Template:Physical constants

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This template provides easy inclusion of the latest CODATA recommended values of physical constants in articles. It gives the most recent values published, and will be updated when newer values become available, which is typically every four years.

The values have been updated to the CODATA 2022 values. This includes the 2019 revision of the SI, which made the values of several constants exact (e.g. e), whereas some previously exactly defined constants acquired an uncertainty (e.g. μ₀).

Usage

Arguments

symbol

If set to yes, the value is preceded by the symbol of the constant, followed by ≈ or = depending on whether round is set.

round

If omitted, the value is shown along with its standard uncertainty. If set to an integer n, the value is rounded to the first n digits after the decimal point.

unit

If set to no, the unit of measurement is omitted; if set to any other nonempty string, this replaces the unit.

ref

If set to no, no reference is given. If set to only, only the reference is given.

after

Text (e.g. punctuation) to be shown after the constant before the reference.

runc

If set to yes, this will provide only the relative standard uncertainty of the value and its reference.

Available constants

Code	Constant	Value	Relative standard uncertainty
c	speed of light	c = 299792458 m⋅s−1	ur(c) = 0‍
e	elementary charge	e = 1.602176634×10−19 C	ur(e) = 0‍
eV	electronvolt	eV = 1.602176634×10−19 J	ur(eV) = 0‍
F	Faraday constant	F = 9.648533212...×104 C⋅mol−1	ur(F) = 0‍
G	Newtonian constant of gravitation	G = 6.67430(15)×10−11 m3⋅kg−1⋅s−2	ur(G) = 2.2×10−5‍
G0	conductance quantum	G0 = 7.748091729...×10−5 S	ur(G0) = 0‍
G0inv	inverse conductance quantum	G0−1 = 12906.40372... Ω	ur(G0−1) = 0‍
GF/hbarc3	Fermi coupling constant	GF/⁠(ħc)3 = 1.1663787(6)×10−5 GeV−2	ur(GF/⁠(ħc)3) = 5.1×10−7‍
h	Planck constant	h = 6.62607015×10−34 J⋅Hz−1	ur(h) = 0‍
h_eV/Hz	Planck constant in eV/⁠Hz	h = 4.135667696...×10−15 eV⋅Hz−1	ur(h) = 0‍
hbar	reduced Planck constant	ħ = 1.054571817...×10−34 J⋅s	ur(ħ) = 0‍
hbar_eVs	reduced Planck constant in eV⋅s	ħ = 6.582119569...×10−16 eV⋅s	ur(ħ) = 0‍
k	Boltzmann constant	k = 1.380649×10−23 J⋅K−1	ur(k) = 0‍
KJ	Josephson constant	KJ = 483597.8484...×109 Hz⋅V−1	ur(KJ) = 0‍
NA	Avogadro constant	NA = 6.02214076×1023 mol−1	ur(NA) = 0‍
NAh	molar Planck constant	NAh = 3.990312712...×10−10 J⋅Hz−1⋅mol−1	ur(NAh) = 0‍
RK	von Klitzing constant	RK = 25812.80745... Ω	ur(RK) = 0‍
Z0	characteristic impedance of vacuum	Z0 = 376.730313412(59) Ω	ur(Z0) = 1.6×10−10‍
alpha	fine-structure constant	α = 0.0072973525643(11)	ur(α) = 1.6×10−10‍
alphainv	inverse fine-structure constant	α−1 = 137.035999177(21)	ur(α−1) = 1.6×10−10‍
eps0	vacuum electric permittivity	ε0 = 8.8541878188(14)×10−12 F⋅m−1	ur(ε0) = 1.6×10−10‍
sin2thW	sine-square weak mixing angle	sin2θW = 0.22305(23)	ur(sin2θW) = 1.0×10−3‍
mu0	vacuum magnetic permeability	μ0 = 1.25663706127(20)×10−6 N⋅A−2	ur(μ0) = 1.6×10−10‍
Phi0	magnetic flux quantum	Φ0 = 2.067833848...×10−15 Wb	ur(Φ0) = 0‍
Thermal radiation
bwien	Wien wavelength displacement law constant	b = 2.897771955...×10−3 m⋅K	ur(b) = 0‍
bwien'	Wien frequency displacement law constant	b′ = 5.878925757...×1010 Hz⋅K−1	ur(b′) = 0‍
c1	first radiation constant	c1 = 3.741771852...×10−16 W⋅m2	ur(c1) = 0‍
c1L	first radiation constant for spectral radiance	c1L = 1.191042972...×10−16 W⋅m2⋅sr−1	ur(c1L) = 0‍
c2	second radiation constant	c2 = 1.438776877...×10−2 m⋅K	ur(c2) = 0‍
sigma	Stefan–Boltzmann constant	σ = 5.670374419...×10−8 W⋅m−2⋅K−4	ur(σ) = 0‍
Particle-related values
asil	lattice parameter of silicon	a = 5.431020511(89)×10−10 m	ur(a) = 1.6×10−8‍
a0	Bohr radius	a0 = 5.29177210544(82)×10−11 m	ur(a0) = 1.6×10−10‍
ae	electron magnetic moment anomaly	ae = 0.00115965218046(18)	ur(ae) = 1.6×10−10‍
Ar(d)	deuteron relative atomic mass	Ar(d) = 2.013553212544(15)	ur(Ar(d)) = 7.4×10−12‍
Ar(e)	electron relative atomic mass	Ar(e) = 5.485799090441(97)×10−4	ur(Ar(e)) = 1.8×10−11‍
Ar(h)	helion relative atomic mass	Ar(h) = 3.014932246932(74)	ur(Ar(h)) = 2.5×10−11‍
Ar(n)	neutron relative atomic mass	Ar(n) = 1.00866491606(40)	ur(Ar(n)) = 4.0×10−10‍
Ar(p)	proton relative atomic mass	Ar(p) = 1.0072764665789(83)	ur(Ar(p)) = 8.3×10−12‍
Ar(t)	triton relative atomic mass	Ar(t) = 3.01550071597(10)	ur(Ar(t)) = 3.4×10−11‍
Ar(alpha)	alpha particle relative atomic mass	Ar(α) = 4.001506179129(62)	ur(Ar(α)) = 1.6×10−11‍
-e/me	electron charge-to-mass ratio	−e/⁠me = −1.75882000838(55)×1011 C⋅kg−1	ur(−e/⁠me) = 3.1×10−10‍
Eh	Hartree energy	Eh = 4.3597447222060(48)×10−18 J	ur(Eh) = 1.1×10−12‍
Eh_eV	Hartree energy in eV	Eh = 27.211386245981(30) eV	ur(Eh) = 1.1×10−12‍
ge	electron g-factor	ge− = −2.00231930436092(36)	ur(ge−) = 1.8×10−13‍
gn	neutron g-factor	gn = −3.82608552(90)	ur(gn) = 2.4×10−7‍
gp	proton g-factor	gp = 5.5856946893(16)	ur(gp) = 2.9×10−10‍
gmu	muon g-factor	gμ− = −2.00233184123(82)	ur(gμ−) = 4.1×10−10‍
h/2me	quantum of circulation	πħ/⁠me = 3.6369475467(11)×10−4 m2⋅s−1	ur(πħ/⁠me) = 3.1×10−10‍
md	deuteron mass	md = 3.3435837768(10)×10−27 kg	ur(md) = 3.1×10−10‍
md_Da	deuteron mass in daltons	md = 2.013553212544(15) Da	ur(md) = 7.4×10−12‍
me	electron mass	me = 9.1093837139(28)×10−31 kg	ur(me) = 3.1×10−10‍
me_Da	electron mass in daltons	me = 5.485799090441(97)×10−4 Da	ur(me) = 1.8×10−11‍
me/mp	electron-to-proton mass ratio	me/mp = 0.0005446170214889(94)	ur(me/mp) = 1.7×10−11‍
me/mmu	electron-to-muon mass ratio	me/⁠mμ = 0.00483633170(11)	ur(me/⁠mμ) = 2.2×10−8‍
mec2	electron mass energy equivalent	mec2 = 8.1871057880(26)×10−14 J	ur(mec2) = 3.1×10−10‍
mec2_MeV	electron mass energy equivalent in MeV	mec2 = 0.51099895069(16) MeV	ur(mec2) = 3.1×10−10‍
mh	helion mass	mh = 5.0064127862(16)×10−27 kg	ur(mh) = 3.1×10−10‍
mh_Da	helion mass in daltons	mh = 3.014932246932(74) Da	ur(mh) = 2.5×10−11‍
mn	neutron mass	mn = 1.67492750056(85)×10−27 kg	ur(mn) = 5.1×10−10‍
mn_Da	neutron mass in daltons	mn = 1.00866491606(40) Da	ur(mn) = 4.0×10−10‍
mnc2	neutron mass energy equivalent	mnc2 = 1.50534976514(76)×10−10 J	ur(mnc2) = 5.1×10−10‍
mnc2_MeV	neutron mass energy equivalent in MeV	mnc2 = 939.56542194(48) MeV	ur(mnc2) = 5.1×10−10‍
mp	proton mass	mp = 1.67262192595(52)×10−27 kg	ur(mp) = 3.1×10−10‍
mp_Da	proton mass in daltons	mp = 1.0072764665789(83) Da	ur(mp) = 8.3×10−12‍
mp/me	proton-to-electron mass ratio	mp/⁠me = 1836.152673426(32)	ur(mp/⁠me) = 1.7×10−11‍
mpc2	proton mass energy equivalent	mpc2 = 1.50327761802(47)×10−10 J	ur(mpc2) = 3.1×10−10‍
mpc2_MeV	proton mass energy equivalent in MeV	mpc2 = 938.27208943(29) MeV	ur(mpc2) = 3.1×10−10‍
mu	atomic mass constant	mu = 1.66053906892(52)×10−27 kg	ur(mu) = 3.1×10−10‍
muc2	atomic mass constant energy equivalent	muc2 = 1.49241808768(46)×10−10 J	ur(muc2) = 3.1×10−10‍
muc2_MeV	atomic mass constant energy equivalent in MeV	muc2 = 931.49410372(29) MeV	ur(muc2) = 3.1×10−10‍
mW/mZ	W-to-Z mass ratio	mW/⁠mZ = 0.88145(13)	ur(mW/⁠mZ) = 1.5×10−4‍
malpha	alpha particle mass	mα = 6.6446573450(21)×10−27 kg	ur(mα) = 3.1×10−10‍
malpha_Da	alpha particle mass in daltons	mα = 4.001506179129(62) Da	ur(mα) = 1.6×10−11‍
malphac2_GeV	alpha particle mass energy equivalent in GeV	mαc2 = 3.7273794118(11) GeV	ur(mαc2) = 3.0×10−10‍
mmu	muon mass	mμ = 1.883531627(42)×10−28 kg	ur(mμ) = 2.2×10−8‍
mmu_Da	muon mass in daltons	mμ = 0.1134289257(22) Da	ur(mμ) = 2.2×10−8‍
mmu/me	muon-to-electron mass ratio	mμ/⁠me = 206.7682827(46)	ur(mμ/⁠me) = 2.2×10−8‍
mmuc2	muon mass energy equivalent	mμc2 = 1.692833804(38)×10−11 J	ur(mμc2) = 2.2×10−8‍
mmuc2_MeV	muon mass energy equivalent in MeV	mμc2 = 105.6583755(23) MeV	ur(mμc2) = 2.2×10−8‍
mtau	tau mass	mτ = 3.16754(21)×10−27 kg	ur(mτ) = 6.8×10−5‍
mtau_Da	tau mass in daltons	mτ = 1.90754(13) Da	ur(mτ) = 6.8×10−5‍
mtau/me	tau-to-electron mass ratio	mτ/⁠me = 3477.23(23)	ur(mτ/⁠me) = 6.8×10−5‍
mtau/mmu	tau-to-muon mass ratio	mτ/⁠mμ = 16.8170(11)	ur(mτ/⁠mμ) = 6.8×10−5‍
mtauc2	tau mass energy equivalent	mτc2 = 2.84684(19)×10−10 J	ur(mτc2) = 6.8×10−5‍
mtauc2_MeV	tau mass energy equivalent in MeV	mτc2 = 1776.86(12) MeV	ur(mτc2) = 6.8×10−5‍
MC12	molar mass of carbon-12	M(12C) = 12.0000000126(37)×10−3 kg⋅mol−1	ur(M(12C)) = 3.1×10−10‍
Mu	molar mass constant	Mu = 1.00000000105(31)×10−3 kg⋅mol−1	ur(Mu) = 3.1×10−10‍
rd	deuteron rms charge radius	rd = 2.12778(27)×10−15 m	ur(rd) = 1.3×10−4‍
re	classical electron radius	re = 2.8179403205(13)×10−15 m	ur(re) = 4.7×10−10‍
rp	proton root-mean-square charge radius	rp = 8.4075(64)×10−16 m	ur(rp) = 7.4×10−4‍
R	molar gas constant	R = 8.314462618... J⋅mol−1⋅K−1	ur(R) = 0‍
Rinf	Rydberg constant	R∞ = 10973731.568157(12) m−1	ur(R∞) = 1.1×10−12‍
Rinfc	Rydberg frequency	R∞c = 3.2898419602500(36)×1015 Hz	ur(R∞c) = 1.1×10−12‍
Rinfhc	Rydberg unit of energy	R∞hc = 2.1798723611030(24)×10−18 J	ur(R∞hc) = 1.1×10−12‍
Rinfhc_eV	Rydberg unit of energy in eV	R∞hc = 13.605693122990(15) eV	ur(R∞hc) = 1.1×10−12‍
VmSi	molar volume of silicon	Vm(Si) = 1.205883199(60)×10−5 m3⋅mol−1	ur(Vm(Si)) = 4.9×10−8‍
gammae	electron gyromagnetic ratio	γe = −1.76085962784(55)×1011 s−1⋅T−1	ur(γe) = 3.1×10−10‍
gammabare	electron Larmor frequency to magnetic flux density ratio	γe/⁠2π = −28024.9513861(87) MHz⋅T−1	ur(γe/⁠2π) = 3.1×10−10‍
gamman	neutron gyromagnetic ratio	γn = −1.83247174(43)×108 s−1⋅T−1	ur(γn) = 2.4×10−7‍
gammabarn	neutron Larmor frequency to magnetic flux density ratio	γn/⁠2π = −29.1646935(69) MHz⋅T−1	ur(γn/⁠2π) = 2.4×10−7‍
gammap	proton gyromagnetic ratio	γp = 2.6752218708(11)×108 s−1⋅T−1	ur(γp) = 4.3×10−10‍
gammabarp	proton Larmor frequency to magnetic flux density ratio	γp/⁠2π = 42.577478461(18) MHz⋅T−1	ur(γp/⁠2π) = 4.3×10−10‍
DnuCs	hyperfine structure transition frequency of caesium-133	Δν(133Cs)hfs = 9192631770 Hz	ur(Δν(133Cs)hfs) = 0‍
muB	Bohr magneton	μB = 9.2740100657(29)×10−24 J⋅T−1	ur(μB) = 3.1×10−10‍
mue	electron magnetic moment	μe = −9.2847646917(29)×10−24 J⋅T−1	ur(μe) = 3.1×10−10‍
mue/muB	electron magnetic moment to Bohr magneton ratio	μe/⁠μB = −1.00115965218046(18)	ur(μe/⁠μB) = 1.8×10−13‍
mun	neutron magnetic moment	μn = −9.6623653(23)×10−27 J⋅T−1	ur(μn) = 2.4×10−7‍
mun/muN	neutron magnetic moment to nuclear magneton ratio	μn/⁠μN = −1.91304276(45)	ur(μn/⁠μN) = 2.4×10−7‍
muN	nuclear magneton	μN = 5.0507837393(16)×10−27 J⋅T−1	ur(μN) = 3.1×10−10‍
mup	proton magnetic moment	μp = 1.41060679545(60)×10−26 J⋅T−1	ur(μp) = 4.3×10−10‍
mup/muB	proton magnetic moment to Bohr magneton ratio	μp/⁠μB = 0.00152103220230(45)	ur(μp/⁠μB) = 3.0×10−10‍
mup/muN	proton magnetic moment to nuclear magneton ratio	μp/⁠μN = 2.79284734463(82)	ur(μp/⁠μN) = 2.9×10−10‍
mumu	muon magnetic moment	μμ = −4.49044830(18)×10−26 J⋅T−1	ur(μμ) = 2.2×10−8‍
sigmae	electron Thomson cross section	σe = 6.6524587051(62)×10−29 m2	ur(σe) = 9.3×10−10‍
Conventional electrical units
KJ90	conventional value of Josephson constant	KJ-90 = 483597.9×109 Hz⋅V−1	ur(KJ-90) = 0‍
RK90	conventional value of von Klitzing constant	RK-90 = 25812.807 Ω	ur(RK-90) = 0‍
A90	conventional ampere	A90 = 1.00000008887... A	ur(A90) = 0‍
C90	conventional coulomb	C90 = 1.00000008887... C	ur(C90) = 0‍
F90	conventional farad	F90 = 0.99999998220... F	ur(F90) = 0‍
H90	conventional henry	H90 = 1.00000001779... H	ur(H90) = 0‍
V90	conventional volt	V90 = 1.00000010666... V	ur(V90) = 0‍
W90	conventional watt	W90 = 1.00000019553... W	ur(W90) = 0‍
ohm90	conventional ohm	Ω90 = 1.00000001779... Ω	ur(Ω90) = 0‍
Atomic units
aulen	atomic unit of length	a0 = 5.29177210544(82)×10−11 m	ur(a0) = 1.6×10−10‍
autime	atomic unit of time	ħ/⁠Eh = 2.4188843265864(26)×10−17 s	ur(ħ/⁠Eh) = 1.1×10−12‍
auvel	atomic unit of velocity	a0Eh/ħ = 2.18769126216(34)×106 m⋅s−1	ur(a0Eh/ħ) = 1.6×10−10‍
aumass	atomic unit of mass	me = 9.1093837139(28)×10−31 kg	ur(me) = 3.1×10−10‍
aumom	atomic unit of momentum	ħ/⁠a0 = 1.99285191545(31)×10−24 kg⋅m⋅s−1	ur(ħ/⁠a0) = 1.6×10−10‍
auener	atomic unit of energy	Eh = 4.3597447222060(48)×10−18 J	ur(Eh) = 1.1×10−12‍
auforce	atomic unit of force	Eh/⁠a0 = 8.2387235038(13)×10−8 N	ur(Eh/⁠a0) = 1.6×10−10‍
auact	atomic unit of action	ħ = 1.054571817...×10−34 J⋅s	ur(ħ) = 0‍
auec	atomic unit of electric charge	e = 1.602176634×10−19 C	ur(e) = 0‍
auedm	atomic unit of electric dipole moment	ea0 = 8.4783536198(13)×10−30 C⋅m	ur(ea0) = 1.6×10−10‍
aueqm	atomic unit of electric quadrupole moment	ea02 = 4.4865515185(14)×10−40 C⋅m2	ur(ea02) = 3.1×10−10‍
auecd	atomic unit of electric charge density	e/⁠a03 = 1.08120238677(51)×1012 C⋅m−3	ur(e/⁠a03) = 0‍
aucur	atomic unit of electric current	eEh/⁠ħ = 6.6236182375082(72)×10−3 A	ur(eEh/⁠ħ) = 1.1×10−12‍
auepot	atomic unit of electric potential	Eh/⁠e = 27.211386245981(30) V	ur(Eh/⁠e) = 1.1×10−12‍
auef	atomic unit of electric field	Eh/⁠ea0 = 5.14220675112(80)×1011 V⋅m−1	ur(Eh/⁠ea0) = 1.6×10−10‍
auefg	atomic unit of electric field gradient	Eh/⁠ea02 = 9.7173624424(30)×1021 V⋅m−2	ur(Eh/⁠ea02) = 3.1×10−10‍
auperm	atomic unit of permittivity	e2/a0Eh = 1.11265005620(17)×10−10 F⋅m−1	ur(e2/a0Eh) = 1.6×10−10‍
auepol	atomic unit of electric polarizability	e2a02/⁠Eh = 1.64877727212(51)×10−41 C2⋅m2⋅J−1	ur(e2a02/⁠Eh) = 3.1×10−10‍
au1hypol	atomic unit of 1st hyperpolarizability	e3a03/⁠Eh2 = 3.2063612996(15)×10−53 C3⋅m3⋅J−2	ur(e3a03/⁠Eh2) = 4.7×10−10‍
au2hypol	atomic unit of 2nd hyperpolarizability	e4a04/⁠Eh3 = 6.2353799735(39)×10−65 C4⋅m4⋅J−3	ur(e4a04/⁠Eh3) = 6.2×10−10‍
aumfd	atomic unit of magnetic flux density	ħ/⁠ea02 = 2.35051757077(73)×105 T	ur(ħ/⁠ea02) = 3.1×10−10‍
aumdm	atomic unit of magnetic dipole moment	ħe/⁠me = 1.85480201315(58)×10−23 J⋅T−1	ur(ħe/⁠me) = 3.1×10−10‍
aumag	atomic unit of magnetizability	e2a02/⁠me = 7.8910365794(49)×10−29 J⋅T−2	ur(e2a02/⁠me) = 6.2×10−10‍
Planck units
lP	Planck length	lP = 1.616255(18)×10−35 m	ur(lP) = 1.1×10−5‍
tP	Planck time	tP = 5.391247(60)×10−44 s	ur(tP) = 1.1×10−5‍
mP	Planck mass	mP = 2.176434(24)×10−8 kg	ur(mP) = 1.1×10−5‍
TP	Planck temperature	TP = 1.416784(16)×1032 K	ur(TP) = 1.1×10−5‍
Standard values
g0	standard acceleration of gravity	g0 = 9.80665 m⋅s−2	ur(g0) = 0‍
atm	standard atmosphere	atm = 101325 Pa	ur(atm) = 0‍
ssp	standard-state pressure	ssp = 100000 Pa	ur(ssp) = 0‍

Examples

{{physconst|c|unit=no|after= [[metre per second|metres per second]].}}

299792458 metres per second.

{{physconst|mu0|symbol=yes}}

μ₀ = 1.25663706127(20)×10⁻⁶ N⋅A⁻²‍

{{physconst|G|symbol=yes}}

G = 6.67430(15)×10⁻¹¹ m³⋅kg⁻¹⋅s⁻²‍

{{physconst|hbar|round=2|symbol=yes}}

ħ ≈ 1.05×10⁻³⁴ J⋅s‍

The relative standard uncertainty of ''m''<sub>u</sub> is {{physconst|mu|runc=yes|after=.}}

The relative standard uncertainty of m_u is 3.1×10⁻¹⁰.

For the electron mass, {{physconst|me|runc=yes|symbol=yes|ref=no}}.

For the electron mass, u_r(m_e) = 3.1×10⁻¹⁰.

NIST publishes the CODATA value of the [[elementary charge]].{{physconst|e|ref=only}}

NIST publishes the CODATA value of the elementary charge.

The elementary charge is {{physconst|e|unit=[[coulomb]]s|after=.}}

The elementary charge is 1.602176634×10⁻¹⁹ coulombs.

See also

• /data, the subtemplate that holds all of the data

References

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