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 redefinition of SI base units, 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 or not 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 (trailing zeros are omitted).

unit

If set to no, the unit of measurement is not shown.

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
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
atm	standard atmosphere	atm = 101325 Pa	ur(atm) = 0
A90	conventional ampere	A90 = 1.00000008887... A	ur(A90) = 0
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
c	speed of light	c = 299792458 m⋅s−1	ur(c) = 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
C90	conventional coulomb	C90 = 1.00000008887... C	ur(C90) = 0
e	elementary charge	e = 1.602176634×10−19 C	ur(e) = 0
eV	electronvolt	eV = 1.602176634×10−19 J	ur(eV) = 0
-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
F	Faraday constant	F = 9.648533212...×104 C⋅mol−1	ur(F) = 0
F90	conventional farad	F90 = 0.99999998220... F	ur(F90) = 0
g0	standard acceleration of gravity	g0 = 9.80665 m⋅s−2	ur(g0) = 0
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
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
h/2me	quantum of circulation	πħ/me = 3.6369475467(11)×10−4 m2⋅s−1	ur(πħ/me) = 3.1×10−10
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
H90	conventional henry	H90 = 1.00000001779... H	ur(H90) = 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
KJ90	conventional value of Josephson constant	KJ-90 = 483597.9×109 Hz⋅V−1	ur(KJ-90) = 0
lP	Planck length	lP = 1.616255(18)×10−35 m	ur(lP) = 1.1×10−5
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
mP	Planck mass	mP = 2.176434(24)×10−8 kg	ur(mP) = 1.1×10−5
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
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
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
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
RK	von Klitzing constant	RK = 25812.80745... Ω	ur(RK) = 0
RK90	conventional value of von Klitzing constant	RK-90 = 25812.807 Ω	ur(RK-90) = 0
tP	Planck time	tP = 5.391247(60)×10−44 s	ur(tP) = 1.1×10−5
TP	Planck temperature	TP = 1.416784(16)×1032 K	ur(TP) = 1.1×10−5
V90	conventional volt	V90 = 1.00000010666... V	ur(V90) = 0
VmSi	molar volume of silicon	Vm(Si) = 1.205883199(60)×10−5 m3⋅mol−1	ur(Vm(Si)) = 4.9×10−8
W90	conventional watt	W90 = 1.00000019553... W	ur(W90) = 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
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
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
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
sigma	Stefan–Boltzmann constant	σ = 5.670374419...×10−8 W⋅m−2⋅K−4	ur(σ) = 0
sigmae	Thomson cross section	σe = 6.6524587051(62)×10−29 m2	ur(σe) = 9.3×10−10
Phi0	magnetic flux quantum	Φ0 = 2.067833848...×10−15 Wb	ur(Φ0) = 0
ohm90	conventional ohm	Ω90 = 1.00000001779... Ω	ur(Ω90) = 0

Examples

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

299792458 metres per second.

{{Physical constants|mu0|symbol=yes}}

μ₀ = 1.25663706127(20)×10⁻⁶ N⋅A⁻²

{{Physical constants|G|symbol=yes}}

G = 6.67430(15)×10⁻¹¹ m³⋅kg⁻¹⋅s⁻²

{{Physical constants|hbar|round=2|symbol=yes}}

ħ ≈ 1.05×10⁻³⁴ J⋅s

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

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

For the electron mass, {{Physical constants|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]].{{Physical constants|e|ref=only}}

NIST publishes the CODATA value of the elementary charge.

See also

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

References

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