mathjs
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Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser and offers an integrated solution to work with numbers, big numbers, complex numbers, units, and matrices.
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# 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, deg, grad, cycle
Time | second (s), seconds, minute (minutes), hour (h, hours), day (days)
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 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 | <i>c</i> | 299792458 | m · s<sup>-1</sup>
gravitationConstant | <i>G</i> | 6.6738480e-11 | m<sup>3</sup> · kg<sup>-1</sup> · s<sup>-2</sup>
planckConstant | <i>h</i> | 6.626069311e-34 | J · s
reducedPlanckConstant | <i><span style="text-decoration:overline">h</span></i> | 1.05457172647e-34 | J · s
### Electromagnetic
Name | Symbol | Value | Unit
--------------------------|--------------------------------------------------|-----------------------|----------------------------------------
magneticConstant | <i>μ<sub>0</sub></i> | 1.2566370614e-6 | N · A<sup>-2</sup>
electricConstant | <i>ε<sub>0</sub></i> | 8.854187817e-12 | F · m<sup>-1</sup>
vacuumImpedance | <i>Z<sub>0</sub></i> | 376.730313461 | Ω
coulomb | <i>κ</i> | 8.9875517873681764e9 | N · m<sup>2</sup> · C<sup>-2</sup>
elementaryCharge | <i>e</i> | 1.60217656535e-19 | C
bohrMagneton | <i>μ<sub>B</sub></i> | 9.2740096820e-24 | J · T<sup>-1</sup>
conductanceQuantum | <i>G<sub>0</sub></i> | 7.748091734625e-5 | S
inverseConductanceQuantum | <i>G<sub>0</sub><sup>-1</sup></i> | 12906.403721742 | Ω
magneticFluxQuantum | <i><font face="Symbol">f</font><sub>0</sub></i> | 2.06783375846e-15 | Wb
nuclearMagneton | <i>μ<sub>N</sub></i> | 5.0507835311e-27 | J · T<sup>-1</sup>
klitzing | <i>R<sub>K</sub></i> | 25812.807443484 | Ω
<!-- TODO: implement josephson
josephson | <i>K<sub>J</sub></i> | 4.8359787011e-14 | Hz · V<sup>-1</sup>
-->
### Atomic and nuclear constants
Name | Symbol | Value | Unit
------------------------|------------------------------|-----------------------|----------------------------------
bohrRadius | <i>a<sub>0</sub></i> | 5.291772109217e-11 | m
classicalElectronRadius | <i>r<sub>e</sub></i> | 2.817940326727e-15 | m
electronMass | <i>m<sub>e</sub></i> | 9.1093829140e-31 | kg
fermiCoupling | <i>G<sub>F</sub></i> | 1.1663645e-5 | GeV<sup>-2</sup>
fineStructure | <i>α</i> | 7.297352569824e-3 | -
hartreeEnergy | <i>E<abbr>h</abbr> </i> | 4.3597443419e-18 | J
protonMass | <i>m<sub>p</sub></i> | 1.67262177774e-27 | kg
deuteronMass | <i>m<sub>d</sub></i> | 3.3435830926e-27 | kg
neutronMass | <i>m<sub>n</sub></i> | 1.6749271613e-27 | kg
quantumOfCirculation | <i>h / (2m<sub>e</sub>)</i> | 3.636947552024e-4 | m<sup>2</sup> · s<sup>-1</sup>
rydberg | <i>R<sub>∞</sub></i> | 10973731.56853955 | m<sup>-1</sup>
thomsonCrossSection | | 6.65245873413e-29 | m<sup>2</sup>
weakMixingAngle | | 0.222321 | -
efimovFactor | | 22.7 | -
### Physico-chemical constants
Name | Symbol | Value | Unit
--------------------|------------------------------|---------------------|--------------------------------------------
atomicMass | <i>m<sub>u</sub></i> | 1.66053892173e-27 | kg
avogadro | <i>N<sub>A</sub></i> | 6.0221412927e23 | mol<sup>-1</sup>
boltzmann | <i>k</i> | 1.380648813e-23 | J · K<sup>-1</sup>
faraday | <i>F</i> | 96485.336521 | C · mol<sup>-1</sup>
firstRadiation | <i>c<sub>1</sub></i> | 3.7417715317e-16 | W · m<sup>2</sup>
loschmidt | <i>n<sub>0</sub></i> | 2.686780524e25 | m<sup>-3</sup>
gasConstant | <i>R</i> | 8.314462175 | J · K<sup>-1</sup> · mol<sup>-1</sup>
molarPlanckConstant | <i>N<sub>A</sub> · h</i>| 3.990312717628e-10| J · s · mol<sup>-1</sup>
molarVolume | <i>V<sub>m</sub></i> | 2.241396820e-10 | m<sup>3</sup> · mol<sup>-1</sup>
sackurTetrode | | -1.164870823 | -
secondRadiation | <i>c<sub>2</sub></i> | 1.438777013e-2 | m · K
stefanBoltzmann | <i>σ</i> | 5.67037321e-8 | W · m<sup>-2</sup> · K<sup>-4</sup>
wienDisplacement | <i>b</i> | 2.897772126e-3 | m · K
<!-- TODO: implement spectralRadiance
spectralRadiance | <i>c<sub>1L</sub></i> | 1.19104286953e-16 | W · m<sup>2</sup> · sr<sup>-1</sup>
-->
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 | <i>M<sub>u</sub></i> | 1e-3 | kg · mol<sup>-1</sup>
molarMassC12 | <i>M(<sub>12</sub>C)</i> | 1.2e-2 | kg · mol<sup>-1</sup>
gravity | <i>g<sub>n</sub></i> | 9.80665 | m · s<sup>-2</sup>
atm | <i>atm</i> | 101325 | Pa
### Natural units
Name | Symbol | Value | Unit
------------------|-----------------------|--------------------|-----
planckLength | <i>l<sub>P</sub></i> | 1.61619997e-35 | m
planckMass | <i>m<sub>P</sub></i> | 2.1765113e-8 | kg
planckTime | <i>t<sub>P</sub></i> | 5.3910632e-44 | s
planckCharge | <i>q<sub>P</sub></i> | 1.87554595641e-18 | C
planckTemperature | <i>T<sub>P</sub></i> | 1.41683385e+32 | K