SI System¶

Namespace: mp_units::si

Module: mp_units.systems

Header: <mp-units/systems/si.h>

Secondary Headers:

<mp-units/systems/si/chrono.h>
<mp-units/systems/si/constants.h>
<mp-units/systems/si/core.h>
<mp-units/systems/si/math.h>
<mp-units/systems/si/prefix_utils.h>
<mp-units/systems/si/prefixes.h>
<mp-units/systems/si/unit_symbols.h>
<mp-units/systems/si/unit_symbols_essential.h>
<mp-units/systems/si/units.h>

Prefixes¶

Name	Symbol	Definition
`quecto`	q	`mag_power<10, -30>`
`ronto`	r	`mag_power<10, -27>`
`yocto`	y	`mag_power<10, -24>`
`zepto`	z	`mag_power<10, -21>`
`atto`	a	`mag_power<10, -18>`
`femto`	f	`mag_power<10, -15>`
`pico`	p	`mag_power<10, -12>`
`nano`	n	`mag_power<10, -9>`
`micro`	µ (u)	`mag_power<10, -6>`
`milli`	m	`mag_power<10, -3>`
`centi`	c	`mag_power<10, -2>`
`deci`	d	`mag_power<10, -1>`
`deca`	da	`mag_power<10, 1>`
`hecto`	h	`mag_power<10, 2>`
`kilo`	k	`mag_power<10, 3>`
`mega`	M	`mag_power<10, 6>`
`giga`	G	`mag_power<10, 9>`
`tera`	T	`mag_power<10, 12>`
`peta`	P	`mag_power<10, 15>`
`exa`	E	`mag_power<10, 18>`
`zetta`	Z	`mag_power<10, 21>`
`yotta`	Y	`mag_power<10, 24>`
`ronna`	R	`mag_power<10, 27>`
`quetta`	Q	`mag_power<10, 30>`

Units¶

Unit Name	Symbol	unit_symbol	Definition
`ampere`	A	`A`	`kind: isq::electric_current`
`becquerel`	Bq	`Bq`	`one / second kind: isq::activity`
`candela`	cd	`cd`	`kind: isq::luminous_intensity`
`coulomb`	C	`C`	`ampere * second`
`degree_Celsius`	℃ (`C)	`deg_C`	`kelvin origin: ice_point`
`farad`	F	`F`	`coulomb / volt kind: isq::capacitance`
`gram`	g	`g`	`kind: isq::mass`
`gray`	Gy	`Gy`	`joule / kilogram kind: isq::absorbed_dose`
`henry`	H	`H`	`weber / ampere`
`hertz`	Hz	`Hz`	`one / second kind: isq::frequency`
`joule`	J	`J`	`newton * metre kind: isq::energy`
`katal`	kat	`kat`	`mole / second kind: isq::catalytic_activity`
`kelvin`	K	`K`	`kind: isq::thermodynamic_temperature origin: absolute_zero`
`kilogram`	—	`kg`	`kilo<gram>`
`lumen`	lm	`lm`	`candela * steradian kind: isq::luminous_flux`
`lux`	lx	`lx`	`lumen / square(metre) kind: isq::illuminance`
`metre`	m	`m`	`kind: isq::length`
`mole`	mol	`mol`	`kind: isq::amount_of_substance`
`newton`	N	`N`	`kilogram * metre / square(second) kind: isq::force`
`ohm`	Ω (ohm)	`Ω`, `ohm`	`volt / ampere kind: isq::impedance`
`pascal`	Pa	`Pa`	`newton / square(metre) kind: isq::pressure`
`radian`	rad	`rad`	`metre / metre kind: isq::angular_measure`
`second`	s	`s`	`kind: isq::duration`
`siemens`	S	`S`	`one / ohm kind: isq::admittance`
`sievert`	Sv	`Sv`	`joule / kilogram kind: isq::dose_equivalent`
`steradian`	sr	`sr`	`square(metre) / square(metre) kind: isq::solid_angular_measure`
`tesla`	T	`T`	`weber / square(metre) kind: isq::magnetic_flux_density`
`volt`	V	`V`	`watt / ampere kind: isq::electric_potential`
`watt`	W	`W`	`joule / second`
`weber`	Wb	`Wb`	`volt * second`

Non-SI units accepted for use with the SI¶

Unit Name	Symbol	unit_symbol	Definition
`arcminute`	′ (')	`arcmin`	`mag_ratio<1, 60> * degree`
`arcsecond`	″ ('')	`arcsec`	`mag_ratio<1, 60> * arcminute`
`are`	a	`a`	`square(deca<metre>)`
`astronomical_unit`	au	`au`	`mag<149'597'870'700> * metre`
`dalton`	Da	`Da`	`mag_ratio<16'605'390'666'050, 10'000'000'000'000> * mag_power<10, -27> * kilogram`
`day`	d	`d`	`mag<24> * hour`
`degree`	° (deg)	`deg`	`mag_ratio<1, 180> * π * radian`
`electronvolt`	eV	`eV`	`mag_ratio<1'602'176'634, 1'000'000'000> * mag_power<10, -19> * joule`
`hectare`	—	`ha`	`hecto<are>`
`hour`	h	`h`	`mag<60> * minute`
`litre`	L	`l`, `L`	`cubic(deci<metre>)`
`minute`	min	`min`	`mag<60> * second`
`tonne`	t	`t`	`mag<1000> * kilogram`

Namespace

These units are defined in the mp_units::non_si namespace and are made available in the mp_units::si namespace through a using-directive.

Prefixed unit symbols¶

Not every unit has a symbol for every prefix. A combination that is not listed here does not exist, however reasonable it looks.

Unit	Essential header	Full header adds
`ampere`	`fA` `pA` `nA` `uA` `µA` `mA` `kA`	`qA` `rA` `yA` `zA` `aA` `cA` `dA` `daA` `hA` `MA` `GA` `TA` `PA` `EA` `ZA` `YA` `RA` `QA`
`becquerel`	`mBq` `kBq` `MBq` `GBq` `TBq` `PBq`	`qBq` `rBq` `yBq` `zBq` `aBq` `fBq` `pBq` `nBq` `uBq` `µBq` `cBq` `dBq` `daBq` `hBq` `EBq` `ZBq` `YBq` `RBq` `QBq`
`candela`	`mcd`	`qcd` `rcd` `ycd` `zcd` `acd` `fcd` `pcd` `ncd` `ucd` `µcd` `ccd` `dcd` `dacd` `hcd` `kcd` `Mcd` `Gcd` `Tcd` `Pcd` `Ecd` `Zcd` `Ycd` `Rcd` `Qcd`
`coulomb`	`pC` `nC` `uC` `µC` `mC`	`qC` `rC` `yC` `zC` `aC` `fC` `cC` `dC` `daC` `hC` `kC` `MC` `GC` `TC` `PC` `EC` `ZC` `YC` `RC` `QC`
`farad`	`fF` `pF` `nF` `uF` `µF` `mF`	`qF` `rF` `yF` `zF` `aF` `cF` `dF` `daF` `hF` `kF` `MF` `GF` `TF` `PF` `EF` `ZF` `YF` `RF` `QF`
`gram`	`fg` `pg` `ng` `ug` `µg` `mg` `Mg`	`qg` `rg` `yg` `zg` `ag` `cg` `dg` `dag` `hg` `Gg` `Tg` `Pg` `Eg` `Zg` `Yg` `Rg` `Qg`
`gray`	`uGy` `µGy` `mGy` `cGy` `kGy`	`qGy` `rGy` `yGy` `zGy` `aGy` `fGy` `pGy` `nGy` `dGy` `daGy` `hGy` `MGy` `GGy` `TGy` `PGy` `EGy` `ZGy` `YGy` `RGy` `QGy`
`henry`	`nH` `uH` `µH` `mH`	`qH` `rH` `yH` `zH` `aH` `fH` `pH` `cH` `dH` `daH` `hH` `kH` `MH` `GH` `TH` `PH` `EH` `ZH` `YH` `RH` `QH`
`hertz`	`nHz` `uHz` `µHz` `mHz` `kHz` `MHz` `GHz` `THz` `PHz`	`qHz` `rHz` `yHz` `zHz` `aHz` `fHz` `pHz` `cHz` `dHz` `daHz` `hHz` `EHz` `ZHz` `YHz` `RHz` `QHz`
`joule`	`aJ` `fJ` `pJ` `nJ` `uJ` `µJ` `mJ` `kJ` `MJ` `GJ` `TJ` `PJ` `EJ` `ZJ`	`qJ` `rJ` `yJ` `zJ` `cJ` `dJ` `daJ` `hJ` `YJ` `RJ` `QJ`
`katal`	`nkat` `ukat` `µkat`	`qkat` `rkat` `ykat` `zkat` `akat` `fkat` `pkat` `mkat` `ckat` `dkat` `dakat` `hkat` `kkat` `Mkat` `Gkat` `Tkat` `Pkat` `Ekat` `Zkat` `Ykat` `Rkat` `Qkat`
`kelvin`	`pK` `nK` `uK` `µK` `mK` `MK`	`qK` `rK` `yK` `zK` `aK` `fK` `cK` `dK` `daK` `hK` `kK` `GK` `TK` `PK` `EK` `ZK` `YK` `RK` `QK`
`lumen`	`klm`	`qlm` `rlm` `ylm` `zlm` `alm` `flm` `plm` `nlm` `ulm` `µlm` `mlm` `clm` `dlm` `dalm` `hlm` `Mlm` `Glm` `Tlm` `Plm` `Elm` `Zlm` `Ylm` `Rlm` `Qlm`
`lux`	`mlx` `klx`	`qlx` `rlx` `ylx` `zlx` `alx` `flx` `plx` `nlx` `ulx` `µlx` `clx` `dlx` `dalx` `hlx` `Mlx` `Glx` `Tlx` `Plx` `Elx` `Zlx` `Ylx` `Rlx` `Qlx`
`metre`	`fm` `pm` `nm` `um` `µm` `mm` `cm` `dm` `km`	`qm` `rm` `ym` `zm` `am` `dam` `hm` `Mm` `Gm` `Tm` `Pm` `Em` `Zm` `Ym` `Rm` `Qm`
`mole`	`fmol` `pmol` `nmol` `umol` `µmol` `mmol` `cmol` `kmol`	`qmol` `rmol` `ymol` `zmol` `amol` `dmol` `damol` `hmol` `Mmol` `Gmol` `Tmol` `Pmol` `Emol` `Zmol` `Ymol` `Rmol` `Qmol`
`newton`	`pN` `nN` `uN` `µN` `mN` `cN` `daN` `kN` `MN`	`qN` `rN` `yN` `zN` `aN` `fN` `dN` `hN` `GN` `TN` `PN` `EN` `ZN` `YN` `RN` `QN`
`ohm`	`uohm` `µΩ` `mohm` `mΩ` `kohm` `kΩ` `Mohm` `MΩ` `Gohm` `GΩ` `Tohm` `TΩ`	`qohm` `qΩ` `rohm` `rΩ` `yohm` `yΩ` `zohm` `zΩ` `aohm` `aΩ` `fohm` `fΩ` `pohm` `pΩ` `nohm` `nΩ` `cohm` `cΩ` `dohm` `dΩ` `daohm` `daΩ` `hohm` `hΩ` `Pohm` `PΩ` `Eohm` `EΩ` `Zohm` `ZΩ` `Yohm` `YΩ` `Rohm` `RΩ` `Qohm` `QΩ`
`pascal`	`uPa` `µPa` `mPa` `daPa` `hPa` `kPa` `MPa` `GPa` `TPa`	`qPa` `rPa` `yPa` `zPa` `aPa` `fPa` `pPa` `nPa` `cPa` `dPa` `PPa` `EPa` `ZPa` `YPa` `RPa` `QPa`
`radian`	`nrad` `urad` `µrad` `mrad`	`qrad` `rrad` `yrad` `zrad` `arad` `frad` `prad` `crad` `drad` `darad` `hrad` `krad` `Mrad` `Grad` `Trad` `Prad` `Erad` `Zrad` `Yrad` `Rrad` `Qrad`
`second`	`as` `fs` `ps` `ns` `us` `µs` `ms` `ks`	`qs` `rs` `ys` `zs` `cs` `ds` `das` `hs` `Ms` `Gs` `Ts` `Ps` `Es` `Zs` `Ys` `Rs` `Qs`
`siemens`	`pS` `nS` `uS` `µS` `mS` `dS` `MS`	`qS` `rS` `yS` `zS` `aS` `fS` `cS` `daS` `hS` `kS` `GS` `TS` `PS` `ES` `ZS` `YS` `RS` `QS`
`sievert`	`nSv` `uSv` `µSv` `mSv`	`qSv` `rSv` `ySv` `zSv` `aSv` `fSv` `pSv` `cSv` `dSv` `daSv` `hSv` `kSv` `MSv` `GSv` `TSv` `PSv` `ESv` `ZSv` `YSv` `RSv` `QSv`
`steradian`	`msr`	`qsr` `rsr` `ysr` `zsr` `asr` `fsr` `psr` `nsr` `usr` `µsr` `csr` `dsr` `dasr` `hsr` `ksr` `Msr` `Gsr` `Tsr` `Psr` `Esr` `Zsr` `Ysr` `Rsr` `Qsr`
`tesla`	`fT` `pT` `nT` `uT` `µT` `mT`	`qT` `rT` `yT` `zT` `aT` `cT` `dT` `daT` `hT` `kT` `MT` `GT` `TT` `PT` `ET` `ZT` `YT` `RT` `QT`
`volt`	`nV` `uV` `µV` `mV` `kV` `MV`	`qV` `rV` `yV` `zV` `aV` `fV` `pV` `cV` `dV` `daV` `hV` `GV` `TV` `PV` `EV` `ZV` `YV` `RV` `QV`
`watt`	`pW` `nW` `uW` `µW` `mW` `kW` `MW` `GW` `TW` `PW`	`qW` `rW` `yW` `zW` `aW` `fW` `cW` `dW` `daW` `hW` `EW` `ZW` `YW` `RW` `QW`
`weber`	—	`qWb` `rWb` `yWb` `zWb` `aWb` `fWb` `pWb` `nWb` `uWb` `µWb` `mWb` `cWb` `dWb` `daWb` `hWb` `kWb` `MWb` `GWb` `TWb` `PWb` `EWb` `ZWb` `YWb` `RWb` `QWb`

Two headers

The essential symbols come from <mp-units/systems/si/unit_symbols_essential.h>. The rest need <mp-units/systems/si/unit_symbols.h>, which is more expensive to compile, so include it only when you need an unusual prefix.

Constants¶

Name	Symbol	unit_symbol	Definition
`magnetic_constant`	μ₀ (u_0)	—	`mag<4> * mag_power<10, -7> * π * henry / metre`
`reduced_planck_constant`	ℏ (hbar)	—	`si2019::planck_constant / (mag<2> * π)`
`si2019::avogadro_constant`	N_A	—	`mag_ratio<602'214'076, 100'000'000> * mag_power<10, 23> / mole`
`si2019::boltzmann_constant`	k	—	`mag_ratio<1'380'649, 1'000'000> * mag_power<10, -23> * joule / kelvin`
`si2019::elementary_charge`	e	—	`mag_ratio<1'602'176'634, 1'000'000'000> * mag_power<10, -19> * coulomb`
`si2019::hyperfine_structure_transition_frequency_of_cs`	Δν_Cs (dv_Cs)	—	`mag<9'192'631'770> * hertz`
`si2019::luminous_efficacy`	K_cd	—	`mag<683> * lumen / watt`
`si2019::planck_constant`	h	—	`mag_ratio<662'607'015, 100'000'000> * mag_power<10, -34> * joule * second`
`si2019::speed_of_light_in_vacuum`	c	—	`mag<299'792'458> * metre / second`
`standard_gravity`	g₀ (g_0)	—	`mag_ratio<980'665, 100'000> * metre / square(second)`

Inline Namespaces

The mp_units::si::si2019 namespace is inline in mp_units::si, making its members directly accessible from the parent namespace.

Point Origins¶

Name	Type	Definition
`absolute_zero`	absolute	`isq::thermodynamic_temperature`
`chrono_point_origin`	absolute	`isq::time`
`ice_point`	relative	`::mp_units::point<milli<kelvin>>(273'150)`
`zeroth_degree_Celsius`	relative	alias to ice_point
`zeroth_kelvin`	absolute	alias to absolute_zero