 / ft
slugf slug force
slinch lbf s^2 / inch # Mass unit derived from inch second
slinchf slinch force # pound-force system. Used in space
# applications where in/sec^2 was a
# natural acceleration measure.
geepound slug
lbf lb force
tonf ton force
lbm lb
kip 1000 lbf # from kilopound
ksi kip / in^2
mil 0.001 inch
thou 0.001 inch
tenth 0.0001 inch # one tenth of one thousandth of an inch
millionth 1e-6 inch # one millionth of an inch
circularinch 1|4 pi in^2 # area of a one-inch diameter circle
circleinch circularinch # A circle with diameter d inches has
# an area of d^2 circularinches
cylinderinch circleinch inch # Cylinder h inch tall, d inches diameter
# has volume d^2 h cylinder inches
circularmil 1|4 pi mil^2 # area of one-mil diameter circle
cmil circularmil
cental 100 pound
centner cental
# Shotgun gauge measures the inside diameter of the barrel by counting
# the number of spherical lead balls you can make to fit that barrel
# using a pound of lead. Equivalently, this means that an n gauge gun
# has a bore diameter that fits a ball of lead that weighs 1|n pounds
shotgungauge(ga) units=[1;m] domain=(0,] range=(0,] \
2 ~spherevol(1 pound / ga leaddensity) ; \
1 pound / leaddensity spherevol(shotgungauge/2)
shotgunga() shotgungauge
caliber 0.01 inch # for measuring bullets
duty ft lbf
celo ft / s^2
jerk ft / s^3
australiapoint 0.01 inch # The "point" is used to measure rainfall
# in Australia
sabin ft^2 # Measure of sound absorption equal to the
# absorbing power of one square foot of
# a perfectly absorbing material. The
# sound absorptivity of an object is the
# area times a dimensionless
# absorptivity coefficient.
standardgauge 4 ft + 8.5 in # Standard width between railroad track
flag 5 ft^2 # Construction term referring to sidewalk.
rollwallpaper 30 ft^2 # Area of roll of wall paper
fillpower in^3 / ounce # Density of down at standard pressure.
# The best down has 750-800 fillpower.
pinlength 1|16 inch # A #17 pin is 17/16 in long in the USA.
buttonline 1|40 inch # The line was used in 19th century USA
# to measure width of buttons.
beespace 1|4 inch # Bees will fill any space that is smaller
# than the bee space and leave open
# spaces that are larger. The size of
# the space varies with species.
diamond 8|5 ft # Marking on US tape measures that is
# useful to carpenters who wish to place
# five studs in an 8 ft distance. Note
# that the numbers appear in red every
# 16 inches as well, giving six
# divisions in 8 feet.
retmaunit 1.75 in # Height of rack mountable equipment.
U retmaunit # Equipment should be 1|32 inch narrower
RU U # than its U measurement indicates to
# allow for clearance, so 4U=(6+31|32)in
# RETMA stands for the former name of
# the standardizing organization, Radio
# Electronics Television Manufacturers
# Association. This organization is now
# called the Electronic Industries
# Alliance (EIA) and the rack standard
# is specified in EIA RS-310-D.
count per pound # For measuring the size of shrimp
flightlevel 100 ft # Flight levels are used to ensure safe
FL flightlevel # vertical separation between aircraft
# despite variations in local air
# pressure. Flight levels define
# altitudes based on a standard air
# pressure so that altimeter calibration
# is not needed. This means that
# aircraft at separated flight levels
# are guaranteed to be separated.
# Hence the definition of 100 feet is
# a nominal, not true, measure.
# Customarily written with no space in
# the form FL290, which will not work in
# units. But note "FL 290" will work.
#
# Other units of work, energy, power, etc
#
# Calorie: approximate energy to raise a gram of water one degree celsius
calorie cal_th # Default is the thermochemical calorie
cal calorie
calorie_th 4.184 J # Thermochemical calorie, defined in 1930
thermcalorie calorie_th # by Frederick Rossini as 4.1833 J to
cal_th calorie_th # avoid difficulties associated with the
# uncertainty in the heat capacity of
# water. In 1948 the value of the joule
# was changed, so the thermochemical
# calorie was redefined to 4.184 J.
# This kept the energy measured by this
# unit the same.
calorie_IT 4.1868 J # International (Steam) Table calorie,
cal_IT calorie_IT # defined in 1929 as watt-hour/860 or
# equivalently 180|43 joules. At this
# time the international joule had a
# different value than the modern joule,
# and the values were different in the
# USA and in Europe. In 1956 at the
# Fifth International Conference on
# Properties of Steam the exact
# definition given here was adopted.
calorie_15 4.18580 J # Energy to go from 14.5 to 15.5 degC
cal_15 calorie_15
calorie_fifteen cal_15
calorie_20 4.18190 J # Energy to go from 19.5 to 20.5 degC
cal_20 calorie_20
calorie_twenty calorie_20
calorie_4 4.204 J # Energy to go from 3.5 to 4.5 degC
cal_4 calorie_4
calorie_four calorie_4
cal_mean 4.19002 J # 1|100 energy to go from 0 to 100 degC
Calorie kilocalorie # the food Calorie
thermie 1e6 cal_15 # Heat required to raise the
# temperature of a tonne of
# water from 14.5 to 15.5 degC.
# btu definitions: energy to raise a pound of water 1 degF
btu btu_IT # International Table BTU is the default
britishthermalunit btu
btu_IT cal_IT lb degF / gram K
btu_th cal_th lb degF / gram K
btu_mean cal_mean lb degF / gram K
btu_15 cal_15 lb degF / gram K
btu_ISO 1055.06 J # Exact, rounded ISO definition based
# on the IT calorie
quad quadrillion btu
ECtherm 1e5 btu_ISO # Exact definition
UStherm 1.054804e8 J # Exact definition
therm UStherm
# Water latent heat from [23]
water_fusion_heat 6.01 kJ/mol / (18.015 g/mol) # At 0 deg C
water_vaporization_heat 2256.4 J/g # At saturation, 100 deg C, 101.42 kPa
# Specific heat capacities of various substances
#
# SPECFIC_HEAT ENERGY / MASS / TEMPERATURE_DIFFERENCE
# SPECFIC_HEAT_CAPACITY ENERGY / MASS / TEMPERATURE_DIFFERENCE
specificheat_water calorie / g K
water_specificheat specificheat_water
# Values from www.engineeringtoolbox.com/specific-heat-metals-d_152.html
specificheat_aluminum 0.91 J/g K
specificheat_antimony 0.21 J/g K
specificheat_barium 0.20 J/g K
specificheat_beryllium 1.83 J/g K
specificheat_bismuth 0.13 J/g K
specificheat_cadmium 0.23 J/g K
specificheat_cesium 0.24 J/g K
specificheat_chromium 0.46 J/g K
specificheat_cobalt 0.42 J/g K
specificheat_copper 0.39 J/g K
specificheat_gallium 0.37 J/g K
specificheat_germanium 0.32 J/g K
specificheat_gold 0.13 J/g K
specificheat_hafnium 0.14 J/g K
specificheat_indium 0.24 J/g K
specificheat_iridium 0.13 J/g K
specificheat_iron 0.45 J/g K
specificheat_lanthanum 0.195 J/g K
specificheat_lead 0.13 J/g K
specificheat_lithium 3.57 J/g K
specificheat_lutetium 0.15 J/g K
specificheat_magnesium 1.05 J/g K
specificheat_manganese 0.48 J/g K
specificheat_mercury 0.14 J/g K
specificheat_molybdenum 0.25 J/g K
specificheat_nickel 0.44 J/g K
specificheat_osmium 0.13 J/g K
specificheat_palladium 0.24 J/g K
specificheat_platinum 0.13 J/g K
specificheat_plutonum 0.13 J/g K
specificheat_potassium 0.75 J/g K
specificheat_rhenium 0.14 J/g K
specificheat_rhodium 0.24 J/g K
specificheat_rubidium 0.36 J/g K
specificheat_ruthenium 0.24 J/g K
specificheat_scandium 0.57 J/g K
specificheat_selenium 0.32 J/g K
specificheat_silicon 0.71 J/g K
specificheat_silver 0.23 J/g K
specificheat_sodium 1.21 J/g K
specificheat_strontium 0.30 J/g K
specificheat_tantalum 0.14 J/g K
specificheat_thallium 0.13 J/g K
specificheat_thorium 0.13 J/g K
specificheat_tin 0.21 J/g K
specificheat_titanium 0.54 J/g K
specificheat_tungsten 0.13 J/g K
specificheat_uranium 0.12 J/g K
specificheat_vanadium 0.39 J/g K
specificheat_yttrium 0.30 J/g K
specificheat_zinc 0.39 J/g K
specificheat_zirconium 0.27 J/g K
specificheat_ethanol 2.3 J/g K
specificheat_ammonia 4.6 J/g K
specificheat_freon 0.91 J/g K # R-12 at 0 degrees Fahrenheit
specificheat_gasoline 2.22 J/g K
specificheat_iodine 2.15 J/g K
specificheat_oliveoil 1.97 J/g K
# en.wikipedia.org/wiki/Heat_capacity#Table_of_specific_heat_capacities
specificheat_hydrogen 14.3 J/g K
specificheat_helium 5.1932 J/g K
specificheat_argon 0.5203 J/g K
specificheat_tissue 3.5 J/g K
specificheat_diamond 0.5091 J/g K
specificheat_granite 0.79 J/g K
specificheat_graphite 0.71 J/g K
specificheat_ice 2.11 J/g K
specificheat_asphalt 0.92 J/g K
specificheat_brick 0.84 J/g K
specificheat_concrete 0.88 J/g K
specificheat_glass_silica 0.84 J/g K
specificheat_glass_flint 0.503 J/g K
specificheat_glass_pyrex 0.753 J/g K
specificheat_gypsum 1.09 J/g K
specificheat_marble 0.88 J/g K
specificheat_sand 0.835 J/g K
specificheat_soil 0.835 J/g K
specificheat_wood 1.7 J/g K
specificheat_sucrose 1.244 J/g K #www.sugartech.co.za/heatcapacity/index.php
# Energy densities of various fuels
#
# Most of these fuels have varying compositions or qualities and hence their
# actual energy densities vary. These numbers are hence only approximate.
#
# E1. http://www.aps.org/policy/reports/popa-reports/energy/units.cfm
# E2. https://web.archive.org/web/20100825042309/http://www.ior.com.au/ecflist.html
tonoil 1e10 cal_IT # Ton oil equivalent. A conventional
# value for the energy released by
toe tonoil # burning one metric ton of oil. [18,E1]
# Note that energy per mass of petroleum
# products is fairly constant.
# Variations in volumetric energy
# density result from variations in the
# density (kg/m^3) of different fuels.
# This definition is given by the
# IEA/OECD.
toncoal 7e9 cal_IT # Energy in metric ton coal from [18].
# This is a nominal value which
# is close to the heat content
# of coal used in the 1950's
barreloil 5.8 Mbtu # Conventional value for barrel of crude
# oil [E1]. Actual range is 5.6 - 6.3.
naturalgas_HHV 1027 btu/ft3 # Energy content of natural gas. HHV
naturalgas_LHV 930 btu/ft3 # is for Higher Heating Value and
naturalgas naturalgas_HHV # includes energy from condensation
# combustion products. LHV is for Lower
# Heating Value and excludes these.
# American publications typically report
# HHV whereas European ones report LHV.
charcoal 30 GJ/tonne
woodenergy_dry 20 GJ/tonne # HHV, a cord weights about a tonne
woodenergy_airdry 15 GJ/tonne # 20% moisture content
coal_bituminous 27 GJ / tonne
coal_lignite 15 GJ / tonne
coal_US 22 GJ / uston # Average for US coal (short ton), 1995
ethanol_HHV 84000 btu/usgallon
ethanol_LHV 75700 btu/usgallon
diesel 130500 btu/usgallon
gasoline_LHV 115000 btu/usgallon
gasoline_HHV 125000 btu/usgallon
gasoline gasoline_HHV
heating 37.3 MJ/liter
fueloil 39.7 MJ/liter # low sulphur
propane 93.3 MJ/m^3
butane 124 MJ/m^3
# The US EPA defines a "miles per gallon equivalent" for alternative
# energy vehicles:
mpg_e miles / gallon gasoline_LHV
MPGe mpg_e
# These values give total energy from uranium fission. Actual efficiency
# of nuclear power plants is around 30%-40%. Note also that some reactors
# use enriched uranium around 3% U-235. Uranium during processing or use
# may be in a compound of uranium oxide or uranium hexafluoride, in which
# case the energy density would be lower depending on how much uranium is
# in the compound.
uranium_pure 200 MeV avogadro / (235.0439299 g/mol) # Pure U-235
uranium_natural 0.7% uranium_pure # Natural uranium: 0.7% U-235
# Celsius heat unit: energy to raise a pound of water 1 degC
celsiusheatunit cal lb degC / gram K
chu celsiusheatunit
# "Apparent" average power in an AC circuit, the product of rms voltage
# and rms current, equal to the true power in watts when voltage and
# current are in phase. In a DC circuit, always equal to the true power.
VA volt ampere
kWh kilowatt hour
# The horsepower is supposedly the power of one horse pulling. Obviously
# different people had different horses.
horsepower 550 foot pound force / sec # Invented by James Watt
mechanicalhorsepower horsepower
hp horsepower
metrichorsepower 75 kilogram force meter / sec # PS=Pferdestaerke in
electrichorsepower 746 W # Germany
boilerhorsepower 9809.50 W
waterhorsepower 746.043 W
brhorsepower horsepower # Value corrected Dec, 2019. Was 745.7 W.
donkeypower 250 W
chevalvapeur metrichorsepower
#
# Heat Transfer
#
# Thermal conductivity, K, measures the rate of heat transfer across
# a material. The heat transferred is
# Q = K dT A t / L
# where dT is the temperature difference across the material, A is the
# cross sectional area, t is the time, and L is the length (thickness).
# Thermal conductivity is a material property.
THERMAL_CONDUCTIVITY POWER / AREA (TEMPERATURE_DIFFERENCE/LENGTH)
THERMAL_RESISTIVITY 1/THERMAL_CONDUCTIVITY
# Thermal conductance is the rate at which heat flows across a given
# object, so the area and thickness have been fixed. It depends on
# the size of the object and is hence not a material property.
THERMAL_CONDUCTANCE POWER / TEMPERATURE_DIFFERENCE
THERMAL_RESISTANCE 1/THERMAL_CONDUCTANCE
# Thermal admittance is the rate of heat flow per area across an
# object whose thickness has been fixed. Its reciprocal, thermal
# insulation, is used to for measuring the heat transfer per area
# of sheets of insulation or cloth that are of specified thickness.
THERMAL_ADMITTANCE THERMAL_CONDUCTIVITY / LENGTH
THERMAL_INSULANCE THERMAL_RESISTIVITY LENGTH
THERMAL_INSULATION THERMAL_RESISTIVITY LENGTH
Rvalue degF ft^2 hr / btu
Uvalue 1/Rvalue
europeanUvalue watt / m^2 K
RSI degC m^2 / W
clo 0.155 degC m^2 / W # Supposed to be the insulance
# required to keep a resting person
# comfortable indoors. The value
# given is from NIST and the CRC,
# but [5] gives a slightly different
# value of 0.875 ft^2 degF hr / btu.
tog 0.1 degC m^2 / W # Also used for clothing.
# Thermal Conductivity of a few materials
diamond_natural_thermal_conductivity 2200 W / m K
diamond_synthetic_thermal_conductivity 3320 W / m K # 99% pure C12
silver_thermal_conductivity 406 W / m K
aluminum_thermal_conductivity 205 W / m K
copper_thermal_conductivity 385 W / m K
gold_thermal_conductivity 314 W / m K
iron_thermal_conductivity 79.5 W / m K
stainless_304_thermal_conductivity 15.5 W / m K # average value
# The bel was defined by engineers of Bell Laboratories to describe the
# reduction in audio level over a length of one mile. It was originally
# called the transmission unit (TU) but was renamed around 1923 to honor
# Alexander Graham Bell. The bel proved inconveniently large so the decibel
# has become more common. The decibel is dimensionless since it reports a
# ratio, but it is used in various contexts to report a signal's power
# relative to some reference level.
bel(x) units=[1;1] range=(0,) 10^(x); log(bel) # Basic bel definition
decibel(x) units=[1;1] range=(0,) 10^(x/10); 10 log(decibel) # Basic decibel
dB() decibel # Abbreviation
dBW(x) units=[1;W] range=(0,) dB(x) W ; ~dB(dBW/W) # Reference = 1 W
dBk(x) units=[1;W] range=(0,) dB(x) kW ; ~dB(dBk/kW) # Reference = 1 kW
dBf(x) units=[1;W] range=(0,) dB(x) fW ; ~dB(dBf/fW) # Reference = 1 fW
dBm(x) units=[1;W] range=(0,) dB(x) mW ; ~dB(dBm/mW) # Reference = 1 mW
dBmW(x) units=[1;W] range=(0,) dBm(x) ; ~dBm(dBmW) # Reference = 1 mW
dBJ(x) units=[1;J] range=(0,) dB(x) J; ~dB(dBJ/J) # Energy relative
# to 1 joule. Used for power spectral
# density since W/Hz = J
# When used to measure amplitude, voltage, or current the signal is squared
# because power is proportional to the square of these measures. The root
# mean square (RMS) voltage is typically used with these units.
dB_amplitude(x) units=[1;1] dB(0.5 x) ; ~dB(dB_amplitude^2)
dBV(x) units=[1;V] range=(0,) dB(0.5 x) V;~dB(dBV^2 / V^2) # Reference = 1 V
dBmV(x) units=[1;V] range=(0,) dB(0.5 x) mV;~dB(dBmV^2/mV^2)# Reference = 1 mV
dBuV(x) units=[1;V] range=(0,) dB(0.5 x) microV ; ~dB(dBuV^2 / microV^2)
# Reference = 1 microvolt
# Here are dB measurements for current. Be aware that dbA is also
# a unit for frequency weighted sound pressure.
dBA(x) units=[1;A] range=(0,) dB(0.5 x) A;~dB(dBA^2 / A^2) # Reference = 1 A
dBmA(x) units=[1;A] range=(0,) dB(0.5 x) mA;~dB(dBmA^2/mA^2)# Reference = 1 mA
dBuA(x) units=[1;A] range=(0,) dB(0.5 x) microA ; ~dB(dBuA^2 / microA^2)
# Reference = 1 microamp
# Referenced to the voltage that causes 1 mW dissipation in a 600 ohm load.
# Originally defined as dBv but changed to prevent confusion with dBV.
# The "u" is for unloaded.
dBu(x) units=[1;V] range=(0,) dB(0.5 x) sqrt(mW 600 ohm) ; \
~dB(dBu^2 / mW 600 ohm)
dBv(x) units=[1;V] range=(0,) dBu(x) ; ~dBu(dBv) # Synonym for dBu
# Measurements for sound in air, referenced to the threshold of human hearing
# Note that sound in other media typically uses 1 micropascal as a reference
# for sound pressure. Units dBA, dBB, dBC, refer to different frequency
# weightings meant to approximate the human ear's response.
# sound pressure level
dBSPL(x) units=[1;Pa] range=(0,) dB(0.5 x) 20 microPa ; \
~dB(dBSPL^2 / (20 microPa)^2)
# sound intensity level
dBSIL(x) units=[1;W/m^2] range=(0,) dB(x) 1e-12 W/m^2; \
~dB(dBSIL / (1e-12 W/m^2))
# sound power level (The W in SWL is for the reference power, 1 W.)
dBSWL(x) units=[1;W] range=(0,) dB(x) 1e-12 W; ~dB(dBSWL/1e-12 W)
# The neper is another similar logarithmic unit. Note that the neper
# is defined based on the ratio of amplitudes rather than the power
# ratio like the decibel. This means that if the data is power, and
# you convert to nepers you should take the square root of the data
# to convert to amplitude. If you want to convert nepers to a power
# measurement you need to square the resulting output.
neper(x) units=[1;1] range=(0,) exp(x); ln(neper)
centineper(x) units=[1;1] range=(0,) exp(x/100); 100 ln(centineper)
Np() neper
cNp() centineper
Np_power(x) units=[1;1] Np(2 x) ; ~Np(Np_power)/2
# Misc other measures
ENTROPY ENERGY / TEMPERATURE
clausius 1e3 cal/K # A unit of physical entropy
langley thermcalorie/cm^2 # Used in radiation theory
poncelet 100 kg force m / s
tonrefrigeration uston 144 btu / lb day # One ton refrigeration is
# the rate of heat extraction required
# turn one ton of water to ice in
# a day. Ice is defined to have a
# latent heat of 144 btu/lb.
tonref tonrefrigeration
refrigeration tonref / ton
frigorie 1000 cal_15 # Used in refrigeration engineering.
airwatt 8.5 (ft^3/min) inH2O # Measure of vacuum power as
# pressure times air flow.
# The unit "tnt" is defined so that you can write "tons tnt". The
# question of which ton, exactly, is intended. The answer is that
# nobody knows:
#
# Quoting the footnote from page 13 of
# The Effects of Nuclear Weapons, 3rd ed.
# https://www.fourmilab.ch/etexts/www/effects/eonw_1.pdf
#
# The majority of the experimental and theoretical values of the
# explosive energy released by TNT range from 900 to 1,100 calories per
# gram. At one time, there was some uncertainty as to whether the term
# "kiloton" of TNT referred to a short kiloton (2*10^6 pounds), a metric
# kiloton (2.205*10^6 pounds), or a long kiloton (2.24*10^6 pounds). In
# order to avoid ambiguity, it was agreed that the term "kiloton" would
# refer to the release of 10^12 calories of explosive energy. This is
# equivalent to 1 short kiloton of TNT if the energy release is 1,102
# calories per gram or to 1 long kiloton if the energy is 984 calories
# per gram of TNT.
#
# It is therefore not well-defined how much energy a "gram of tnt" is,
# though this term does appear in some references.
tnt 1e9 cal_th / ton # Defined exact value
# Nuclear weapon yields
davycrocket 10 ton tnt # lightest US tactical nuclear weapon
hiroshima 15.5 kiloton tnt # Uranium-235 fission bomb
nagasaki 21 kiloton tnt # Plutonium-239 fission bomb
fatman nagasaki
littleboy hiroshima
ivyking 500 kiloton tnt # most powerful fission bomb
castlebravo 15 megaton tnt # most powerful US test
tsarbomba 50 megaton tnt # most powerful test ever: USSR,
# 30 October 1961
b53bomb 9 megaton tnt
# http://rarehistoricalphotos.com/gadget-first-atomic-bomb/
trinity 18 kiloton tnt # July 16, 1945
gadget trinity
#
# Permeability: The permeability or permeance, n, of a substance determines
# how fast vapor flows through the substance. The formula W = n A dP
# holds where W is the rate of flow (in mass/time), n is the permeability,
# A is the area of the flow path, and dP is the vapor pressure difference.
#
perm_0C grain / hr ft^2 inHg
perm_zero perm_0C
perm_0 perm_0C
perm perm_0C
perm_23C grain / hr ft^2 in Hg23C
perm_twentythree perm_23C
#
# Counting measures
#
pair 2
brace 2
nest 3 # often used for items like bowls that
# nest together
hattrick 3 # Used in sports, especially cricket and ice
# hockey to report the number of goals.
dicker 10
dozen 12
bakersdozen 13
score 20
flock 40
timer 40
shock 60
toncount 100 # Used in sports in the UK
longhundred 120 # From a germanic counting system
gross 144
greatgross 12 gross
tithe 1|10 # From Anglo-Saxon word for tenth
# Paper counting measure
shortquire 24
quire 25
shortream 480
ream 500
perfectream 516
bundle 2 reams
bale 5 bundles
#
# Paper measures
#
# USA paper sizes
lettersize 8.5 inch 11 inch
legalsize 8.5 inch 14 inch
ledgersize 11 inch 17 inch
executivesize 7.25 inch 10.5 inch
Apaper 8.5 inch 11 inch
Bpaper 11 inch 17 inch
Cpaper 17 inch 22 inch
Dpaper 22 inch 34 inch
Epaper 34 inch 44 inch
# Correspondence envelope sizes. #10 is the standard business
# envelope in the USA.
envelope6_25size 3.5 inch 6 inch
envelope6_75size 3.625 inch 6.5 inch
envelope7size 3.75 inch 6.75 inch
envelope7_75size 3.875 inch 7.5 inch
envelope8_625size 3.625 inch 8.625 inch
envelope9size 3.875 inch 8.875 inch
envelope10size 4.125 inch 9.5 inch
envelope11size 4.5 inch 10.375 inch
envelope12size 4.75 inch 11 inch
envelope14size 5 inch 11.5 inch
envelope16size 6 inch 12 inch
# Announcement envelope sizes (no relation to metric paper sizes like A4)
envelopeA1size 3.625 inch 5.125 inch # same as 4bar
envelopeA2size 4.375 inch 5.75 inch
envelopeA6size 4.75 inch 6.5 inch
envelopeA7size 5.25 inch 7.25 inch
envelopeA8size 5.5 inch 8.125 inch
envelopeA9size 5.75 inch 8.75 inch
envelopeA10size 6 inch 9.5 inch
# Baronial envelopes
envelope4bar 3.625 inch 5.125 inch # same as A1
envelope5_5bar 4.375 inch 5.75 inch
envelope6bar 4.75 inch 6.5 inch
# Coin envelopes
envelope1baby 2.25 inch 3.5 inch # same as #1 coin
envelope00coin 1.6875 inch 2.75 inch
envelope1coin 2.25 inch 3.5 inch
envelope3coin 2.5 inch 4.25 inch
envelope4coin 3 inch 4.5 inch
envelope4_5coin 3 inch 4.875 inch
envelope5coin 2.875 inch 5.25 inch
envelope5_5coin 3.125 inch 5.5 inch
envelope6coin 3.375 inch 6 inch
envelope7coin 3.5 inch 6.5 inch
# The metric paper sizes are defined so that if a sheet is cut in half
# along the short direction, the result is two sheets which are
# similar to the original sheet. This means that for any metric size,
# the long side is close to sqrt(2) times the length of the short
# side. Each series of sizes is generated by repeated cuts in half,
# with the values rounded down to the nearest millimeter.
A0paper 841 mm 1189 mm # The basic size in the A series
A1paper 594 mm 841 mm # is defined to have an area of
A2paper 420 mm 594 mm # one square meter.
A3paper 297 mm 420 mm
A4paper 210 mm 297 mm
A5paper 148 mm 210 mm
A6paper 105 mm 148 mm
A7paper 74 mm 105 mm
A8paper 52 mm 74 mm
A9paper 37 mm 52 mm
A10paper 26 mm 37 mm
B0paper 1000 mm 1414 mm # The basic B size has an area
B1paper 707 mm 1000 mm # of sqrt(2) square meters.
B2paper 500 mm 707 mm
B3paper 353 mm 500 mm
B4paper 250 mm 353 mm
B5paper 176 mm 250 mm
B6paper 125 mm 176 mm
B7paper 88 mm 125 mm
B8paper 62 mm 88 mm
B9paper 44 mm 62 mm
B10paper 31 mm 44 mm
C0paper 917 mm 1297 mm # The basic C size has an area
C1paper 648 mm 917 mm # of sqrt(sqrt(2)) square meters.
C2paper 458 mm 648 mm
C3paper 324 mm 458 mm # Intended for envelope sizes
C4paper 229 mm 324 mm
C5paper 162 mm 229 mm
C6paper 114 mm 162 mm
C7paper 81 mm 114 mm
C8paper 57 mm 81 mm
C9paper 40 mm 57 mm
C10paper 28 mm 40 mm
# gsm (Grams per Square Meter), a sane, metric paper weight measure
gsm grams / meter^2
# In the USA, a collection of crazy historical paper measures are used. Paper
# is measured as a weight of a ream of that particular type of paper. This is
# sometimes called the "substance" or "basis" (as in "substance 20" paper).
# The standard sheet size or "basis size" varies depending on the type of
# paper. As a result, 20 pound bond paper and 50 pound text paper are actually
# about the same weight. The different sheet sizes were historically the most
# convenient for printing or folding in the different applications. These
# different basis weights are standards maintained by American Society for
# Testing Materials (ASTM) and the American Forest and Paper Association
# (AF&PA).
poundbookpaper lb / 25 inch 38 inch ream
lbbook poundbookpaper
poundtextpaper poundbookpaper
lbtext poundtextpaper
poundoffsetpaper poundbookpaper # For offset printing
lboffset poundoffsetpaper
poundbiblepaper poundbookpaper # Designed to be lightweight, thin,
lbbible poundbiblepaper # strong and opaque.
poundtagpaper lb / 24 inch 36 inch ream
lbtag poundtagpaper
poundbagpaper poundtagpaper
lbbag poundbagpaper
poundnewsprintpaper poundtagpaper
lbnewsprint poundnewsprintpaper
poundposterpaper poundtagpaper
lbposter poundposterpaper
poundtissuepaper poundtagpaper
lbtissue poundtissuepaper
poundwrappingpaper poundtagpaper
lbwrapping poundwrappingpaper
poundwaxingpaper poundtagpaper
lbwaxing poundwaxingpaper
poundglassinepaper poundtagpaper
lbglassine poundglassinepaper
poundcoverpaper lb / 20 inch 26 inch ream
lbcover poundcoverpaper
poundindexpaper lb / 25.5 inch 30.5 inch ream
lbindex poundindexpaper
poundindexbristolpaper poundindexpaper
lbindexbristol poundindexpaper
poundbondpaper lb / 17 inch 22 inch ream # Bond paper is stiff and
lbbond poundbondpaper # durable for repeated
poundwritingpaper poundbondpaper # filing, and it resists
lbwriting poundwritingpaper # ink penetration.
poundledgerpaper poundbondpaper
lbledger poundledgerpaper
poundcopypaper poundbondpaper
lbcopy poundcopypaper
poundblottingpaper lb / 19 inch 24 inch ream
lbblotting poundblottingpaper
poundblankspaper lb / 22 inch 28 inch ream
lbblanks poundblankspaper
poundpostcardpaper lb / 22.5 inch 28.5 inch ream
lbpostcard poundpostcardpaper
poundweddingbristol poundpostcardpaper
lbweddingbristol poundweddingbristol
poundbristolpaper poundweddingbristol
lbbristol poundbristolpaper
poundboxboard lb / 1000 ft^2
lbboxboard poundboxboard
poundpaperboard poundboxboard
lbpaperboard poundpaperboard
# When paper is marked in units of M, it means the weight of 1000 sheets of the
# given size of paper. To convert this to paper weight, divide by the size of
# the paper in question.
paperM lb / 1000
# In addition paper weight is reported in "caliper" which is simply the
# thickness of one sheet, typically in inches. Thickness is also reported in
# "points" where a point is 1|1000 inch. These conversions are supplied to
# convert these units roughly (using an approximate density) into the standard
# paper weight values.
pointthickness 0.001 in
paperdensity 0.8 g/cm^3 # approximate--paper densities vary!
papercaliper in paperdensity
paperpoint pointthickness paperdensity
#
# Printing
#
fournierpoint 0.1648 inch / 12 # First definition of the printers
# point made by Pierre Fournier who
# defined it in 1737 as 1|12 of a
# cicero which was 0.1648 inches.
olddidotpoint 1|72 frenchinch # Francois Ambroise Didot, one of
# a family of printers, changed
# Fournier's definition around 1770
# to fit to the French units then in
# use.
bertholdpoint 1|2660 m # H. Berthold tried to create a
# metric version of the didot point
# in 1878.
INpoint 0.4 mm # This point was created by a
# group directed by Fermin Didot in
# 1881 and is associated with the
# imprimerie nationale. It doesn't
# seem to have been used much.
germandidotpoint 0.376065 mm # Exact definition appears in DIN
# 16507, a German standards document
# of 1954. Adopted more broadly in
# 1966 by ???
metricpoint 3|8 mm # Proposed in 1977 by Eurograf
oldpoint 1|72.27 inch # The American point was invented
printerspoint oldpoint # by Nelson Hawks in 1879 and
texpoint oldpoint # dominates USA publishing.
# It was standardized by the American
# Typefounders Association at the
# value of 0.013837 inches exactly.
# Knuth uses the approximation given
# here (which is very close). The
# comp.fonts FAQ claims that this
# value is supposed to be 1|12 of a
# pica where 83 picas is equal to 35
# cm. But this value differs from
# the standard.
texscaledpoint 1|65536 texpoint # The TeX typesetting system uses
texsp texscaledpoint # this for all computations.
computerpoint 1|72 inch # The American point was rounded
point computerpoint
computerpica 12 computerpoint # to an even 1|72 inch by computer
postscriptpoint computerpoint # people at some point.
pspoint postscriptpoint
twip 1|20 point # TWentieth of an Imperial Point
Q 1|4 mm # Used in Japanese phototypesetting
# Q is for quarter
frenchprinterspoint olddidotpoint
didotpoint germandidotpoint # This seems to be the dominant value
europeanpoint didotpoint # for the point used in Europe
cicero 12 didotpoint
stick 2 inches
# Type sizes
excelsior 3 oldpoint
brilliant 3.5 oldpoint
diamondtype 4 oldpoint
pearl 5 oldpoint
agate 5.5 oldpoint # Originally agate type was 14 lines per
# inch, giving a value of 1|14 in.
ruby agate # British
nonpareil 6 oldpoint
mignonette 6.5 oldpoint
emerald mignonette # British
minion 7 oldpoint
brevier 8 oldpoint
bourgeois 9 oldpoint
longprimer 10 oldpoint
smallpica 11 oldpoint
pica 12 oldpoint
english 14 oldpoint
columbian 16 oldpoint
greatprimer 18 oldpoint
paragon 20 oldpoint
meridian 44 oldpoint
canon 48 oldpoint
# German type sizes
nonplusultra 2 didotpoint
brillant 3 didotpoint
diamant 4 didotpoint
perl 5 didotpoint
nonpareille 6 didotpoint
kolonel 7 didotpoint
petit 8 didotpoint
borgis 9 didotpoint
korpus 10 didotpoint
corpus korpus
garamond korpus
mittel 14 didotpoint
tertia 16 didotpoint
text 18 didotpoint
kleine_kanon 32 didotpoint
kanon 36 didotpoint
grobe_kanon 42 didotpoint
missal 48 didotpoint
kleine_sabon 72 didotpoint
grobe_sabon 84 didotpoint
#
# Information theory units. Note that the name "entropy" is used both
# to measure information and as a physical quantity.
#
INFORMATION bit
nat (1/ln(2)) bits # Entropy measured base e
hartley log2(10) bits # Entropy of a uniformly
ban hartley # distributed random variable
# over 10 symbols.
dit hartley # from Decimal digIT
#
# Computer
#
bps bit/sec # Sometimes the term "baud" is
# incorrectly used to refer to
# bits per second. Baud refers
# to symbols per second. Modern
# modems transmit several bits
# per symbol.
byte 8 bit # Not all machines had 8 bit
B byte # bytes, but these days most of
# them do. But beware: for
# transmission over modems, a
# few extra bits are used so
# there are actually 10 bits per
# byte.
octet 8 bits # The octet is always 8 bits
nybble 4 bits # Half of a byte. Sometimes
# equal to different lengths
# such as 3 bits.
nibble nybble
nyp 2 bits # Donald Knuth asks in an exercise
# for a name for a 2 bit
# quantity and gives the "nyp"
# as a solution due to Gregor
# Purdy. Not in common use.
meg megabyte # Some people consider these
# units along with the kilobyte
gig gigabyte # to be defined according to
# powers of 2 with the kilobyte
# equal to 2^10 bytes, the
# megabyte equal to 2^20 bytes and
# the gigabyte equal to 2^30 bytes
# but these usages are forbidden
# by SI. Binary prefixes have
# been defined by IEC to replace
# the SI prefixes. Use them to
# get the binary units KiB, MiB,
# GiB, etc.
jiffy 0.01 sec # This is defined in the Jargon File
jiffies jiffy # (http://www.jargon.org) as being the
# duration of a clock tick for measuring
# wall-clock time. Supposedly the value
# used to be 1|60 sec or 1|50 sec
# depending on the frequency of AC power,
# but then 1|100 sec became more common.
# On linux systems, this term is used and
# for the Intel based chips, it does have
# the value of .01 sec. The Jargon File
# also lists two other definitions:
# millisecond, and the time taken for
# light to travel one foot.
cdaudiospeed 44.1 kHz 2*16 bits # CD audio data rate at 44.1 kHz with 2
# samples of sixteen bits each.
cdromspeed 75 2048 bytes / sec # For data CDs (mode1) 75 sectors are read
# each second with 2048 bytes per sector.
# Audio CDs do not have sectors, but
# people sometimes divide the bit rate by
# 75 and claim a sector length of 2352.
# Data CDs have a lower rate due to
# increased error correction overhead.
# There is a rarely used mode (mode2) with
# 2336 bytes per sector that has fewer
# error correction bits than mode1.
dvdspeed 1385 kB/s # This is the "1x" speed of a DVD using
# constant linear velocity (CLV) mode.
# Modern DVDs may vary the linear velocity
# as they go from the inside to the
# outside of the disc.
# See http://www.osta.org/technology/dvdqa/dvdqa4.htm
FIT / 1e9 hour # Failures In Time, number of failures per billion hours
#
# The IP address space is divided into subnets. The number of hosts
# in a subnet depends on the length of the subnet prefix. This is
# often written as /N where N is the number of bits in the prefix.
#
# https://en.wikipedia.org/wiki/Subnetwork
#
# These definitions gives the number of hosts for a subnet whose
# prefix has the specified length in bits.
#
ipv4subnetsize(prefix_len) units=[1;1] domain=[0,32] range=[1,4294967296] \
2^(32-prefix_len) ; 32-log2(ipv4subnetsize)
ipv4classA ipv4subnetsize(8)
ipv4classB ipv4subnetsize(16)
ipv4classC ipv4subnetsize(24)
ipv6subnetsize(prefix_len) units=[1;1] domain=[0,128] \
range=[1,340282366920938463463374607431768211456] \
2^(128-prefix_len) ; 128-log2(ipv6subnetsize)
#
# Musical measures. Musical intervals expressed as ratios. Multiply
# two intervals together to get the sum of the interval. The function
# musicalcent can be used to convert ratios to cents.
#
# Perfect intervals
octave 2
majorsecond musicalfifth^2 / octave
majorthird 5|4
minorthird 6|5
musicalfourth 4|3
musicalfifth 3|2
majorsixth musicalfourth majorthird
minorsixth musicalfourth minorthird
majorseventh musicalfifth majorthird
minorseventh musicalfifth minorthird
pythagoreanthird majorsecond musicalfifth^2 / octave
syntoniccomma pythagoreanthird / majorthird
pythagoreancomma musicalfifth^12 / octave^7
# Equal tempered definitions
semitone octave^(1|12)
musicalcent(x) units=[1;1] range=(0,) semitone^(x/100) ; \
100 log(musicalcent)/log(semitone)
#
# Musical note lengths.
#
wholenote !
MUSICAL_NOTE_LENGTH wholenote
halfnote 1|2 wholenote
quarternote 1|4 wholenote
eighthnote 1|8 wholenote
sixteenthnote 1|16 wholenote
thirtysecondnote 1|32 wholenote
sixtyfourthnote 1|64 wholenote
dotted 3|2
doubledotted 7|4
breve doublewholenote
semibreve wholenote
minimnote halfnote
crotchet quarternote
quaver eighthnote
semiquaver sixteenthnote
demisemiquaver thirtysecondnote
hemidemisemiquaver sixtyfourthnote
semidemisemiquaver hemidemisemiquaver
#
# yarn and cloth measures
#
# yarn linear density
woolyarnrun 1600 yard/pound # 1600 yds of "number 1 yarn" weighs
# a pound.
yarncut 300 yard/pound # Less common system used in
# Pennsylvania for wool yarn
cottonyarncount 840 yard/pound
linenyarncount 300 yard/pound # Also used for hemp and ramie
worstedyarncount 1680 ft/pound
metricyarncount meter/gram
denier 1|9 tex # used for silk and rayon
manchesteryarnnumber drams/1000 yards # old system used for silk
pli lb/in
typp 1000 yd/lb # abbreviation for Thousand Yard Per Pound
asbestoscut 100 yd/lb # used for glass and asbestos yarn
tex gram / km # rational metric yarn measure, meant
drex 0.1 tex # to be used for any kind of yarn
poumar lb / 1e6 yard
# yarn and cloth length
skeincotton 80*54 inch # 80 turns of thread on a reel with a
# 54 in circumference (varies for other
# kinds of thread)
cottonbolt 120 ft # cloth measurement
woolbolt 210 ft
bolt cottonbolt
heer 600 yards
cut 300 yards # used for wet-spun linen yarn
lea 300 yards
sailmakersyard 28.5 in
sailmakersounce oz / sailmakersyard 36 inch
silkmomme momme / 25 yards 1.49 inch # Traditional silk weight
silkmm silkmomme # But it is also defined as
# lb/100 yd 45 inch. The two
# definitions are slightly different
# and neither one seems likely to be
# the true source definition.
#
# drug dosage
#
mcg microgram # Frequently used for vitamins
iudiptheria 62.8 microgram # IU is for international unit
iupenicillin 0.6 microgram
iuinsulin 41.67 microgram
drop 1|20 ml # The drop was an old "unit" that was
# replaced by the minim. But I was
# told by a pharmacist that in his
# profession, the conversion of 20
# drops per ml is actually used.
bloodunit 450 ml # For whole blood. For blood
# components, a blood unit is the
# quantity of the component found in a
# blood unit of whole blood. The
# human body contains about 12 blood
# units of whole blood.
#
# misc medical measure
#
frenchcathetersize 1|3 mm # measure used for the outer diameter
# of a catheter
charriere frenchcathetersize
#
# fixup units for times when prefix handling doesn't do the job
#
hectare hectoare
megohm megaohm
kilohm kiloohm
microhm microohm
megalerg megaerg # 'L' added to make it pronounceable [18].
#
# Money
#
# Note that US$ is the primitive unit so other currencies are
# generally given in US$.
#
unitedstatesdollar US$
usdollar US$
$ dollar
mark germanymark
#bolivar venezuelabolivar # Not all databases are
#venezuelabolivarfuerte 1e-5 bolivar # supplying these
#bolivarfuerte 1e-5 bolivar # The currency was revalued
#oldbolivar 1|1000 bolivarfuerte # twice
peseta spainpeseta
rand southafricarand
escudo portugalescudo
guilder netherlandsguilder
hollandguilder netherlandsguilder
peso mexicopeso
yen japanyen
lira turkeylira
rupee indiarupee
drachma greecedrachma
franc francefranc
markka finlandmarkka
britainpound unitedkingdompound
greatbritainpound unitedkingdompound
unitedkingdompound ukpound
poundsterling britainpound
yuan chinayuan
# Unicode Currency Names
!utf8
icelandkróna icelandkrona
polandzłoty polandzloty
tongapa’anga tongapa'anga
#venezuelabolívar venezuelabolivar
vietnamđồng vietnamdong
mongoliatögrög mongoliatugrik
sãotomé&príncipedobra saotome&principedobra
!endutf8
UKP GBP # Not an ISO code, but looks like one, and
# sometimes used on usenet.
!include currency.units
# Money on the gold standard, used in the late 19th century and early
# 20th century.
olddollargold 23.22 grains goldprice # Used until 1934
newdollargold 96|7 grains goldprice # After Jan 31, 1934
dollargold newdollargold
poundgold 113 grains goldprice # British pound
# Precious metals
goldounce goldprice troyounce
silverounce silverprice troyounce
platinumounce platinumprice troyounce
XAU goldounce
XPT platinumounce
XAG silverounce
# Nominal masses of US coins. Note that dimes, quarters and half dollars
# have weight proportional to value. Before 1965 it was $40 / kg.
USpennyweight 2.5 grams # Since 1982, 48 grains before
USnickelweight 5 grams
USdimeweight US$ 0.10 / (20 US$ / lb) # Since 1965
USquarterweight US$ 0.25 / (20 US$ / lb) # Since 1965
UShalfdollarweight US$ 0.50 / (20 US$ / lb) # Since 1971
USdollarweight 8.1 grams # Weight of Susan B. Anthony and
# Sacagawea dollar coins
# British currency
quid britainpound # Slang names
fiver 5 quid
tenner 10 quid
monkey 500 quid
brgrand 1000 quid
bob shilling
shilling 1|20 britainpound # Before decimalisation, there
oldpence 1|12 shilling # were 20 shillings to a pound,
farthing 1|4 oldpence # each of twelve old pence
guinea 21 shilling # Still used in horse racing
crown 5 shilling
florin 2 shilling
groat 4 oldpence
tanner 6 oldpence
brpenny 0.01 britainpound
pence brpenny
tuppence 2 pence
tuppenny tuppence
ha'penny halfbrpenny
hapenny ha'penny
oldpenny oldpence
oldtuppence 2 oldpence
oldtuppenny oldtuppence
threepence 3 oldpence # threepence never refers to new money
threepenny threepence
oldthreepence threepence
oldthreepenny threepence
oldhalfpenny halfoldpenny
oldha'penny oldhalfpenny
oldhapenny oldha'penny
brpony 25 britainpound
# Canadian currency
loony 1 canadadollar # This coin depicts a loon
toony 2 canadadollar
# Cryptocurrency
satoshi 1e-8 bitcoin
XBT bitcoin # nonstandard code
# Inflation.
#
# Currently US inflation as reported by the BLS CPI index is available.
# The UScpi() table reports the USA consumer price index. Note that
# if you specify a year like 2015, that refers to the CPI reported
# for December of 2014 (which is released in mid January 2015),
# so it refers to the point right at the start of the given year.
# Months are increments of 1|12 on the year, so the January 2015
# release will be 2015+1|12 = 2015.08333.
!include cpi.units
USCPI() UScpi
USCPI_now UScpi_now
USCPI_lastdate UScpi_lastdate
cpi() UScpi
CPI() UScpi
cpi_now UScpi_now
CPI_now UScpi_now
cpi_lastdate UScpi_lastdate
CPI_lastdate UScpi_lastdate
# These definitions hide the CPI index and directly convert US dollars
# from a specified date to current dollars. You can use this to convert
# historical dollars to present value or to convert money in the past
# between two dates.
dollars_in() USdollars_in
US$in() USdollars_in
$in() USdollars_in
# This definition gives the dimensionless US inflation factor since the
# specified date.
inflation_since() USinflation_since
#
# Units used for measuring volume of wood
#
cord 4*4*8 ft^3 # 4 ft by 4 ft by 8 ft bundle of wood
facecord 1|2 cord
cordfoot 1|8 cord # One foot long section of a cord
cordfeet cordfoot
housecord 1|3 cord # Used to sell firewood for residences,
# often confusingly called a "cord"
boardfoot ft^2 inch # Usually 1 inch thick wood
boardfeet boardfoot
fbm boardfoot # feet board measure
stack 4 yard^3 # British, used for firewood and coal [18]
rick 4 ft 8 ft 16 inches # Stack of firewood, supposedly
# sometimes called a face cord, but this
# value is equal to 1|3 cord. Name
# comes from an old Norse word for a
# stack of wood.
stere m^3
timberfoot ft^3 # Used for measuring solid blocks of wood
standard 120 12 ft 11 in 1.5 in # This is the St Petersburg or
# Pittsburg standard. Apparently the
# term is short for "standard hundred"
# which was meant to refer to 100 pieces
# of wood (deals). However, this
# particular standard is equal to 120
# deals which are 12 ft by 11 in by 1.5
# inches (not the standard deal).
hoppusfoot (4/pi) ft^3 # Volume calculation suggested in 1736
hoppusboardfoot 1|12 hoppusfoot # forestry manual by Edward Hoppus, for
hoppuston 50 hoppusfoot # estimating the usable volume of a log.
# It results from computing the volume
# of a cylindrical log of length, L, and
# girth (circumference), G, by V=L(G/4)^2.
# The hoppus ton is apparently still in
# use for shipments from Southeast Asia.
# In Britain, the deal is apparently any piece of wood over 6 feet long, over
# 7 wide and 2.5 inches thick. The OED doesn't give a standard size. A piece
# of wood less than 7 inches wide is called a "batten". This unit is now used
# exclusively for fir and pine.
deal 12 ft 11 in 2.5 in # The standard North American deal [OED]
wholedeal 12 ft 11 in 1.25 in # If it's half as thick as the standard
# deal it's called a "whole deal"!
splitdeal 12 ft 11 in 5|8 in # And half again as thick is a split deal.
# Used for shellac mixing rate
poundcut pound / gallon
lbcut poundcut
#
# Gas and Liquid flow units
#
FLUID_FLOW VOLUME / TIME
# Some obvious volumetric gas flow units (cu is short for cubic)
cumec m^3/s
cusec ft^3/s
# Conventional abbreviations for fluid flow units
gph gal/hr
gpm gal/min
mgd megagal/day
brgph brgallon/hr
brgpm brgallon/min
brmgd mega brgallon/day
usgph usgallon/hr
usgpm usgallon/min
usmgd mega usgallon/day
cfs ft^3/s
cfh ft^3/hour
cfm ft^3/min
lpm liter/min
lfm ft/min # Used to report air flow produced by fans.
# Multiply by cross sectional area to get a
# flow in cfm.
pru mmHg / (ml/min) # peripheral resistance unit, used in
# medicine to assess blood flow in
# the capillaries.
# Miner's inch: This is an old historic unit used in the Western United
# States. It is generally defined as the rate of flow through a one square
# inch hole at a specified depth such as 4 inches. In the late 19th century,
# volume of water was sometimes measured in the "24 hour inch". Values for the
# miner's inch were fixed by state statues. (This information is from a web
# site operated by the Nevada Division of Water Planning: The Water Words
# Dictionary at http://water.nv.gov/WaterPlanDictionary.aspx, specifically
# http://water.nv.gov/programs/planning/dictionary/wwords-M.pdf. All
# but minersinchNV are s.v. Miner's Inch [Western United States])
minersinchAZ 1.5 ft^3/min
minersinchCA 1.5 ft^3/min
minersinchMT 1.5 ft^3/min
minersinchNV 1.5 ft^3/min
minersinchOR 1.5 ft^3/min
minersinchID 1.2 ft^3/min
minersinchKS 1.2 ft^3/min
minersinchNE 1.2 ft^3/min
minersinchNM 1.2 ft^3/min
minersinchND 1.2 ft^3/min
minersinchSD 1.2 ft^3/min
minersinchUT 1.2 ft^3/min
minersinchCO 1 ft^3/sec / 38.4 # 38.4 miner's inches = 1 ft^3/sec
minersinchBC 1.68 ft^3/min # British Columbia
# Oceanographic flow
sverdrup 1e6 m^3 / sec # Used to express flow of ocean
# currents. Named after Norwegian
# oceanographer H. Sverdrup.
# In vacuum science and some other applications, gas flow is measured
# as the product of volumetric flow and pressure. This is useful
# because it makes it easy to compare with the flow at standard
# pressure (one atmosphere). It also directly relates to the number
# of gas molecules per unit time, and hence to the mass flow if the
# molecular mass is known.
GAS_FLOW PRESSURE FLUID_FLOW
sccm atm cc/min # 's' is for "standard" to indicate
sccs atm cc/sec # flow at standard pressure
scfh atm ft^3/hour #
scfm atm ft^3/min
slpm atm liter/min
slph atm liter/hour
lusec liter micron Hg / s # Used in vacuum science
# US Standard Atmosphere (1976)
# Atmospheric temperature and pressure vs. geometric height above sea level
# This definition covers only the troposphere (the lowest atmospheric
# layer, up to 11 km), and assumes the layer is polytropic.
# A polytropic process is one for which PV^k = const, where P is the
# pressure, V is the volume, and k is the polytropic exponent. The
# polytropic index is n = 1 / (k - 1). As noted in the Wikipedia article
# https://en.wikipedia.org/wiki/Polytropic_process, some authors reverse
# the definitions of "exponent" and "index." The functions below assume
# the following parameters:
# temperature lapse rate, -dT/dz, in troposphere
lapserate 6.5 K/km # US Std Atm (1976)
# air molecular weight, including constituent mol wt, given
# in Table 3, p. 3; CH4 (16.04303) and N2O (44.0128) from
# Table 15, p. 33. Values for molecular weights are slightly
# different from current values, so the original numerical
# values are retained.
air_1976 78.084 % 28.0134 \
+ 20.9476 % 31.9988 \
+ 9340 ppm 39.948 \
+ 314 ppm 44.00995 \
+ 18.18 ppm 20.183 \
+ 5.24 ppm 4.0026 \
+ 1.5 ppm 16.04303 \
+ 1.14 ppm 83.80 \
+ 0.5 ppm 2.01594 \
+ 0.27 ppm 44.0128 \
+ 0.087 ppm 131.30
# from US Standard Atmosphere, 1962, Table I.2.7, p. 9
air_1962 78.084 % 28.0134 \
+ 20.9476 % 31.9988 \
+ 9340 ppm 39.948 \
+ 314 ppm 44.00995 \
+ 18.18 ppm 20.183 \
+ 5.24 ppm 4.0026 \
+ 2 ppm 16.04303 \
+ 1.14 ppm 83.80 \
+ 0.5 ppm 2.01594 \
+ 0.5 ppm 44.0128 \
+ 0.087 ppm 131.30
# Average molecular weight of air
#
# Concentration of greenhouse gases CO2, CH4, and N20 are from
# https://gml.noaa.gov/ccgg/trends/global.html (accessed 2023-04-10);
# others are from NASA Earth Fact Sheet
# https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html (accessed 2023-04-10)
# Numbers do not add up to exactly 100% due to roundoff and uncertainty. Water
# is highly variable, typically makes up about 1%
air_2023 78.08% nitrogen 2 \
+ 20.95% oxygen 2 \
+ 9340 ppm argon \
+ 419 ppm (carbon + oxygen 2) \
+ 18.18 ppm neon \
+ 5.24 ppm helium \
+ 1.92 ppm (carbon + 4 hydrogen) \
+ 1.14 ppm krypton \
+ 0.55 ppm hydrogen 2 \
+ 0.34 ppm (nitrogen 2 + oxygen)
# from NASA Earth Fact Sheet (accessed 28 August 2015)
# http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
air_2015 78.08% nitrogen 2 \
+ 20.95% oxygen 2 \
+ 9340 ppm argon \
+ 400 ppm (carbon + oxygen 2) \
+ 18.18 ppm neon \
+ 5.24 ppm helium \
+ 1.7 ppm (carbon + 4 hydrogen) \
+ 1.14 ppm krypton \
+ 0.55 ppm hydrogen 2
air air_2023
# universal gas constant
R_1976 8.31432e3 N m/(kmol K)
# polytropic index n
polyndx_1976 air_1976 (kg/kmol) gravity/(R_1976 lapserate) - 1
# If desired, redefine using current values for air mol wt and R
polyndx polyndx_1976
# polyndx air (kg/kmol) gravity/(R lapserate) - 1
# for comparison with various references
polyexpnt (polyndx + 1) / polyndx
# The model assumes the following reference values:
# sea-level temperature and pressure
stdatmT0 288.15 K
stdatmP0 atm
# "effective radius" for relation of geometric to geopotential height,
# at a latitude at which g = 9.80665 m/s (approximately 45.543 deg); no
# relation to actual radius
earthradUSAtm 6356766 m
# Temperature vs. geopotential height h
# Assumes 15 degC at sea level
# Based on approx 45 deg latitude
# Lower limits of domain and upper limits of range are those of the
# tables in US Standard Atmosphere (NASA 1976)
stdatmTH(h) units=[m;K] domain=[-5000,11e3] range=[217,321] \
stdatmT0+(-lapserate h) ; (stdatmT0+(-stdatmTH))/lapserate
# Temperature vs. geometric height z; based on approx 45 deg latitude
stdatmT(z) units=[m;K] domain=[-5000,11e3] range=[217,321] \
stdatmTH(geop_ht(z)) ; ~geop_ht(~stdatmTH(stdatmT))
# Pressure vs. geopotential height h
# Assumes 15 degC and 101325 Pa at sea level
# Based on approx 45 deg latitude
# Lower limits of domain and upper limits of range are those of the
# tables in US Standard Atmosphere (NASA 1976)
stdatmPH(h) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \
atm (1 - (lapserate/stdatmT0) h)^(polyndx + 1) ; \
(stdatmT0/lapserate) (1+(-(stdatmPH/stdatmP0)^(1/(polyndx + 1))))
# Pressure vs. geometric height z; based on approx 45 deg latitude
stdatmP(z) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \
stdatmPH(geop_ht(z)); ~geop_ht(~stdatmPH(stdatmP))
# Geopotential height from geometric height
# Based on approx 45 deg latitude
# Lower limits of domain and range are somewhat arbitrary; they
# correspond to the limits in the US Std Atm tables
geop_ht(z) units=[m;m] domain=[-5000,) range=[-5004,) \
(earthradUSAtm z) / (earthradUSAtm + z) ; \
(earthradUSAtm geop_ht) / (earthradUSAtm + (-geop_ht))
# The standard value for the sea-level acceleration due to gravity is
# 9.80665 m/s^2, but the actual value varies with latitude (Harrison 1949)
# R_eff = 2 g_phi / denom
# g_phi = 978.0356e-2 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2)
# or
# g_phi = 980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2)
# denom = 3.085462e-6+2.27e-9 cos(2 lat)+(-2e-12) cos(4 lat) (minutes?)
# There is no inverse function; the standard value applies at a latitude
# of about 45.543 deg
g_phi(lat) units=[deg;m/s2] domain=[0,90] noerror \
980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2) m/s2
# effective Earth radius for relation of geometric height to
# geopotential height, as function of latitude (Harrison 1949)
earthradius_eff(lat) units=[deg;m] domain=[0,90] noerror \
m 2 9.780356 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2) / \
(3.085462e-6 + 2.27e-9 cos(2 lat) + (-2e-12) cos(4 lat))
# References
# Harrison, L.P. 1949. Relation Between Geopotential and Geometric
# Height. In Smithsonian Meteorological Tables. List, Robert J., ed.
# 6th ed., 4th reprint, 1968. Washington, DC: Smithsonian Institution.
# NASA. US National Aeronautics and Space Administration. 1976.
# US Standard Atmosphere 1976. Washington, DC: US Government Printing Office.
# Gauge pressure functions
#
# Gauge pressure is measured relative to atmospheric pressure. In the English
# system, where pressure is often given in pounds per square inch, gauge
# pressure is often indicated by 'psig' to distinguish it from absolute
# pressure, often indicated by 'psia'. At the standard atmospheric pressure
# of 14.696 psia, a gauge pressure of 0 psig is an absolute pressure of 14.696
# psia; an automobile tire inflated to 31 psig has an absolute pressure of
# 45.696 psia.
#
# With gaugepressure(), the units must be specified (e.g., gaugepressure(1.5
# bar)); with psig(), the units are taken as psi, so the example above of tire
# pressure could be given as psig(31).
#
# If the normal elevation is significantly different from sea level, change
# Patm appropriately, and adjust the lower domain limit on the gaugepressure
# definition.
Patm atm
gaugepressure(x) units=[Pa;Pa] domain=[-101325,) range=[0,) \
x + Patm ; gaugepressure+(-Patm)
psig(x) units=[1;Pa] domain=[-14.6959487755135,) range=[0,) \
gaugepressure(x psi) ; ~gaugepressure(psig) / psi
# Pressure for underwater diving
seawater 0.1 bar / meter
msw meter seawater
fsw foot seawater
#
# Wire Gauge
#
# This area is a nightmare with huge charts of wire gauge diameters
# that usually have no clear origin. There are at least 5 competing wire gauge
# systems to add to the confusion. The use of wire gauge is related to the
# manufacturing method: a metal rod is heated and drawn through a hole. The
# size change can't be too big. To get smaller wires, the process is repeated
# with a series of smaller holes. Generally larger gauges mean smaller wires.
# The gauges often have values such as "00" and "000" which are larger sizes
# than simply "0" gauge. In the tables that appear below, these gauges must be
# specified as negative numbers (e.g. "00" is -1, "000" is -2, etc).
# Alternatively, you can use the following units:
#
g00 (-1)
g000 (-2)
g0000 (-3)
g00000 (-4)
g000000 (-5)
g0000000 (-6)
# American Wire Gauge (AWG) or Brown & Sharpe Gauge appears to be the most
# important gauge. ASTM B-258 specifies that this gauge is based on geometric
# interpolation between gauge 0000, which is 0.46 inches exactly, and gauge 36
# which is 0.005 inches exactly. Therefore, the diameter in inches of a wire
# is given by the formula 1|200 92^((36-g)/39). Note that 92^(1/39) is close
# to 2^(1/6), so diameter is approximately halved for every 6 gauges. For the
# repeated zero values, use negative numbers in the formula. The same document
# also specifies rounding rules which seem to be ignored by makers of tables.
# Gauges up to 44 are to be specified with up to 4 significant figures, but no
# closer than 0.0001 inch. Gauges from 44 to 56 are to be rounded to the
# nearest 0.00001 inch.
#
# In addition to being used to measure wire thickness, this gauge is used to
# measure the thickness of sheets of aluminum, copper, and most metals other
# than steel, iron and zinc.
wiregauge(g) units=[1;m] range=(0,) \
1|200 92^((36+(-g))/39) in; 36+(-39)ln(200 wiregauge/in)/ln(92)
awg() wiregauge
# Next we have the SWG, the Imperial or British Standard Wire Gauge. This one
# is piecewise linear. It was used for aluminum sheets but also shows up for
# wire used in jewelry.
brwiregauge[in] \
-6 0.5 \
-5 0.464 \
-3 0.4 \
-2 0.372 \
3 0.252 \
6 0.192 \
10 0.128 \
14 0.08 \
19 0.04 \
23 0.024 \
26 0.018 \
28 0.0148 \
30 0.0124 \
39 0.0052 \
49 0.0012 \
50 0.001
swg() brwiregauge
# The following is from the Appendix to ASTM B 258
#
# For example, in U.S. gage, the standard for sheet metal is based on the
# weight of the metal, not on the thickness. 16-gage is listed as
# approximately .0625 inch thick and 40 ounces per square foot (the original
# standard was based on wrought iron at .2778 pounds per cubic inch; steel
# has almost entirely superseded wrought iron for sheet use, at .2833 pounds
# per cubic inch). Smaller numbers refer to greater thickness. There is no
# formula for converting gage to thickness or weight.
#
# It's rather unclear from the passage above whether the plate gauge values are
# therefore wrong if steel is being used. Reference [15] states that steel is
# in fact measured using this gauge (under the name Manufacturers' Standard
# Gauge) with a density of 501.84 lb/ft3 = 0.2904 lb/in3 used for steel.
# But this doesn't seem to be the correct density of steel (.2833 lb/in3 is
# closer).
#
# This gauge was established in 1893 for purposes of taxation.
# Old plate gauge for iron
plategauge[(oz/ft^2)/(480*lb/ft^3)] \
-5 300 \
1 180 \
14 50 \
16 40 \
17 36 \
20 24 \
26 12 \
31 7 \
36 4.5 \
38 4
# Manufacturers Standard Gage
stdgauge[(oz/ft^2)/(501.84*lb/ft^3)] \
-5 300 \
1 180 \
14 50 \
16 40 \
17 36 \
20 24 \
26 12 \
31 7 \
36 4.5 \
38 4
# A special gauge is used for zinc sheet metal. Notice that larger gauges
# indicate thicker sheets.
zincgauge[in] \
1 0.002 \
10 0.02 \
15 0.04 \
19 0.06 \
23 0.1 \
24 0.125 \
27 0.5 \
28 1
#
# Imperial drill bit sizes are reported in inches or in a numerical or
# letter gauge.
#
drillgauge[in] \
1 0.2280 \
2 0.2210 \
3 0.2130 \
4 0.2090 \
5 0.2055 \
6 0.2040 \
7 0.2010 \
8 0.1990 \
9 0.1960 \
10 0.1935 \
11 0.1910 \
12 0.1890 \
13 0.1850 \
14 0.1820 \
15 0.1800 \
16 0.1770 \
17 0.1730 \
18 0.1695 \
19 0.1660 \
20 0.1610 \
22 0.1570 \
23 0.1540 \
24 0.1520 \
25 0.1495 \
26 0.1470 \
27 0.1440 \
28 0.1405 \
29 0.1360 \
30 0.1285 \
31 0.1200 \
32 0.1160 \
33 0.1130 \
34 0.1110 \
35 0.1100 \
36 0.1065 \
38 0.1015 \
39 0.0995 \
40 0.0980 \
41 0.0960 \
42 0.0935 \
43 0.0890 \
44 0.0860 \
45 0.0820 \
46 0.0810 \
48 0.0760 \
51 0.0670 \
52 0.0635 \
53 0.0595 \
54 0.0550 \
55 0.0520 \
56 0.0465 \
57 0.0430 \
65 0.0350 \
66 0.0330 \
68 0.0310 \
69 0.0292 \
70 0.0280 \
71 0.0260 \
73 0.0240 \
74 0.0225 \
75 0.0210 \
76 0.0200 \
78 0.0160 \
79 0.0145 \
80 0.0135 \
88 0.0095 \
104 0.0031
drillA 0.234 in
drillB 0.238 in
drillC 0.242 in
drillD 0.246 in
drillE 0.250 in
drillF 0.257 in
drillG 0.261 in
drillH 0.266 in
drillI 0.272 in
drillJ 0.277 in
drillK 0.281 in
drillL 0.290 in
drillM 0.295 in
drillN 0.302 in
drillO 0.316 in
drillP 0.323 in
drillQ 0.332 in
drillR 0.339 in
drillS 0.348 in
drillT 0.358 in
drillU 0.368 in
drillV 0.377 in
drillW 0.386 in
drillX 0.397 in
drillY 0.404 in
drillZ 0.413 in
#
# Screw sizes
#
# In the USA, screw diameters for both wood screws and machine screws
# are reported using a gauge number. Metric machine screws are
# reported as Mxx where xx is the diameter in mm.
#
screwgauge(g) units=[1;m] range=[0,) \
(.06 + .013 g) in ; (screwgauge/in + (-.06)) / .013
#
# Abrasive grit size
#
# Standards governing abrasive grit sizes are complicated, specifying
# fractions of particles that are passed or retained by different mesh
# sizes. As a result, it is not possible to make precise comparisons
# of different grit standards. The tables below allow the
# determination of rough equivlants by using median particle size.
#
# Standards in the USA are determined by the Unified Abrasives
# Manufacturers' Association (UAMA), which resulted from the merger of
# several previous organizations. One of the old organizations was
# CAMI (Coated Abrasives Manufacturers' Institute).
#
# UAMA has a web page with plots showing abrasive particle ranges for
# various different grits and comparisons between standards.
#
# https://uama.org/abrasives-101/
#
# Abrasives are grouped into "bonded" abrasives for use with grinding
# wheels and "coated" abrasives for sandpapers and abrasive films.
# The industry uses different grit standards for these two
# categories.
#
# Another division is between "macrogrits", grits below 240 and
# "microgrits", which are above 240. Standards differ, as do methods
# for determining particle size. In the USA, ANSI B74.12 is the
# standard governing macrogrits. ANSI B74.10 covers bonded microgrit
# abrasives, and ANSI B74.18 covers coated microgrit abrasives. It
# appears that the coated standard is identical to the bonded standard
# for grits up through 600 but then diverges significantly.
#
# European grit sizes are determined by the Federation of European
# Producers of Abrasives. http://www.fepa-abrasives.org
#
# They give two standards, the "F" grit for bonded abrasives and the
# "P" grit for coated abrasives. This data is taken directly from
# their web page.
# FEPA P grit for coated abrasives is commonly seen on sandpaper in
# the USA where the paper will be marked P600, for example. FEPA P
# grits are said to be more tightly constrained than comparable ANSI
# grits so that the particles are more uniform in size and hence give
# a better finish.
grit_P[micron] \
12 1815 \
16 1324 \
20 1000 \
24 764 \
30 642 \
36 538 \
40 425 \
50 336 \
60 269 \
80 201 \
100 162 \
120 125 \
150 100 \
180 82 \
220 68 \
240 58.5 \
280 52.2 \
320 46.2 \
360 40.5 \
400 35 \
500 30.2 \
600 25.8 \
800 21.8 \
1000 18.3 \
1200 15.3 \
1500 12.6 \
2000 10.3 \
2500 8.4
# The F grit is the European standard for bonded abrasives such as
# grinding wheels
grit_F[micron] \
4 4890 \
5 4125 \
6 3460 \
7 2900 \
8 2460 \
10 2085 \
12 1765 \
14 1470 \
16 1230 \
20 1040 \
22 885 \
24 745 \
30 625 \
36 525 \
40 438 \
46 370 \
54 310 \
60 260 \
70 218 \
80 185 \
90 154 \
100 129 \
120 109 \
150 82 \
180 69 \
220 58 \
230 53 \
240 44.5 \
280 36.5 \
320 29.2 \
360 22.8 \
400 17.3 \
500 12.8 \
600 9.3 \
800 6.5 \
1000 4.5 \
1200 3 \
1500 2.0 \
2000 1.2
# According to the UAMA web page, the ANSI bonded and ANSI coated standards
# are identical to FEPA F in the macrogrit range (under 240 grit), so these
# values are taken from the FEPA F table. The values for 240 and above are
# from the UAMA web site and represent the average of the "d50" range
# endpoints listed there.
ansibonded[micron] \
4 4890 \
5 4125 \
6 3460 \
7 2900 \
8 2460 \
10 2085 \
12 1765 \
14 1470 \
16 1230 \
20 1040 \
22 885 \
24 745 \
30 625 \
36 525 \
40 438 \
46 370 \
54 310 \
60 260 \
70 218 \
80 185 \
90 154 \
100 129 \
120 109 \
150 82 \
180 69 \
220 58 \
240 50 \
280 39.5 \
320 29.5 \
360 23 \
400 18.25 \
500 13.9 \
600 10.55 \
800 7.65 \
1000 5.8 \
1200 3.8
grit_ansibonded() ansibonded
# Like the bonded grit, the coated macrogrits below 240 are taken from the
# FEPA F table. Data above this is from the UAMA site. Note that the coated
# and bonded standards are evidently the same from 240 up to 600 grit, but
# starting at 800 grit, the coated standard diverges. The data from UAMA show
# that 800 grit coated has an average size slightly larger than the average
# size of 600 grit coated/bonded. However, the 800 grit has a significantly
# smaller particle size variation.
#
# Because of this non-monotonicity from 600 grit to 800 grit this definition
# produces a warning about the lack of a unique inverse.
ansicoated[micron] noerror \
4 4890 \
5 4125 \
6 3460 \
7 2900 \
8 2460 \
10 2085 \
12 1765 \
14 1470 \
16 1230 \
20 1040 \
22 885 \
24 745 \
30 625 \
36 525 \
40 438 \
46 370 \
54 310 \
60 260 \
70 218 \
80 185 \
90 154 \
100 129 \
120 109 \
150 82 \
180 69 \
220 58 \
240 50 \
280 39.5 \
320 29.5 \
360 23 \
400 18.25 \
500 13.9 \
600 10.55 \
800 11.5 \
1000 9.5 \
2000 7.2 \
2500 5.5 \
3000 4 \
4000 3 \
6000 2 \
8000 1.2
grit_ansicoated() ansicoated
#
# Is this correct? This is the JIS Japanese standard used on waterstones
#
jisgrit[micron] \
150 75 \
180 63 \
220 53 \
280 48 \
320 40 \
360 35 \
400 30 \
600 20 \
700 17 \
800 14 \
1000 11.5 \
1200 9.5 \
1500 8 \
2000 6.7 \
2500 5.5 \
3000 4 \
4000 3 \
6000 2 \
8000 1.2
# The "Finishing Scale" marked with an A (e.g. A75). This information
# is from the web page of the sand paper manufacturer Klingspor
# https://www.klingspor.com/ctemplate1.aspx?page=default/html/gritGradingSystems_en-US.html
#
# I have no information about what this scale is used for.
grit_A[micron]\
16 15.3 \
25 21.8 \
30 23.6 \
35 25.75 \
45 35 \
60 46.2 \
65 53.5 \
75 58.5 \
90 65 \
110 78 \
130 93 \
160 127 \
200 156
#
# Grits for DMT brand diamond sharpening stones from
# https://www.dmtsharp.com/resources/dmt-catalog-product-information.html
# "DMT Diamond Grits" PDF download
dmtxxcoarse 120 micron # 120 mesh
dmtsilver dmtxxcoarse
dmtxx dmtxxcoarse
dmtxcoarse 60 micron # 220 mesh
dmtx dmtxcoarse
dmtblack dmtxcoarse
dmtcoarse 45 micron # 325 mesh
dmtc dmtcoarse
dmtblue dmtcoarse
dmtfine 25 micron # 600 mesh
dmtred dmtfine
dmtf dmtfine
dmtefine 9 micron # 1200 mesh
dmte dmtefine
dmtgreen dmtefine
dmtceramic 7 micron # 2200 mesh
dmtcer dmtceramic
dmtwhite dmtceramic
dmteefine 3 micron # 8000 mesh
dmttan dmteefine
dmtee dmteefine
#
# The following values come from a page in the Norton Stones catalog,
# available at their web page, http://www.nortonstones.com.
#
hardtranslucentarkansas 6 micron # Natural novaculite (silicon quartz)
softarkansas 22 micron # stones
extrafineindia 22 micron # India stones are Norton's manufactured
fineindia 35 micron # aluminum oxide product
mediumindia 53.5 micron
coarseindia 97 micron
finecrystolon 45 micron # Crystolon stones are Norton's
mediumcrystalon 78 micron # manufactured silicon carbide product
coarsecrystalon 127 micron
# The following are not from the Norton catalog
hardblackarkansas 6 micron
hardwhitearkansas 11 micron
washita 35 micron
#
# Mesh systems for measuring particle sizes by sifting through a wire
# mesh or sieve
#
# The Tyler system and US Sieve system are based on four steps for
# each factor of 2 change in the size, so each size is 2^1|4 different
# from the adjacent sizes. Unfortunately, the mesh numbers are
# arbitrary, so the sizes cannot be expressed with a functional form.
# Various references round the values differently. The mesh numbers
# are supposed to correspond to the number of holes per inch, but this
# correspondence is only approximate because it doesn't include the
# wire size of the mesh.
# The Tyler Mesh system was apparently introduced by the WS Tyler
# company, but it appears that they no longer use it. They follow the
# ASTM E11 standard.
meshtyler[micron] \
2.5 8000 \
3 6727 \
3.5 5657 \
4 4757 \
5 4000 \
6 3364 \
7 2828 \
8 2378 \
9 2000 \
10 1682 \
12 1414 \
14 1189 \
16 1000 \
20 841 \
24 707 \
28 595 \
32 500 \
35 420 \
42 354 \
48 297 \
60 250 \
65 210 \
80 177 \
100 149 \
115 125 \
150 105 \
170 88 \
200 74 \
250 63 \
270 53 \
325 44 \
400 37
# US Sieve size, ASTM E11
#
# The WS Tyler company prints the list from ASTM E11 in
# A Calculator for ASTM E11 Standard Sieve Designations
# https://blog.wstyler.com/particle-analysis/astm-e11-standard-designations
sieve[micron] \
3.5 5600 \
4 4750 \
5 4000 \
6 3350 \
7 2800 \
8 2360 \
10 2000 \
12 1700 \
14 1400 \
16 1180 \
18 1000 \
20 850 \
25 710 \
30 600 \
35 500 \
40 425 \
45 355 \
50 300 \
60 250 \
70 212 \
80 180 \
100 150 \
120 125 \
140 106 \
170 90 \
200 75 \
230 63 \
270 53 \
325 45 \
400 38 \
450 32 \
500 25 \
625 20 # These last two values are not in the standard series
# but were included in the ASTM standard because they
meshUS() sieve # were in common usage.
# British Mesh size, BS 410: 1986
# This system appears to correspond to the Tyler and US system, but
# with different mesh numbers.
#
# http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf
#
meshbritish[micron] \
3 5657 \
3.5 4757 \
4 4000 \
5 3364 \
6 2828 \
7 2378 \
8 2000 \
10 1682 \
12 1414 \
14 1189 \
16 1000 \
18 841 \
22 707 \
25 595 \
30 500 \
36 420 \
44 354 \
52 297 \
60 250 \
72 210 \
85 177 \
100 149 \
120 125 \
150 105 \
170 88 \
200 74 \
240 63 \
300 53 \
350 44 \
400 37
# French system, AFNOR NFX11-501: 1970
# The system appears to be based on size doubling every 3 mesh
# numbers, though the values have been aggressively rounded.
# It's not clear if the unrounded values would be considered
# incorrect, so this is given as a table rather than a function.
# Functional form:
# meshtamis(mesh) units=[1;m] 5000 2^(1|3 (mesh-38)) micron
#
# http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf
meshtamis[micron] \
17 40 \
18 50 \
19 63 \
20 80 \
21 100 \
22 125 \
23 160 \
24 200 \
25 250 \
26 315 \
27 400 \
28 500 \
29 630 \
30 800 \
31 1000 \
32 1250 \
33 1600 \
34 2000 \
35 2500 \
36 3150 \
37 4000 \
38 5000
#
# Ring size. All ring sizes are given as the circumference of the ring.
#
# USA ring sizes. Several slightly different definitions seem to be in
# circulation. According to [15], the interior diameter of size n ring in
# inches is 0.32 n + 0.458 for n ranging from 3 to 13.5 by steps of 0.5. The
# size 2 ring is inconsistently 0.538in and no 2.5 size is listed.
#
# However, other sources list 0.455 + 0.0326 n and 0.4525 + 0.0324 n as the
# diameter and list no special case for size 2. (Or alternatively they are
# 1.43 + .102 n and 1.4216+.1018 n for measuring circumference in inches.) One
# reference claimed that the original system was that each size was 1|10 inch
# circumference, but that source doesn't have an explanation for the modern
# system which is somewhat different.
ringsize(n) units=[1;in] domain=[2,) range=[1.6252,) \
(1.4216+.1018 n) in ; (ringsize/in + (-1.4216))/.1018
# Old practice in the UK measured rings using the "Wheatsheaf gauge" with sizes
# specified alphabetically and based on the ring inside diameter in steps of
# 1|64 inch. This system was replaced in 1987 by British Standard 6820 which
# specifies sizes based on circumference. Each size is 1.25 mm different from
# the preceding size. The baseline is size C which is 40 mm circumference.
# The new sizes are close to the old ones. Sometimes it's necessary to go
# beyond size Z to Z+1, Z+2, etc.
sizeAring 37.50 mm
sizeBring 38.75 mm
sizeCring 40.00 mm
sizeDring 41.25 mm
sizeEring 42.50 mm
sizeFring 43.75 mm
sizeGring 45.00 mm
sizeHring 46.25 mm
sizeIring 47.50 mm
sizeJring 48.75 mm
sizeKring 50.00 mm
sizeLring 51.25 mm
sizeMring 52.50 mm
sizeNring 53.75 mm
sizeOring 55.00 mm
sizePring 56.25 mm
sizeQring 57.50 mm
sizeRring 58.75 mm
sizeSring 60.00 mm
sizeTring 61.25 mm
sizeUring 62.50 mm
sizeVring 63.75 mm
sizeWring 65.00 mm
sizeXring 66.25 mm
sizeYring 67.50 mm
sizeZring 68.75 mm
# Japanese sizes start with size 1 at a 13mm inside diameter and each size is
# 1|3 mm larger in diameter than the previous one. They are multiplied by pi
# to give circumference.
jpringsize(n) units=[1;mm] domain=[1,) range=[0.040840704,) \
(38|3 + n/3) pi mm ; 3 jpringsize/ pi mm + (-38)
# The European ring sizes are the length of the circumference in mm minus 40.
euringsize(n) units=[1;mm] (n+40) mm ; euringsize/mm + (-40)
#
# Abbreviations
#
mph mile/hr
brmpg mile/brgallon
usmpg mile/usgallon
mpg mile/gal
kph km/hr
fL footlambert
fpm ft/min
fps ft/s
rpm rev/min
rps rev/sec
mi mile
smi mile
nmi nauticalmile
mbh 1e3 btu/hour
mcm 1e3 circularmil
ipy inch/year # used for corrosion rates
ccf 100 ft^3 # used for selling water [18]
Mcf 1000 ft^3 # not million cubic feet [18]
kp kilopond
kpm kp meter
Wh W hour
hph hp hour
plf lb / foot # pounds per linear foot
#
# Compatibility units with Unix version
#
pa Pa
ev eV
hg Hg
oe Oe
mh mH
rd rod
pf pF
gr grain
nt N
hz Hz
hd hogshead
dry drygallon/gallon
nmile nauticalmile
beV GeV
bev beV
coul C
#
# Radioactivity units
#
event !dimensionless
becquerel event /s # Activity of radioactive source
Bq becquerel #
curie 3.7e10 Bq # Defined in 1910 as the radioactivity
Ci curie # emitted by the amount of radon that is
# in equilibrium with 1 gram of radium.
rutherford 1e6 Bq #
RADIATION_DOSE gray
gray J/kg # Absorbed dose of radiation
Gy gray #
rad 1e-2 Gy # From Radiation Absorbed Dose
rep 8.38 mGy # Roentgen Equivalent Physical, the amount
# of radiation which , absorbed in the
# body, would liberate the same amount
# of energy as 1 roentgen of X rays
# would, or 97 ergs.
sievert J/kg # Dose equivalent: dosage that has the
Sv sievert # same effect on human tissues as 200
rem 1e-2 Sv # keV X-rays. Different types of
# radiation are weighted by the
# Relative Biological Effectiveness
# (RBE).
#
# Radiation type RBE
# X-ray, gamma ray 1
# beta rays, > 1 MeV 1
# beta rays, < 1 MeV 1.08
# neutrons, < 1 MeV 4-5
# neutrons, 1-10 MeV 10
# protons, 1 MeV 8.5
# protons, .1 MeV 10
# alpha, 5 MeV 15
# alpha, 1 MeV 20
#
# The energies are the kinetic energy
# of the particles. Slower particles
# interact more, so they are more
# effective ionizers, and hence have
# higher RBE values.
#
# rem stands for Roentgen Equivalent
# Mammal
banana_dose 0.1e-6 sievert # Informal measure of the dose due to
# eating one average sized banana
roentgen 2.58e-4 C / kg # Ionizing radiation that produces
# 1 statcoulomb of charge in 1 cc of
# dry air at stp.
rontgen roentgen # Sometimes it appears spelled this way
sievertunit 8.38 rontgen # Unit of gamma ray dose delivered in one
# hour at a distance of 1 cm from a
# point source of 1 mg of radium
# enclosed in platinum .5 mm thick.
eman 1e-7 Ci/m^3 # radioactive concentration
mache 3.7e-7 Ci/m^3
#
# Atomic weights. The atomic weight of an element is the ratio of the mass of
# a mole of the element to 1|12 of a mole of Carbon 12. For each element, we
# list the atomic weights of all of the isotopes. The Standard Atomic Weights
# apply to the elements in the isotopic composition that occurs naturally on
# Earth. These are computed values based on the isotopic distribution, and
# may vary for specific samples. Elements which do not occur naturally do
# not have Standard Atomic Weights. For these elements, if data on the most
# stable isotope is available, is given. Otherwise, the user must specify the
# desired isotope.
!include elements.units
# Density of the elements
#
# Note some elements occur in multiple forms (allotropes) with different
# densities, and they are accordingly listed multiple times.
# Density of gas phase elements at STP
hydrogendensity 0.08988 g/l
heliumdensity 0.1786 g/l
neondensity 0.9002 g/l
nitrogendensity 1.2506 g/l
oxygendensity 1.429 g/l
fluorinedensity 1.696 g/l
argondensity 1.784 g/l
chlorinedensity 3.2 g/l
kryptondensity 3.749 g/l
xenondensity 5.894 g/l
radondensity 9.73 g/l
# Density of liquid phase elements near room temperature
brominedensity 3.1028 g/cm^3
mercurydensity 13.534 g/cm^3
# Density of solid elements near room temperature
lithiumdensity 0.534 g/cm^3
potassiumdensity 0.862 g/cm^3
sodiumdensity 0.968 g/cm^3
rubidiumdensity 1.532 g/cm^3
calciumdensity 1.55 g/cm^3
magnesiumdensity 1.738 g/cm^3
phosphorus_white_density 1.823 g/cm^3
berylliumdensity 1.85 g/cm^3
sulfur_gamma_density 1.92 g/cm^3
cesiumdensity 1.93 g/cm^3
carbon_amorphous_density 1.95 g/cm^3 # average value
sulfur_betadensity 1.96 g/cm^3
sulfur_alpha_density 2.07 g/cm^3
carbon_graphite_density 2.267 g/cm^3
phosphorus_red_density 2.27 g/cm^3 # average value
silicondensity 2.3290 g/cm^3
phosphorus_violet_density 2.36 g/cm^3
borondensity 2.37 g/cm^3
strontiumdensity 2.64 g/cm^3
phosphorus_black_density 2.69 g/cm^3
aluminumdensity 2.7 g/cm^3
bariumdensity 3.51 g/cm^3
carbon_diamond_density 3.515 g/cm^3
scandiumdensity 3.985 g/cm^3
selenium_vitreous_density 4.28 g/cm^3
selenium_alpha_density 4.39 g/cm^3
titaniumdensity 4.406 g/cm^3
yttriumdensity 4.472 g/cm^3
selenium_gray_density 4.81 g/cm^3
iodinedensity 4.933 g/cm^3
europiumdensity 5.264 g/cm^3
germaniumdensity 5.323 g/cm^3
radiumdensity 5.5 g/cm^3
arsenicdensity 5.727 g/cm^3
tin_alpha_density 5.769 g/cm^3
galliumdensity 5.91 g/cm^3
vanadiumdensity 6.11 g/cm^3
lanthanumdensity 6.162 g/cm^3
telluriumdensity 6.24 g/cm^3
zirconiumdensity 6.52 g/cm^3
antimonydensity 6.697 g/cm^3
ceriumdensity 6.77 g/cm^3
praseodymiumdensity 6.77 g/cm^3
ytterbiumdensity 6.9 g/cm^3
neodymiumdensity 7.01 g/cm^3
zincdensity 7.14 g/cm^3
chromiumdensity 7.19 g/cm^3
manganesedensity 7.21 g/cm^3
promethiumdensity 7.26 g/cm^3
tin_beta_density 7.265 g/cm^3
indiumdensity 7.31 g/cm^3
samariumdensity 7.52 g/cm^3
irondensity 7.874 g/cm^3
gadoliniumdensity 7.9 g/cm^3
terbiumdensity 8.23 g/cm^3
dysprosiumdensity 8.54 g/cm^3
niobiumdensity 8.57 g/cm^3
cadmiumdensity 8.65 g/cm^3
holmiumdensity 8.79 g/cm^3
cobaltdensity 8.9 g/cm^3
nickeldensity 8.908 g/cm^3
erbiumdensity 9.066 g/cm^3
polonium_alpha_density 9.196 g/cm^3
thuliumdensity 9.32 g/cm^3
polonium_beta_density 9.398 g/cm^3
bismuthdensity 9.78 g/cm^3
lutetiumdensity 9.841 g/cm^3
actiniumdensity 10 g/cm^3
molybdenumdensity 10.28 g/cm^3
silverdensity 10.49 g/cm^3
technetiumdensity 11 g/cm^3
leaddensity 11.34 g/cm^3
thoriumdensity 11.7 g/cm^3
thalliumdensity 11.85 g/cm^3
americiumdensity 12 g/cm^3
palladiumdensity 12.023 g/cm^3
rhodiumdensity 12.41 g/cm^3
rutheniumdensity 12.45 g/cm^3
berkelium_beta_density 13.25 g/cm^3
hafniumdensity 13.31 g/cm^3
curiumdensity 13.51 g/cm^3
berkelium_alphadensity 14.78 g/cm^3
californiumdensity 15.1 g/cm^3
protactiniumdensity 15.37 g/cm^3
tantalumdensity 16.69 g/cm^3
uraniumdensity 19.1 g/cm^3
tungstendensity 19.3 g/cm^3
golddensity 19.30 g/cm^3
plutoniumdensity 19.816 g/cm^3
neptuniumdensity 20.45 g/cm^3 # alpha form, only one at room temp
rheniumdensity 21.02 g/cm^3
platinumdensity 21.45 g/cm^3
iridiumdensity 22.56 g/cm^3
osmiumdensity 22.59 g/cm^3
# A few alternate names
tin_gray tin_alpha_density
tin_white tin_beta_density
graphitedensity carbon_graphite_density
diamonddensity carbon_diamond_density
# Predicted density of elements that have not been made in sufficient
# quantities for measurement.
franciumdensity 2.48 g/cm^3 # liquid, predicted melting point 8 degC
astatinedensity 6.35 g/cm^3
einsteiniumdensity 8.84 g/cm^3
fermiumdensity 9.7 g/cm^3
nobeliumdensity 9.9 g/cm^3
mendeleviumdensity 10.3 g/cm^3
lawrenciumdensity 16 g/cm^3
rutherfordiumdensity 23.2 g/cm^3
roentgeniumdensity 28.7 g/cm^3
dubniumdensity 29.3 g/cm^3
darmstadtiumdensity 34.8 g/cm^3
seaborgiumdensity 35 g/cm^3
bohriumdensity 37.1 g/cm^3
meitneriumdensity 37.4 g/cm^3
hassiumdensity 41 g/cm^3
#
# population units
#
people 1
person people
death people
capita people
percapita per capita
# TGM dozen based unit system listed on the "dozenal" forum
# http://www.dozenalsociety.org.uk/apps/tgm.htm. These units are
# proposed as an allegedly more rational alternative to the SI system.
Tim 12^-4 hour # Time
Grafut gravity Tim^2 # Length based on gravity
Surf Grafut^2 # area
Volm Grafut^3 # volume
Vlos Grafut/Tim # speed
Denz Maz/Volm # density
Mag Maz gravity # force
Maz Volm kg / oldliter # mass based on water
# Abbreviations
# Tm Tim # Conflicts with Tm = Terameter
Gf Grafut
Sf Surf
Vm Volm
Vl Vlos
Mz Maz
Dz Denz
# Dozen based unit prefixes
Zena- 12
Duna- 12^2
Trina- 12^3
Quedra- 12^4
Quena- 12^5
Hesa- 12^6
Seva- 12^7
Aka- 12^8
Neena- 12^9
Dexa- 12^10
Lefa- 12^11
Zennila- 12^12
Zeni- 12^-1
Duni- 12^-2
Trini- 12^-3
Quedri- 12^-4
Queni- 12^-5
Hesi- 12^-6
Sevi- 12^-7
Aki- 12^-8
Neeni- 12^-9
Dexi- 12^-10
Lefi- 12^-11
Zennili- 12^-12
#
# Traditional Japanese units (shakkanhou)
#
# The traditional system of weights and measures is called shakkanhou from the
# shaku and the ken. Japan accepted SI units in 1891 and legalized conversions
# to the traditional system. In 1909 the inch-pound system was also legalized,
# so Japan had three legally approved systems. A change to the metric system
# started in 1921 but there was a lot of resistance. The Measurement Law of
# October 1999 prohibits sales in anything but SI units. However, the old
# units still live on in construction and as the basis for paper sizes of books
# and tools used for handicrafts.
#
# Note that units below use the Hepburn romanization system. Some other
# systems would render "mou", "jou", and "chou" as "mo", "jo" and "cho".
#
#
# http://hiramatu-hifuka.com/onyak/onyindx.html
# Japanese Proportions. These are still in everyday use. They also
# get used as units to represent the proportion of the standard unit.
wari_proportion 1|10
wari wari_proportion
bu_proportion 1|100 # The character bu can also be read fun or bun
# but usually "bu" is used for units.
rin_proportion 1|1000
mou_proportion 1|10000
# Japanese Length Measures
#
# The length system is called kanejaku or
# square and originated in China. It was
# adopted as Japan's official measure in 701
# by the Taiho Code. This system is still in
# common use in architecture and clothing.
shaku 1|3.3 m
mou 1|10000 shaku
rin 1|1000 shaku
bu_distance 1|100 shaku
sun 1|10 shaku
jou_distance 10 shaku
jou jou_distance
kanejakusun sun # Alias to emphasize architectural name
kanejaku shaku
kanejakujou jou
# http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement
taichi shaku # http://zh.wikipedia.org/wiki/台尺
taicun sun # http://zh.wikipedia.org/wiki/台制
!utf8
台尺 taichi # via Hanyu Pinyin romanizations
台寸 taicun
!endutf8
# In context of clothing, shaku is different from architecture
kujirajaku 10|8 shaku
kujirajakusun 1|10 kujirajaku
kujirajakubu 1|100 kujirajaku
kujirajakujou 10 kujirajaku
tan_distance 3 kujirajakujou
ken 6 shaku # Also sometimes 6.3, 6.5, or 6.6
# http://www.homarewood.co.jp/syakusun.htm
# mostly unused
chou_distance 60 ken
chou chou_distance
ri 36 chou
# Japanese Area Measures
# Tsubo is still used for land size, though the others are more
# recognized by their homonyms in the other measurements.
gou_area 1|10 tsubo
tsubo 36 shaku^2 # Size of two tatami = ken^2 ??
se 30 tsubo
tan_area 10 se
chou_area 10 tan_area
# http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement
ping tsubo # http://zh.wikipedia.org/wiki/坪
jia 2934 ping # http://zh.wikipedia.org/wiki/甲_(单位)
fen 1|10 jia # http://zh.wikipedia.org/wiki/分
fen_area 1|10 jia # Protection against future collisions
!utf8
坪 ping # via Hanyu Pinyin romanizations
甲 jia
分 fen
分地 fen_area # Protection against future collisions
!endutf8
# Japanese architecture is based on a "standard" size of tatami mat.
# Room sizes today are given in number of tatami, and this number
# determines the spacing between colums and hence sizes of sliding
# doors and paper screens. However, every region has its own slightly
# different tatami size. Edoma, used in and around Tokyo and
# Hokkaido, is becoming a nationwide standard. Kyouma is used around
# Kyoto, Osaka and Kyuushu, and Chuukyouma is used around Nagoya.
# Note that the tatami all have the aspect ratio 2:1 so that the mats
# can tile the room with some of them turned 90 degrees.
#
# http://www.moon2.net/tatami/infotatami/structure.html
edoma (5.8*2.9) shaku^2
kyouma (6.3*3.15) shaku^2
chuukyouma (6*3) shaku^2
jou_area edoma
tatami jou_area
# Japanese Volume Measures
# The "shou" is still used for such things as alcohol and seasonings.
# Large quantities of paint are still purchased in terms of "to".
shaku_volume 1|10 gou_volume
gou_volume 1|10 shou
gou gou_volume
shou (4.9*4.9*2.7) sun^3 # The character shou which is
# the same as masu refers to a
# rectangular wooden cup used to
# measure liquids and cereal.
# Sake is sometimes served in a masu
# Note that it happens to be
# EXACTLY 7^4/11^3 liters.
to 10 shou
koku 10 to # No longer used; historically a measure of rice
# Japanese Weight Measures
#
# https://web.archive.org/web/20040927115452/http://wyoming.hp.infoseek.co.jp/zatugaku/zamoney.html
# https://en.wikipedia.org/wiki/Japanese_units_of_measurement
# Not really used anymore.
rin_weight 1|10 bu_weight
bu_weight 1|10 monme
fun 1|10 monme
monme momme
kin 160 monme
kan 1000 monme
kwan kan # This was the old pronunciation of the unit.
# The old spelling persisted a few centuries
# longer and was not changed until around
# 1950.
# http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement
# says: "Volume measure in Taiwan is largely metric".
taijin kin # http://zh.wikipedia.org/wiki/台斤
tailiang 10 monme # http://zh.wikipedia.org/wiki/台斤
taiqian monme # http://zh.wikipedia.org/wiki/台制
!utf8
台斤 taijin # via Hanyu Pinyin romanizations
台兩 tailiang
台錢 taiqian
!endutf8
#
# Australian unit
#
australiasquare (10 ft)^2 # Used for house area
#
# A few German units as currently in use.
#
zentner 50 kg
doppelzentner 2 zentner
pfund 500 g
# The klafter, which was used in central Europe, was derived from the span of
# outstretched arms.
#
# https://en.wikipedia.org/wiki/Obsolete_Austrian_units_of_measurement
# https://www.llv.li/files/abi/klafter-m2-en.pdf
austriaklafter 1.89648384 m # Exact definition, 23 July 1871
austriafoot 1|6 austriaklafter
prussiaklafter 1.88 m
prussiafoot 1|6 prussiaklafter
bavariaklafter 1.751155 m
bavariafoot 1|6 bavariaklafter
hesseklafter 2.5 m
hessefoot 1|6 hesseklafter
switzerlandklafter metricklafter
switzerlandfoot 1|6 switzerlandklafter
swissklafter switzerlandklafter
swissfoot 1|6 swissklafter
metricklafter 1.8 m
austriayoke 8 austriaklafter * 200 austriaklafter
liechtensteinsquareklafter 3.596652 m^2 # Used until 2017 to measure land area
liechtensteinklafter sqrt(liechtensteinsquareklafter)
# The klafter was also used to measure volume of wood, generally being a stack
# of wood one klafter wide, one klafter long, with logs 3 feet (half a klafter)
# in length
prussiawoodklafter 0.5 prussiaklafter^3
austriawoodklafter 0.5 austriaklafter^3
festmeter m^3 # modern measure of wood, solid cube
raummeter 0.7 festmeter # Air space between the logs, stacked
schuettraummeter 0.65 raummeter # A cubic meter volume of split and cut
# firewood in a loose, unordered
# pile, not stacked. This is called
# "tipped".
!utf8
schüttraummeter schuettraummeter
!endutf8
#
# Swedish (Sweden) pre-metric units of 1739.
# The metric system was adopted in 1878.
# https://sv.wikipedia.org/wiki/Verkm%C3%A5tt
#
verklinje 2.0618125 mm
verktum 12 verklinje
kvarter 6 verktum
fot 2 kvarter
aln 2 fot
famn 3 aln
#
# Some traditional Russian measures
#
# If you would like to help expand this section and understand
# cyrillic transliteration, let me know. These measures are meant to
# reflect common usage, e.g. in translated literature.
#
dessiatine 2400 sazhen^2 # Land measure
dessjatine dessiatine
funt 409.51718 grams # similar to pound
zolotnik 1|96 funt # used for precious metal measure
pood 40 funt # common in agricultural measure
arshin (2 + 1|3) feet
sazhen 3 arshin # analogous to fathom
verst 500 sazhen # of similar use to mile
versta verst
borderverst 1000 sazhen
russianmile 7 verst
#
# Old French distance measures, from French Weights and Measures
# Before the Revolution by Zupko
#
frenchfoot 144|443.296 m # pied de roi, the standard of Paris.
pied frenchfoot # Half of the hashimicubit,
frenchfeet frenchfoot # instituted by Charlemagne.
frenchinch 1|12 frenchfoot # This exact definition comes from
frenchthumb frenchinch # a law passed on 10 Dec 1799 which
pouce frenchthumb # fixed the meter at
# 3 frenchfeet + 11.296 lignes.
frenchline 1|12 frenchinch # This is supposed to be the size
ligne frenchline # of the average barleycorn
frenchpoint 1|12 frenchline
toise 6 frenchfeet
arpent 180^2 pied^2 # The arpent is 100 square perches,
# but the perche seems to vary a lot
# and can be 18 feet, 20 feet, or 22
# feet. This measure was described
# as being in common use in Canada in
# 1934 (Websters 2nd). The value
# given here is the Paris standard
# arpent.
frenchgrain 1|18827.15 kg # Weight of a wheat grain, hence
# smaller than the British grain.
frenchpound 9216 frenchgrain
#
# Before the Imperial Weights and Measures Act of 1824, various different
# weights and measures were in use in different places.
#
# Scots linear measure
scotsinch 1.00540054 UKinch
scotslink 1|100 scotschain
scotsfoot 12 scotsinch
scotsfeet scotsfoot
scotsell 37 scotsinch
scotsfall 6 scotsell
scotschain 4 scotsfall
scotsfurlong 10 scotschain
scotsmile 8 scotsfurlong
# Scots area measure
scotsrood 40 scotsfall^2
scotsacre 4 scotsrood
# Irish linear measure
irishinch UKinch
irishpalm 3 irishinch
irishspan 3 irishpalm
irishfoot 12 irishinch
irishfeet irishfoot
irishcubit 18 irishinch
irishyard 3 irishfeet
irishpace 5 irishfeet
irishfathom 6 irishfeet
irishpole 7 irishyard # Only these values
irishperch irishpole # are different from
irishchain 4 irishperch # the British Imperial
irishlink 1|100 irishchain # or English values for
irishfurlong 10 irishchain # these lengths.
irishmile 8 irishfurlong #
# Irish area measure
irishrood 40 irishpole^2
irishacre 4 irishrood
# English wine capacity measures (Winchester measures)
winepint 1|2 winequart
winequart 1|4 winegallon
winegallon 231 UKinch^3 # Sometimes called the Winchester Wine Gallon,
# it was legalized in 1707 by Queen Anne, and
# given the definition of 231 cubic inches. It
# had been in use for a while as 8 pounds of wine
# using a merchant's pound, but the definition of
# the merchant's pound had become uncertain. A
# pound of 15 tower ounces (6750 grains) had been
# common, but then a pound of 15 troy ounces
# (7200 grains) gained popularity. Because of
# the switch in the value of the merchants pound,
# the size of the wine gallon was uncertain in
# the market, hence the official act in 1707.
# The act allowed that a six inch tall cylinder
# with a 7 inch diameter was a lawful wine
# gallon. (This comes out to 230.9 in^3.)
# Note also that in Britain a legal conversion
# was established to the 1824 Imperial gallon
# then taken as 277.274 in^3 so that the wine
# gallon was 0.8331 imperial gallons. This is
# 231.1 cubic inches (using the international
# inch).
winerundlet 18 winegallon
winebarrel 31.5 winegallon
winetierce 42 winegallon
winehogshead 2 winebarrel
winepuncheon 2 winetierce
winebutt 2 winehogshead
winepipe winebutt
winetun 2 winebutt
# English beer and ale measures used 1803-1824 and used for beer before 1688
beerpint 1|2 beerquart
beerquart 1|4 beergallon
beergallon 282 UKinch^3
beerbarrel 36 beergallon
beerhogshead 1.5 beerbarrel
# English ale measures used from 1688-1803 for both ale and beer
alepint 1|2 alequart
alequart 1|4 alegallon
alegallon beergallon
alebarrel 34 alegallon
alehogshead 1.5 alebarrel
# Scots capacity measure
scotsgill 1|4 mutchkin
mutchkin 1|2 choppin
choppin 1|2 scotspint
scotspint 1|2 scotsquart
scotsquart 1|4 scotsgallon
scotsgallon 827.232 UKinch^3
scotsbarrel 8 scotsgallon
jug scotspint
# Scots dry capacity measure
scotswheatlippy 137.333 UKinch^3 # Also used for peas, beans, rye, salt
scotswheatlippies scotswheatlippy
scotswheatpeck 4 scotswheatlippy
scotswheatfirlot 4 scotswheatpeck
scotswheatboll 4 scotswheatfirlot
scotswheatchalder 16 scotswheatboll
scotsoatlippy 200.345 UKinch^3 # Also used for barley and malt
scotsoatlippies scotsoatlippy
scotsoatpeck 4 scotsoatlippy
scotsoatfirlot 4 scotsoatpeck
scotsoatboll 4 scotsoatfirlot
scotsoatchalder 16 scotsoatboll
# Scots Tron weight
trondrop 1|16 tronounce
tronounce 1|20 tronpound
tronpound 9520 grain
tronstone 16 tronpound
# Irish liquid capacity measure
irishnoggin 1|4 irishpint
irishpint 1|2 irishquart
irishquart 1|2 irishpottle
irishpottle 1|2 irishgallon
irishgallon 217.6 UKinch^3
irishrundlet 18 irishgallon
irishbarrel 31.5 irishgallon
irishtierce 42 irishgallon
irishhogshead 2 irishbarrel
irishpuncheon 2 irishtierce
irishpipe 2 irishhogshead
irishtun 2 irishpipe
# Irish dry capacity measure
irishpeck 2 irishgallon
irishbushel 4 irishpeck
irishstrike 2 irishbushel
irishdrybarrel 2 irishstrike
irishquarter 2 irishbarrel
# English Tower weights, abolished in 1528
towerpound 5400 grain
towerounce 1|12 towerpound
towerpennyweight 1|20 towerounce
towergrain 1|32 towerpennyweight
# English Mercantile weights, used since the late 12th century
mercpound 6750 grain
mercounce 1|15 mercpound
mercpennyweight 1|20 mercounce
# English weights for lead
leadstone 12.5 lb
fotmal 70 lb
leadwey 14 leadstone
fothers 12 leadwey
# English Hay measure
newhaytruss 60 lb # New and old here seem to refer to "new"
newhayload 36 newhaytruss # hay and "old" hay rather than a new unit
oldhaytruss 56 lb # and an old unit.
oldhayload 36 oldhaytruss
# English wool measure
woolclove 7 lb
woolstone 2 woolclove
wooltod 2 woolstone
woolwey 13 woolstone
woolsack 2 woolwey
woolsarpler 2 woolsack
woollast 6 woolsarpler
#
# Ancient history units: There tends to be uncertainty in the definitions
# of the units in this section
# These units are from [11]
# Roman measure. The Romans had a well defined distance measure, but their
# measures of weight were poor. They adopted local weights in different
# regions without distinguishing among them so that there are half a dozen
# different Roman "standard" weight systems.
romanfoot 296 mm # There is some uncertainty in this definition
romanfeet romanfoot # from which all the other units are derived.
pes romanfoot # This value appears in numerous sources. In "The
pedes romanfoot # Roman Land Surveyors", Dilke gives 295.7 mm.
romaninch 1|12 romanfoot # The subdivisions of the Roman foot have the
romandigit 1|16 romanfoot # same names as the subdivisions of the pound,
romanpalm 1|4 romanfoot # but we can't have the names for different
romancubit 18 romaninch # units.
romanpace 5 romanfeet # Roman double pace (basic military unit)
passus romanpace
romanperch 10 romanfeet
stade 125 romanpaces
stadia stade
stadium stade
romanmile 8 stadia # 1000 paces
romanleague 1.5 romanmile
schoenus 4 romanmile
# Other values for the Roman foot (from Dilke)
earlyromanfoot 29.73 cm
pesdrusianus 33.3 cm # or 33.35 cm, used in Gaul & Germany in 1st c BC
lateromanfoot 29.42 cm
# Roman areas
actuslength 120 romanfeet # length of a Roman furrow
actus 120*4 romanfeet^2 # area of the furrow
squareactus 120^2 romanfeet^2 # actus quadratus
acnua squareactus
iugerum 2 squareactus
iugera iugerum
jugerum iugerum
jugera iugerum
heredium 2 iugera # heritable plot
heredia heredium
centuria 100 heredia
centurium centuria
# Roman volumes
sextarius 35.4 in^3 # Basic unit of Roman volume. As always,
sextarii sextarius # there is uncertainty. Six large Roman
# measures survive with volumes ranging from
# 34.4 in^3 to 39.55 in^3. Three of them
# cluster around the size given here.
#
# But the values for this unit vary wildly
# in other sources. One reference gives 0.547
# liters, but then says the amphora is a
# cubic Roman foot. This gives a value for the
# sextarius of 0.540 liters. And the
# encyclopedia Britannica lists 0.53 liters for
# this unit. Both [7] and [11], which were
# written by scholars of weights and measures,
# give the value of 35.4 cubic inches.
cochlearia 1|48 sextarius
cyathi 1|12 sextarius
acetabula 1|8 sextarius
quartaria 1|4 sextarius
quartarius quartaria
heminae 1|2 sextarius
hemina heminae
cheonix 1.5 sextarii
# Dry volume measures (usually)
semodius 8 sextarius
semodii semodius
modius 16 sextarius
modii modius
# Liquid volume measures (usually)
congius 12 heminae
congii congius
amphora 8 congii
amphorae amphora # Also a dry volume measure
culleus 20 amphorae
quadrantal amphora
# Roman weights
libra 5052 grain # The Roman pound varied significantly
librae libra # from 4210 grains to 5232 grains. Most of
romanpound libra # the standards were obtained from the weight
uncia 1|12 libra # of particular coins. The one given here is
unciae uncia # based on the Gold Aureus of Augustus which
romanounce uncia # was in use from BC 27 to AD 296.
deunx 11 uncia
dextans 10 uncia
dodrans 9 uncia
bes 8 uncia
seprunx 7 uncia
semis 6 uncia
quincunx 5 uncia
triens 4 uncia
quadrans 3 uncia
sextans 2 uncia
sescuncia 1.5 uncia
semuncia 1|2 uncia
siscilius 1|4 uncia
sextula 1|6 uncia
semisextula 1|12 uncia
scriptulum 1|24 uncia
scrupula scriptulum
romanobol 1|2 scrupula
romanaspound 4210 grain # Old pound based on bronze coinage, the
# earliest money of Rome BC 338 to BC 268.
# Egyptian length measure
egyptianroyalcubit 20.63 in # plus or minus .2 in
egyptianpalm 1|7 egyptianroyalcubit
egyptiandigit 1|4 egyptianpalm
egyptianshortcubit 6 egyptianpalm
doubleremen 29.16 in # Length of the diagonal of a square with
remendigit 1|40 doubleremen # side length of 1 royal egyptian cubit.
# This is divided into 40 digits which are
# not the same size as the digits based on
# the royal cubit.
# Greek length measures
greekfoot 12.45 in # Listed as being derived from the
greekfeet greekfoot # Egyptian Royal cubit in [11]. It is
greekcubit 1.5 greekfoot # said to be 3|5 of a 20.75 in cubit.
pous greekfoot
podes greekfoot
orguia 6 greekfoot
greekfathom orguia
stadion 100 orguia
akaina 10 greekfeet
plethron 10 akaina
greekfinger 1|16 greekfoot
homericcubit 20 greekfingers # Elbow to end of knuckles.
shortgreekcubit 18 greekfingers # Elbow to start of fingers.
ionicfoot 296 mm
doricfoot 326 mm
olympiccubit 25 remendigit # These olympic measures were not as
olympicfoot 2|3 olympiccubit # common as the other greek measures.
olympicfinger 1|16 olympicfoot # They were used in agriculture.
olympicfeet olympicfoot
olympicdakylos olympicfinger
olympicpalm 1|4 olympicfoot
olympicpalestra olympicpalm
olympicspithame 3|4 foot
olympicspan olympicspithame
olympicbema 2.5 olympicfeet
olympicpace olympicbema
olympicorguia 6 olympicfeet
olympicfathom olympicorguia
olympiccord 60 olympicfeet
olympicamma olympiccord
olympicplethron 100 olympicfeet
olympicstadion 600 olympicfeet
# Greek capacity measure
greekkotyle 270 ml # This approximate value is obtained
xestes 2 greekkotyle # from two earthenware vessels that
khous 12 greekkotyle # were reconstructed from fragments.
metretes 12 khous # The kotyle is a day's corn ration
choinix 4 greekkotyle # for one man.
hekteos 8 choinix
medimnos 6 hekteos
# Greek weight. Two weight standards were used, an Aegina standard based
# on the Beqa shekel and an Athens (attic) standard.
aeginastater 192 grain # Varies up to 199 grain
aeginadrachmae 1|2 aeginastater
aeginaobol 1|6 aeginadrachmae
aeginamina 50 aeginastaters
aeginatalent 60 aeginamina # Supposedly the mass of a cubic foot
# of water (whichever foot was in use)
atticstater 135 grain # Varies 134-138 grain
atticdrachmae 1|2 atticstater
atticobol 1|6 atticdrachmae
atticmina 50 atticstaters
attictalent 60 atticmina # Supposedly the mass of a cubic foot
# of water (whichever foot was in use)
# "Northern" cubit and foot. This was used by the pre-Aryan civilization in
# the Indus valley. It was used in Mesopotamia, Egypt, North Africa, China,
# central and Western Europe until modern times when it was displaced by
# the metric system.
northerncubit 26.6 in # plus/minus .2 in
northernfoot 1|2 northerncubit
sumeriancubit 495 mm
kus sumeriancubit
sumerianfoot 2|3 sumeriancubit
assyriancubit 21.6 in
assyrianfoot 1|2 assyriancubit
assyrianpalm 1|3 assyrianfoot
assyriansusi 1|20 assyrianpalm
susi assyriansusi
persianroyalcubit 7 assyrianpalm
# Arabic measures. The arabic standards were meticulously kept. Glass weights
# accurate to .2 grains were made during AD 714-900.
hashimicubit 25.56 in # Standard of linear measure used
# in Persian dominions of the Arabic
# empire 7-8th cent. Is equal to two
# French feet.
blackcubit 21.28 in
arabicfeet 1|2 blackcubit
arabicfoot arabicfeet
arabicinch 1|12 arabicfoot
arabicmile 4000 blackcubit
silverdirhem 45 grain # The weights were derived from these two
tradedirhem 48 grain # units with two identically named systems
# used for silver and used for trade purposes
silverkirat 1|16 silverdirhem
silverwukiyeh 10 silverdirhem
silverrotl 12 silverwukiyeh
arabicsilverpound silverrotl
tradekirat 1|16 tradedirhem
tradewukiyeh 10 tradedirhem
traderotl 12 tradewukiyeh
arabictradepound traderotl
# Miscellaneous ancient units
parasang 3.5 mile # Persian unit of length usually thought
# to be between 3 and 3.5 miles
biblicalcubit 21.8 in
hebrewcubit 17.58 in
li 10|27.8 mile # Chinese unit of length
# 100 li is considered a day's march
liang 11|3 oz # Chinese weight unit
# Medieval time units. According to the OED, these appear in Du Cange
# by Papias.
timepoint 1|5 hour # also given as 1|4
timeminute 1|10 hour
timeostent 1|60 hour
timeounce 1|8 timeostent
timeatom 1|47 timeounce
# Given in [15], these subdivisions of the grain were supposedly used
# by jewelers. The mite may have been used but the blanc could not
# have been accurately measured.
mite 1|20 grain
droit 1|24 mite
periot 1|20 droit
blanc 1|24 periot
#
# Localization
#
!var UNITS_ENGLISH US
hundredweight ushundredweight
ton uston
scruple apscruple
fluidounce usfluidounce
gallon usgallon
bushel usbushel
quarter quarterweight
cup uscup
tablespoon ustablespoon
teaspoon usteaspoon
dollar US$
cent $ 0.01
penny cent
minim minimvolume
pony ponyvolume
grand usgrand
firkin usfirkin
hogshead ushogshead
cable uscable
!endvar
!var UNITS_ENGLISH GB
hundredweight brhundredweight
ton brton
scruple brscruple
fluidounce brfluidounce
gallon brgallon
bushel brbushel
quarter brquarter
chaldron brchaldron
cup brcup
teacup brteacup
tablespoon brtablespoon
teaspoon brteaspoon
dollar US$
cent $ 0.01
penny brpenny
minim minimnote
pony brpony
grand brgrand
firkin brfirkin
hogshead brhogshead
cable brcable
!endvar
!varnot UNITS_ENGLISH GB US
!message Unknown value for environment variable UNITS_ENGLISH. Should be GB or US.
!endvar
!utf8
⅛- 1|8
¼- 1|4
⅜- 3|8
½- 1|2
⅝- 5|8
¾- 3|4
⅞- 7|8
⅙- 1|6
⅓- 1|3
⅔- 2|3
⅚- 5|6
⅕- 1|5
⅖- 2|5
⅗- 3|5
⅘- 4|5
# U+2150- 1|7 For some reason these characters are getting
# U+2151- 1|9 flagged as invalid UTF8.
# U+2152- 1|10
#⅐- 1|7 # fails under MacOS
#⅑- 1|9 # fails under MacOS
#⅒- 1|10 # fails under MacOS
ℯ exp(1) # U+212F, base of natural log
µ- micro # micro sign U+00B5
μ- micro # small mu U+03BC
ångström angstrom
Å angstrom # angstrom symbol U+212B
Å angstrom # A with ring U+00C5
röntgen roentgen
°C degC
°F degF
°K K # °K is incorrect notation
°R degR
° degree
℃ degC
℉ degF
K K # Kelvin symbol, U+212A
ℓ liter # unofficial abbreviation used in some places
Ω ohm # Ohm symbol U+2126
Ω ohm # Greek capital omega U+03A9
℧ mho
G₀ G0
H₀ H0
Z₀ Z0
a₀ a0
n₀ n0
ε₀ epsilon0
μ₀ mu0
Φ₀ Phi0
R∞ Rinfinity
R_∞ Rinfinity
λ_C lambda_C
μ_B mu_B
ν_133Cs nu_133Cs
ʒ dram # U+0292
℈ scruple
℥ ounce
℔ lb
ℎ h
ℏ hbar
τ tau
π pi # Greek letter pi
𝜋 pi # mathematical italic small pi
α alpha
σ sigma
‰ 1|1000
‱ 1|10000
′ ' # U+2032
″ " # U+2033
#
# Unicode currency symbols
#
¢ cent
£ britainpound
¥ japanyen
€ euro
₩ southkoreawon
₪ israelnewshekel
₤ lira
# ₺ turkeylira # fails under MacOS
₨ rupee # unofficial legacy rupee sign
# ₹ indiarupee # official rupee sign # MacOS fail
#؋ afghanafghani # fails under MacOS
฿ thailandbaht
₡ costaricacolon
₣ francefranc
₦ nigerianaira
₧ spainpeseta
₫ vietnamdong
₭ laokip
₮ mongoliatugrik
₯ greecedrachma
₱ philippinepeso
# ₲ paraguayguarani # fails under MacOS
#₴ ukrainehryvnia # fails under MacOS
#₵ ghanacedi # fails under MacOS
#₸ kazakhstantenge # fails under MacOS
#₼ azerbaijanmanat # fails under MacOS
#₽ russiaruble # fails under MacOS
#₾ georgialari # fails under MacOS
﷼ iranrial
﹩ $
￠ ¢
￡ £
￥ ¥
￦ ₩
#
# Square Unicode symbols starting at U+3371
#
㍱ hPa
㍲ da
㍳ au
㍴ bar
# ㍵ oV???
㍶ pc
#㍷ dm invalid on Mac
#㍸ dm^2 invalid on Mac
#㍹ dm^3 invalid on Mac
㎀ pA
㎁ nA
㎂ µA
㎃ mA
㎄ kA
㎅ kB
㎆ MB
㎇ GB
㎈ cal
㎉ kcal
㎊ pF
㎋ nF
㎌ µF
㎍ µg
㎎ mg
㎏ kg
㎐ Hz
㎑ kHz
㎒ MHz
㎓ GHz
㎔ THz
㎕ µL
㎖ mL
㎗ dL
㎘ kL
㎙ fm
㎚ nm
㎛ µm
㎜ mm
㎝ cm
㎞ km
㎟ mm^2
㎠ cm^2
㎡ m^2
㎢ km^2
㎣ mm^3
㎤ cm^3
㎥ m^3
㎦ km^3
㎧ m/s
㎨ m/s^2
㎩ Pa
㎪ kPa
㎫ MPa
㎬ GPa
㎭ rad
㎮ rad/s
㎯ rad/s^2
㎰ ps
㎱ ns
㎲ µs
㎳ ms
㎴ pV
㎵ nV
㎶ µV
㎷ mV
㎸ kV
㎹ MV
㎺ pW
㎻ nW
㎼ µW
㎽ mW
㎾ kW
㎿ MW
㏀ kΩ
㏁ MΩ
㏃ Bq
㏄ cc
㏅ cd
㏆ C/kg
㏈() dB
㏉ Gy
㏊ ha
# ㏋ HP??
㏌ in
# ㏍ KK??
# ㏎ KM???
㏏ kt
㏐ lm
# ㏑ ln
# ㏒ log
㏓ lx
㏔ mb
㏕ mil
㏖ mol
㏗() pH
㏙ ppm
# ㏚ PR???
㏛ sr
㏜ Sv
㏝ Wb
#㏞ V/m Invalid on Mac
#㏟ A/m Invalid on Mac
#㏿ gal Invalid on Mac
!endutf8
############################################################################
#
# Unit list aliases
#
# These provide a shorthand for conversions to unit lists.
#
############################################################################
!unitlist uswt lb;oz
!unitlist hms hr;min;sec
!unitlist time year;day;hr;min;sec
!unitlist dms deg;arcmin;arcsec
!unitlist ftin ft;in;1|8 in
!unitlist inchfine in;1|8 in;1|16 in;1|32 in;1|64 in
!unitlist usvol cup;3|4 cup;2|3 cup;1|2 cup;1|3 cup;1|4 cup;\
tbsp;tsp;1|2 tsp;1|4 tsp;1|8 tsp
############################################################################
#
# The following units were in the Unix units database but do not appear in
# this file:
#
# wey used for cheese, salt and other goods. Measured mass or
# waymass volume depending on what was measured and where the measuring
# took place. A wey of cheese ranged from 200 to 324 pounds.
#
# sack No precise definition
#
# spindle The length depends on the type of yarn
#
# block Defined variously on different computer systems
#
# erlang A unit of telephone traffic defined variously.
# Omitted because there are no other units for this
# dimension. Is this true? What about CCS = 1/36 erlang?
# Erlang is supposed to be dimensionless. One erlang means
# a single channel occupied for one hour.
#
############################################################################
#
# The following have been suggested or considered and deemed out of scope.
# They will not be added to GNU units.
#
# Conversions between different calendar systems used in different countries or
# different historical periods are out of scope for units and will not be added.
#
# Wind chill and heat index cannot be handled because they are bivarite,
# with dependence on both the temperature and wind speed or humidity.
#
# Plain english text output like "one hectare is equivalent to one hundred
# million square centimeters" is out of scope.
#