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definitions.units.patched
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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
#
# September 2022 Version 3.15
#
# Copyright (C) 1996-2002, 2004-2020, 2022
# 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
# http://www.ukmetrication.com/history.htm
# 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 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.
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 (m^2*kg/s^2) 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 (m^2*kg/s^2)/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 A s # 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.
#
# 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 # The angle subtended at the center of a circle by
# an arc equal in length to the radius of the
# circle
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
#
# A primitive non-SI unit
#
B !
byte B
bit 1|8 B # 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.
#
###########################################################################
# #
# Prefixes (longer names must come first) #
# #
###########################################################################
quetta- 1e30
ronna- 1e27
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
quecto- 1e-30
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
mu- micro
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
# postgresql-unit: Define some units before they are used elsewhere before their original definition
pi 3.14159265358979323846
π pi
astronomicalunit 149597870700 m # IAU definition from 2012, exact
au astronomicalunit # ephemeris for the above described
m2 m^2
#############################################################################
# #
# 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
H henry
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
VELOCITY LENGTH / TIME
ACCELERATION VELOCITY / TIME
MOMENTUM MASS VELOCITY
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
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
# valule 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 milliarcsec # 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