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 2018 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
a0	Bohr radius	a0 = 5.29177210903(80)×10−11 m	ur(a0) = 1.5×10−10
alpha	fine-structure constant	α = 7.2973525693(11)×10−3	ur(α) = 1.5×10−10
A90	conventional ampere	A90 = 1.00000008887... A	ur(A90) = 0
atm	standard atmosphere	atm = 101325 Pa	ur(atm) = 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
DnuCs	hyperfine structure transition frequency of caesium-133	Δν(133Cs)hfs = 9192631770 Hz	ur(Δν(133Cs)hfs) = 0
e	elementary charge	e = 1.602176634×10−19 C	ur(e) = 0
Eh	Hartree energy	Eh = 4.3597447222071(85)×10−18 J	ur(Eh) = 1.9×10−12
Eh_eV	Hartree energy in eV	Eh = 27.211386245988(53) eV	ur(Eh) = 1.9×10−12
eps0	vacuum electric permittivity	ε0 = 8.8541878128(13)×10−12 F⋅m−1	ur(ε0) = 1.5×10−10
eV	electronvolt	eV = 1.602176634×10−19 J	ur(eV) = 0
F	Faraday constant	F = 9.648533212...×104 C⋅mol−1	ur(F) = 0
F90	conventional farad	F90 = 0.99999998220... F	ur(F90) = 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
g0	standard acceleration of gravity	g0 = 9.80665 m⋅s−2	ur(g0) = 0
gammae	electron gyromagnetic ratio	γe = 1.76085963023(53)×1011 s−1⋅T−1	ur(γe) = 3.0×10−10
gamman	neutron gyromagnetic ratio	γn = 1.83247171(43)×108 s−1⋅T−1	ur(γn) = 2.4×10−7
gammap	proton gyromagnetic ratio	γp = 2.6752218744(11)×108 s−1⋅T−1	ur(γp) = 4.2×10−10
ge	electron g-factor	ge− = −2.00231930436256(35)	ur(ge−) = 1.7×10−13
GF/hbarc3	Fermi coupling constant	GF/(ħc)3 = 1.1663787(6)×10−5 GeV−2	ur(GF/(ħc)3) = 5.1×10−7
gmu	muon g-factor	gμ− = −2.0023318418(13)	ur(gμ−) = 6.3×10−10
gn	neutron g-factor	gn = −3.82608545(90)	ur(gn) = 2.4×10−7
gp	proton g-factor	gp = 5.5856946893(16)	ur(gp) = 2.9×10−10
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
H90	conventional henry	H90 = 1.00000001779... H	ur(H90) = 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
hcRinf	Rydberg unit of energy	hcR∞ = 2.1798723611035(42)×10−18 J	ur(hcR∞) = 1.9×10−12
h/2me	quantum of circulation	h/2me = 3.6369475516(11)×10−4 m2⋅s−1	ur(h/2me) = 3.0×10−10
invalpha	inverse fine-structure constant	1/α = 137.035999084(21)	ur(1/α) = 1.5×10−10
invG0	inverse conductance quantum	G0−1 = 12906.40372... Ω	ur(G0−1) = 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
malpha	alpha particle mass	mα = 6.6446573357(20)×10−27 kg	ur(mα) = 3.0×10−10
malphac2_GeV	alpha particle mass energy equivalent in GeV	mαc2 = 3.7273794066(11) GeV	ur(mαc2) = 3.0×10−10
md	deuteron mass	md = 3.3435837724(10)×10−27 kg	ur(md) = 3.0×10−10
md_Da	deuteron mass in daltons	md = 2.013553212745(40) Da	ur(md) = 2.0×10−11
me	electron mass	me = 9.1093837015(28)×10−31 kg	ur(me) = 3.0×10−10
me_Da	electron mass in daltons	me = 5.48579909065(16)×10−4 Da	ur(me) = 2.9×10−11
mec2_MeV	electron mass energy equivalent in MeV	mec2 = 0.51099895000(15) MeV	ur(mec2) = 3.0×10−10
mh	helion mass	mh = 5.0064127796(15)×10−27 kg	ur(mh) = 3.0×10−10
mh_Da	helion mass in daltons	mh = 3.014932247175(97) Da	ur(mh) = 3.2×10−11
mmu	muon mass	mμ = 1.883531627(42)×10−28 kg	ur(mμ) = 2.2×10−8
mmu/me	muon-to-electron mass ratio	mμ/me = 206.7682830(46)	ur(mμ/me) = 2.2×10−8
mn	neutron mass	mn = 1.67492749804(95)×10−27 kg	ur(mn) = 5.7×10−10
mn_Da	neutron mass in daltons	mn = 1.00866491595(49) Da	ur(mn) = 4.8×10−10
mnc2_MeV	neutron mass energy equivalent in MeV	mnc2 = 939.56542052(54) MeV	ur(mnc2) = 5.7×10−10
mP	Planck mass	mP = 2.176434(24)×10−8 kg	ur(mP) = 1.1×10−5
mp	proton mass	mp = 1.67262192369(51)×10−27 kg	ur(mp) = 3.1×10−10
mp_Da	proton mass in daltons	mp = 1.007276466621(53) Da	ur(mp) = 5.3×10−11
mp/me	proton-to-electron mass ratio	mp/me = 1836.15267343(11)	ur(mp/me) = 6.0×10−11
mpc2_MeV	proton mass energy equivalent in MeV	mpc2 = 938.27208816(29) MeV	ur(mpc2) = 3.1×10−10
mtau	tau mass	mτ = 3.16754(21)×10−27 kg	ur(mτ) = 6.8×10−5
MC12	molar mass of carbon-12	M(12C) = 11.9999999958(36)×10−3 kg⋅mol−1	ur(M(12C)) = 3.0×10−10
Mu	molar mass constant	Mu = 0.99999999965(30)×10−3 kg⋅mol−1	ur(Mu) = 3.0×10−10
mu	atomic mass constant	mu = 1.66053906660(50)×10−27 kg	ur(mu) = 3.0×10−10
muc2	atomic mass constant energy equivalent	muc2 = 1.49241808560(45)×10−10 J	ur(muc2) = 3.0×10−10
muc2_MeV	atomic mass constant energy equivalent in MeV	muc2 = 931.49410242(28) MeV	ur(muc2) = 3.0×10−10
mu0	vacuum magnetic permeability	μ0 = 1.25663706212(19)×10−6 N⋅A−2	ur(μ0) = 1.5×10−10
muB	Bohr magneton	μB = 9.2740100783(28)×10−24 J⋅T−1	ur(μB) = 3.0×10−10
mue	electron magnetic moment	μe = −9.2847647043(28)×10−24 J⋅T−1	ur(μe) = 3.0×10−10
mue/muB	electron magnetic moment to Bohr magneton ratio	μe/μB = −1.00115965218128(18)	ur(μe/μB) = 1.7×10−13
mumu	muon magnetic moment	μμ = −4.49044830(18)×10−26 J⋅T−1	ur(μμ) = 2.2×10−8
muN	nuclear magneton	μN = 5.0507837461(15)×10−27 J⋅T−1	ur(μN) = 3.1×10−10
mun	neutron magnetic moment	μn = −9.6623651(23)×10−27 J⋅T−1	ur(μn) = 2.4×10−7
mun/muN	neutron magnetic moment to nuclear magneton ratio	μn/μN = −1.91304273(45)	ur(μn/μN) = 2.4×10−7
mup	proton magnetic moment	μp = 1.41060679736(60)×10−26 J⋅T−1	ur(μp) = 4.2×10−10
mup/muB	proton magnetic moment to Bohr magneton ratio	μp/μB = 1.52103220230(46)×10−3	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
mW/mZ	W-to-Z mass ratio	mW/mZ = 0.88153(17)	ur(mW/mZ) = 1.9×10−4
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
ohm90	conventional ohm	Ω90 = 1.00000001779... Ω	ur(Ω90) = 0
Phi0	magnetic flux quantum	Φ0 = 2.067833848...×10−15 Wb	ur(Φ0) = 0
R	molar gas constant	R = 8.314462618... J⋅mol−1⋅K−1	ur(R) = 0
re	classical electron radius	re = 2.8179403262(13)×10−15 m	ur(re) = 4.5×10−10
Rinf	Rydberg constant	R∞ = 10973731.568160(21) m−1	ur(R∞) = 1.9×10−12
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
rp	proton root-mean-square charge radius	rp = 0.8414(19) fm	ur(rp) = 2.2×10−3
sigma	Stefan–Boltzmann constant	σ = 5.670374419...×10−8 W⋅m−2⋅K−4	ur(σ) = 0
sigmae	Thomson cross section	σe = 6.6524587321(60)×10−29 m2	ur(σe) = 9.1×10−10
TP	Planck temperature	TP = 1.416784(16)×1032 K	ur(TP) = 1.1×10−5
tP	Planck time	tP = 5.391247(60)×10−44 s	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 = 376.730313668(57) Ω	ur(Z0) = 1.5×10−10

Examples

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

299792458 metres per second.

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

μ₀ = 1.25663706212(19)×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 3.0×10⁻¹⁰.

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

For the electron mass, u_r(m_e) = 3.0×10⁻¹⁰.

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
• {{CODATA2010}}, the older version of this template used for the 2010 values

References

The above documentation is transcluded from Template:Physical constants/doc. (edit | history)
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