# Unit reference
This page lists all available units, prefixes, and physical constants.
How to use units is explained on the page [Units](../datatypes/units.md).
## 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](http://en.wikipedia.org/wiki/Physical_constants) 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