mathjs/docs/reference/units.md

Unit reference

This page lists all available units, prefixes, and physical constants. How to use units is explained on the page Units.

Units

Math.js comes with the following built-in units.

Base	Unit
Length	meter (m), inch (in), foot (ft), yard (yd), mile (mi), link (li), rod (rd), chain (ch), angstrom, mil
Surface	m2, sqin, sqft, sqyd, sqmi, sqrd, sqch, sqmil
Volume	m3, litre (l, L, lt, liter), cc, cuin, cuft, cuyd, teaspoon, tablespoon
Liquid volume	minim (min), fluiddram (fldr), fluidounce (floz), gill (gi), cup (cp), pint (pt), quart (qt), gallon (gal), beerbarrel (bbl), oilbarrel (obl), hogshead, drop (gtt)
Angles	rad (radian), deg (degree), grad (gradian), cycle, arcsec (arcsecond), arcmin (arcminute)
Time	second (s), seconds, minute (minutes), hour (h, hours), day (days), week (weeks), month (months), year (years), decade (decades), century (centuries), millennium (millennia)
Frequency	hertz (Hz)
Mass	gram(g), tonne, ton, grain (gr), dram(dr), ounce (oz), poundmass (lbm, lb, lbs), hundredweight (cwt), stick, stone
Electric current	ampere (A)
Temperature	kelvin (K), celsius (degC), fahrenheit (degF), rankine (degR)
Amount of substance	mole (mol)
Luminous intensity	candela (cd)
Force	newton (N), dyne (dyn), poundforce (lbf)
Energy	joule (J), erg, Wh, BTU, electronvolt (eV)
Power	watt (W), hp
Pressure	Pa, psi, atm
Electricity and magnetism	ampere (A), coulomb (C), watt (W), volt (V), ohm, farad (F), weber (Wb), tesla (T), henry (H), siemens (S), electronvolt (eV)
Binary	bit (b), byte (B)

Note: all time units are based on the Julian year, with one month being 1/12th of a Julian year, a year being one Julian year, a decade being 10 Julian years, a century being 100, and a millennium being 1000.

Note that all relevant units can also be written in plural form, for example 5 meters instead of 5 meter or 10 seconds instead of 10 second.

Surface and volume units can alternatively be expressed in terms of length units raised to a power, for example 100 in^2 instead of 100 sqin.

Prefixes

The following decimal prefixes are available.

Name	Abbreviation	Value
deca	da	1e1
hecto	h	1e2
kilo	k	1e3
mega	M	1e6
giga	G	1e9
tera	T	1e12
peta	P	1e15
exa	E	1e18
zetta	Z	1e21
yotta	Y	1e24

Name	Abbreviation	Value
deci	d	1e-1
centi	c	1e-2
milli	m	1e-3
micro	u	1e-6
nano	n	1e-9
pico	p	1e-12
femto	f	1e-15
atto	a	1e-18
zepto	z	1e-21
yocto	y	1e-24

The following binary prefixes are available. They can be used with units bit (b) and byte (B).

Name	Abbreviation	Value
kibi	Ki	1024
mebi	Mi	1024^2
gibi	Gi	1024^3
tebi	Ti	1024^4
pebi	Pi	1024^5
exi	Ei	1024^6
zebi	Zi	1024^7
yobi	Yi	1024^8

Name	Abbreviation	Value
kilo	k	1e3
mega	M	1e6
giga	G	1e9
tera	T	1e12
peta	P	1e15
exa	E	1e18
zetta	Z	1e21
yotta	Y	1e24

Physical Constants

Math.js includes the following physical constants. See Wikipedia for more information.

Universal constants

Name	Symbol	Value	Unit
speedOfLight	c	299792458	m · s-1
gravitationConstant	G	6.6738480e-11	m3 · kg-1 · s-2
planckConstant	h	6.626069311e-34	J · s
reducedPlanckConstant	h	1.05457172647e-34	J · s

Electromagnetic

Name	Symbol	Value	Unit
magneticConstant	μ0	1.2566370614e-6	N · A-2
electricConstant	ε0	8.854187817e-12	F · m-1
vacuumImpedance	Z0	376.730313461	Ω
coulomb	κ	8.9875517873681764e9	N · m2 · C-2
elementaryCharge	e	1.60217656535e-19	C
bohrMagneton	μB	9.2740096820e-24	J · T-1
conductanceQuantum	G0	7.748091734625e-5	S
inverseConductanceQuantum	G0-1	12906.403721742	Ω
magneticFluxQuantum	f0	2.06783375846e-15	Wb
nuclearMagneton	μN	5.0507835311e-27	J · T-1
klitzing	RK	25812.807443484	Ω

Atomic and nuclear constants

Name	Symbol	Value	Unit
bohrRadius	a0	5.291772109217e-11	m
classicalElectronRadius	re	2.817940326727e-15	m
electronMass	me	9.1093829140e-31	kg
fermiCoupling	GF	1.1663645e-5	GeV-2
fineStructure	α	7.297352569824e-3	-
hartreeEnergy	Eh	4.3597443419e-18	J
protonMass	mp	1.67262177774e-27	kg
deuteronMass	md	3.3435830926e-27	kg
neutronMass	mn	1.6749271613e-27	kg
quantumOfCirculation	h / (2me)	3.636947552024e-4	m2 · s-1
rydberg	R∞	10973731.56853955	m-1
thomsonCrossSection		6.65245873413e-29	m2
weakMixingAngle		0.222321	-
efimovFactor		22.7	-

Physico-chemical constants

Name	Symbol	Value	Unit
atomicMass	mu	1.66053892173e-27	kg
avogadro	NA	6.0221412927e23	mol-1
boltzmann	k	1.380648813e-23	J · K-1
faraday	F	96485.336521	C · mol-1
firstRadiation	c1	3.7417715317e-16	W · m2
loschmidt	n0	2.686780524e25	m-3
gasConstant	R	8.314462175	J · K-1 · mol-1
molarPlanckConstant	NA · h	3.990312717628e-10	J · s · mol-1
molarVolume	Vm	2.241396820e-10	m3 · mol-1
sackurTetrode		-1.164870823	-
secondRadiation	c2	1.438777013e-2	m · K
stefanBoltzmann	σ	5.67037321e-8	W · m-2 · K-4
wienDisplacement	b	2.897772126e-3	m · K

Note that the values of loschmidt and molarVolume are at T = 273.15 K and p = 101.325 kPa. The value of sackurTetrode is at T = 1 K and p = 101.325 kPa.

Adopted values

Name	Symbol	Value	Unit
molarMass	Mu	1e-3	kg · mol-1
molarMassC12	M(12C)	1.2e-2	kg · mol-1
gravity	gn	9.80665	m · s-2
atm	atm	101325	Pa

Natural units

Name	Symbol	Value	Unit
planckLength	lP	1.61619997e-35	m
planckMass	mP	2.1765113e-8	kg
planckTime	tP	5.3910632e-44	s
planckCharge	qP	1.87554595641e-18	C
planckTemperature	TP	1.41683385e+32	K