# 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 | 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 | μ_B | 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 | μ_N | 5.0507835311e-27 | J · T^-1 klitzing | R_K | 25812.807443484 | Ω ### Atomic and nuclear constants Name | Symbol | Value | Unit ------------------------|------------------------------|-----------------------|---------------------------------- bohrRadius | a₀ | 5.291772109217e-11 | m classicalElectronRadius | r_e | 2.817940326727e-15 | m electronMass | m_e | 9.1093829140e-31 | kg fermiCoupling | G_F | 1.1663645e-5 | GeV^-2 fineStructure | α | 7.297352569824e-3 | - hartreeEnergy | Eh | 4.3597443419e-18 | J protonMass | m_p | 1.67262177774e-27 | kg deuteronMass | m_d | 3.3435830926e-27 | kg neutronMass | m_n | 1.6749271613e-27 | kg quantumOfCirculation | h / (2m_e) | 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 | m_u | 1.66053892173e-27 | kg avogadro | N_A | 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 | N_A · h| 3.990312717628e-10| J · s · mol^-1 molarVolume | V_m | 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 | M_u | 1e-3 | kg · mol^-1 molarMassC12 | M(₁₂C) | 1.2e-2 | kg · mol^-1 gravity | g_n | 9.80665 | m · s^-2 atm | atm | 101325 | Pa ### Natural units Name | Symbol | Value | Unit ------------------|-----------------------|--------------------|----- planckLength | l_P | 1.61619997e-35 | m planckMass | m_P | 2.1765113e-8 | kg planckTime | t_P | 5.3910632e-44 | s planckCharge | q_P | 1.87554595641e-18 | C planckTemperature | T_P | 1.41683385e+32 | K