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194 lines
10 KiB
Markdown
194 lines
10 KiB
Markdown
# Unit reference
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This page lists all available units, prefixes, and physical constants.
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How to use units is explained on the page [Units](../datatypes/units.md).
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## Units
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Math.js comes with the following built-in units.
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Base | Unit
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------------------- | ---
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Length | meter (m), inch (in), foot (ft), yard (yd), mile (mi), link (li), rod (rd), chain (ch), angstrom, mil
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Surface | m2, sqin, sqft, sqyd, sqmi, sqrd, sqch, sqmil
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Volume | m3, litre (l, L, lt, liter), cc, cuin, cuft, cuyd, teaspoon, tablespoon
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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)
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Angles | rad (radian), deg (degree), grad (gradian), cycle, arcsec (arcsecond), arcmin (arcminute)
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Time | second (s), seconds, minute (minutes), hour (h, hours), day (days), week (weeks), month (months), year (years), decade (decades), century (centuries), millennium (millennia)
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Frequency | hertz (Hz)
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Mass | gram(g), tonne, ton, grain (gr), dram(dr), ounce (oz), poundmass (lbm, lb, lbs), hundredweight (cwt), stick, stone
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Electric current | ampere (A)
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Temperature | kelvin (K), celsius (degC), fahrenheit (degF), rankine (degR)
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Amount of substance | mole (mol)
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Luminous intensity | candela (cd)
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Force | newton (N), dyne (dyn), poundforce (lbf)
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Energy | joule (J), erg, Wh, BTU, electronvolt (eV)
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Power | watt (W), hp
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Pressure | Pa, psi, atm
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Electricity and magnetism | ampere (A), coulomb (C), watt (W), volt (V), ohm, farad (F), weber (Wb), tesla (T), henry (H), siemens (S), electronvolt (eV)
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Binary | bit (b), byte (B)
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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.
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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`.
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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`.
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## Prefixes
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The following decimal prefixes are available.
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Name | Abbreviation | Value
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------- | ------------- | -----
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deca | da | 1e1
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hecto | h | 1e2
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kilo | k | 1e3
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mega | M | 1e6
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giga | G | 1e9
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tera | T | 1e12
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peta | P | 1e15
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exa | E | 1e18
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zetta | Z | 1e21
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yotta | Y | 1e24
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Name | Abbreviation | Value
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------ | ------------- | -----
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deci | d | 1e-1
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centi | c | 1e-2
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milli | m | 1e-3
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micro | u | 1e-6
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nano | n | 1e-9
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pico | p | 1e-12
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femto | f | 1e-15
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atto | a | 1e-18
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zepto | z | 1e-21
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yocto | y | 1e-24
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The following binary prefixes are available.
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They can be used with units `bit` (`b`) and `byte` (`B`).
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Name | Abbreviation | Value
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---- | ------------ | -----
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kibi | Ki | 1024
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mebi | Mi | 1024^2
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gibi | Gi | 1024^3
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tebi | Ti | 1024^4
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pebi | Pi | 1024^5
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exi | Ei | 1024^6
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zebi | Zi | 1024^7
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yobi | Yi | 1024^8
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Name | Abbreviation | Value
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----- | ------------ | -----
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kilo | k | 1e3
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mega | M | 1e6
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giga | G | 1e9
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tera | T | 1e12
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peta | P | 1e15
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exa | E | 1e18
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zetta | Z | 1e21
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yotta | Y | 1e24
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## Physical Constants
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Math.js includes the following physical constants. See [Wikipedia](http://en.wikipedia.org/wiki/Physical_constants) for more information.
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### Universal constants
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Name | Symbol | Value | Unit
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----------------------|--------------------------------------------------------|-------------------|-------------------------------------------------------
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speedOfLight | <i>c</i> | 299792458 | m · s<sup>-1</sup>
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gravitationConstant | <i>G</i> | 6.6738480e-11 | m<sup>3</sup> · kg<sup>-1</sup> · s<sup>-2</sup>
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planckConstant | <i>h</i> | 6.626069311e-34 | J · s
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reducedPlanckConstant | <i><span style="text-decoration:overline">h</span></i> | 1.05457172647e-34 | J · s
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### Electromagnetic
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Name | Symbol | Value | Unit
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--------------------------|--------------------------------------------------|-----------------------|----------------------------------------
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magneticConstant | <i>μ<sub>0</sub></i> | 1.2566370614e-6 | N · A<sup>-2</sup>
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electricConstant | <i>ε<sub>0</sub></i> | 8.854187817e-12 | F · m<sup>-1</sup>
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vacuumImpedance | <i>Z<sub>0</sub></i> | 376.730313461 | Ω
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coulomb | <i>κ</i> | 8.9875517873681764e9 | N · m<sup>2</sup> · C<sup>-2</sup>
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elementaryCharge | <i>e</i> | 1.60217656535e-19 | C
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bohrMagneton | <i>μ<sub>B</sub></i> | 9.2740096820e-24 | J · T<sup>-1</sup>
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conductanceQuantum | <i>G<sub>0</sub></i> | 7.748091734625e-5 | S
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inverseConductanceQuantum | <i>G<sub>0</sub><sup>-1</sup></i> | 12906.403721742 | Ω
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magneticFluxQuantum | <i><font face="Symbol">f</font><sub>0</sub></i> | 2.06783375846e-15 | Wb
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nuclearMagneton | <i>μ<sub>N</sub></i> | 5.0507835311e-27 | J · T<sup>-1</sup>
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klitzing | <i>R<sub>K</sub></i> | 25812.807443484 | Ω
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<!-- TODO: implement josephson
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josephson | <i>K<sub>J</sub></i> | 4.8359787011e-14 | Hz · V<sup>-1</sup>
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-->
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### Atomic and nuclear constants
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Name | Symbol | Value | Unit
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------------------------|------------------------------|-----------------------|----------------------------------
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bohrRadius | <i>a<sub>0</sub></i> | 5.291772109217e-11 | m
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classicalElectronRadius | <i>r<sub>e</sub></i> | 2.817940326727e-15 | m
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electronMass | <i>m<sub>e</sub></i> | 9.1093829140e-31 | kg
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fermiCoupling | <i>G<sub>F</sub></i> | 1.1663645e-5 | GeV<sup>-2</sup>
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fineStructure | <i>α</i> | 7.297352569824e-3 | -
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hartreeEnergy | <i>E<abbr>h</abbr> </i> | 4.3597443419e-18 | J
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protonMass | <i>m<sub>p</sub></i> | 1.67262177774e-27 | kg
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deuteronMass | <i>m<sub>d</sub></i> | 3.3435830926e-27 | kg
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neutronMass | <i>m<sub>n</sub></i> | 1.6749271613e-27 | kg
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quantumOfCirculation | <i>h / (2m<sub>e</sub>)</i> | 3.636947552024e-4 | m<sup>2</sup> · s<sup>-1</sup>
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rydberg | <i>R<sub>∞</sub></i> | 10973731.56853955 | m<sup>-1</sup>
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thomsonCrossSection | | 6.65245873413e-29 | m<sup>2</sup>
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weakMixingAngle | | 0.222321 | -
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efimovFactor | | 22.7 | -
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### Physico-chemical constants
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Name | Symbol | Value | Unit
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--------------------|------------------------------|---------------------|--------------------------------------------
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atomicMass | <i>m<sub>u</sub></i> | 1.66053892173e-27 | kg
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avogadro | <i>N<sub>A</sub></i> | 6.0221412927e23 | mol<sup>-1</sup>
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boltzmann | <i>k</i> | 1.380648813e-23 | J · K<sup>-1</sup>
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faraday | <i>F</i> | 96485.336521 | C · mol<sup>-1</sup>
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firstRadiation | <i>c<sub>1</sub></i> | 3.7417715317e-16 | W · m<sup>2</sup>
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loschmidt | <i>n<sub>0</sub></i> | 2.686780524e25 | m<sup>-3</sup>
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gasConstant | <i>R</i> | 8.314462175 | J · K<sup>-1</sup> · mol<sup>-1</sup>
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molarPlanckConstant | <i>N<sub>A</sub> · h</i>| 3.990312717628e-10| J · s · mol<sup>-1</sup>
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molarVolume | <i>V<sub>m</sub></i> | 2.241396820e-10 | m<sup>3</sup> · mol<sup>-1</sup>
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sackurTetrode | | -1.164870823 | -
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secondRadiation | <i>c<sub>2</sub></i> | 1.438777013e-2 | m · K
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stefanBoltzmann | <i>σ</i> | 5.67037321e-8 | W · m<sup>-2</sup> · K<sup>-4</sup>
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wienDisplacement | <i>b</i> | 2.897772126e-3 | m · K
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<!-- TODO: implement spectralRadiance
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spectralRadiance | <i>c<sub>1L</sub></i> | 1.19104286953e-16 | W · m<sup>2</sup> · sr<sup>-1</sup>
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-->
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Note that the values of `loschmidt` and `molarVolume` are at `T = 273.15 K` and `p = 101.325 kPa`.
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The value of `sackurTetrode` is at `T = 1 K` and `p = 101.325 kPa`.
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### Adopted values
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Name | Symbol | Value | Unit
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--------------|------------------------------|---------|-------------------------
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molarMass | <i>M<sub>u</sub></i> | 1e-3 | kg · mol<sup>-1</sup>
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molarMassC12 | <i>M(<sub>12</sub>C)</i> | 1.2e-2 | kg · mol<sup>-1</sup>
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gravity | <i>g<sub>n</sub></i> | 9.80665 | m · s<sup>-2</sup>
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atm | <i>atm</i> | 101325 | Pa
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### Natural units
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Name | Symbol | Value | Unit
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------------------|-----------------------|--------------------|-----
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planckLength | <i>l<sub>P</sub></i> | 1.61619997e-35 | m
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planckMass | <i>m<sub>P</sub></i> | 2.1765113e-8 | kg
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planckTime | <i>t<sub>P</sub></i> | 5.3910632e-44 | s
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planckCharge | <i>q<sub>P</sub></i> | 1.87554595641e-18 | C
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planckTemperature | <i>T<sub>P</sub></i> | 1.41683385e+32 | K
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