Supported phisical costants
This section lists all available units, prefixes, and physical constants. These can be used via the Unit object, or via math.eval()
.
Reference
Mathlion 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 area | m2, sqin, sqft, sqyd, sqmi, sqrd, sqch, sqmil, acre, hectare |
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, secs, seconds), minute (mins, minutes), hour (h, hr, hrs, 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), kip |
Energy | joule (J), erg, Wh, BTU, electronvolt (eV) |
Power | watt (W), hp |
Pressure | Pa, psi, atm, torr, bar, mmHg, mmH2O, cmH2O |
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
Mathlion 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 constants
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 |