List of physical constants

Table of physical constants

Symbol	Quantity	Value	Relative standard uncertainty	Group
$c$	speed of light in vacuum	299792458 m⋅s−1	0	ud
$h$	Planck constant	6.62607015×10−34 J⋅Hz−1	0	ud   f
$\hbar =h/2\pi$	reduced Planck constant	1.054571817...×10−34 J⋅s	0	ud   f
$G$	Newtonian constant of gravitation	6.67430(15)×10−11 m3⋅kg−1⋅s−2	2.2×10−5	u    f
$\varepsilon _{0}=1/\mu _{0}c^{2}$	vacuum electric permittivity	8.8541878188(14)×10−12 F⋅m−1	1.6×10−10	u    f
$\mu _{0}$	vacuum magnetic permeability	1.25663706127(20)×10−6 N⋅A−2	1.6×10−10	u    f
$Z_{0}=\mu _{0}c$	characteristic impedance of vacuum	376.730313412(59) Ω	1.6×10−10	u
$e,q_{\text{e}}$	elementary charge	1.602176634×10−19 C	0	de  f
$\Delta \nu _{\text{Cs}}$	hyperfine transition frequency of 133Cs	9192631770 Hz	0	d
$N_{\text{A}},L$	Avogadro constant	6.02214076×1023 mol−1	0	d  pf
$k,k_{\text{B}}$	Boltzmann constant	1.380649×10−23 J⋅K−1	0	d  pf
$G_{0}=2e^{2}/h$	conductance quantum	7.748091729...×10−5 S	0	e  f
$K_{\mathrm {J} }=2e/h$	Josephson constant	483597.8484...×109 Hz⋅V−1	0	e  f
$R_{\mathrm {K} }=h/e^{2}$	von Klitzing constant	25812.80745... Ω	0	e  f
$\Phi _{0}=h/2e$	magnetic flux quantum	2.067833848...×10−15 Wb	0	e  f
$G_{0}^{-1}=h/2e^{2}$	inverse conductance quantum	12906.40372... Ω	0	e
$\mu _{\mathrm {B} }=e\hbar /2m_{\mathrm {e} }$	Bohr magneton	9.2740100657(29)×10−24 J⋅T−1	3.1×10−10	e
$\mu _{\mathrm {N} }=e\hbar /2m_{\mathrm {p} }$	nuclear magneton	5.0507837393(16)×10−27 J⋅T−1	3.1×10−10	e
$\alpha =e^{2}/4\pi \varepsilon _{0}\hbar c$	fine-structure constant	0.0072973525643(11)	1.6×10−10	a f
$\alpha ^{-1}$	inverse fine-structure constant	137.035999177(21)	1.6×10−10	a f
$m_{\mathrm {e} }$	electron mass	9.1093837139(28)×10−31 kg	3.1×10−10	a f
$m_{\mathrm {p} }$	proton mass	1.67262192595(52)×10−27 kg	3.1×10−10	a f
$m_{\mathrm {n} }$	neutron mass	1.67492750056(85)×10−27 kg	5.1×10−10	a
$a_{0}=\hbar /\alpha m_{\text{e}}c$	Bohr radius	5.29177210544(82)×10−11 m	1.6×10−10	a
$r_{\mathrm {e} }=e^{2}/4\pi \varepsilon _{0}m_{\mathrm {e} }c^{2}$	classical electron radius	2.8179403205(13)×10−15 m	4.7×10−10	a
$g_{\mathrm {e} }$	electron g-factor	−2.00231930436092(36)	1.8×10−13	a
$G_{\mathrm {F} }/(\hbar c)^{3}$	Fermi coupling constant	1.1663787(6)×10−5 GeV−2	5.1×10−7	a
$E_{\mathrm {h} }=2R_{\infty }hc$	Hartree energy	4.3597447222060(48)×10−18 J	1.1×10−12	a
$h/2m_{\mathrm {e} }$	quantum of circulation	3.6369475467(11)×10−4 m2⋅s−1	3.1×10−10	a
$R_{\infty }=\alpha ^{2}m_{\mathrm {e} }c/2h$	Rydberg constant	10973731.568157(12) m−1	1.1×10−12	a
$\sigma _{\text{e}}=(8\pi /3)r_{\mathrm {e} }^{2}$	Thomson cross section	6.6524587051(62)×10−29 m2	9.3×10−10	a
$m_{\mathrm {W} }/m_{\mathrm {Z} }$	W-to-Z mass ratio	0.88145(13)	1.5×10−4
$\sin ^{2}\theta _{\mathrm {W} }=1-(m_{\mathrm {W} }/m_{\mathrm {Z} })^{2}$	weak mixing angle	0.22290(30)	1.3×10−3	a
$m_{\text{u}}=1\,{\text{Da}}$	atomic mass constant	1.66053906892(52)×10−27 kg	3.1×10−10	pf
$F=N_{\text{A}}e$	Faraday constant	9.648533212...×104 C⋅mol−1	0	pf
$R=N_{\text{A}}k_{\text{B}}$	molar gas constant	8.314462618... J⋅mol−1⋅K−1	0	pf
$M_{\text{u}}=M({}^{12}{\text{C}})/12$	molar mass constant	1.00000000105(31)×10−3 kg⋅mol−1	3.1×10−10	pf
$\sigma =\pi ^{2}k^{4}/60\hbar ^{3}c^{2}$	Stefan–Boltzmann constant	5.670374419...×10−8 W⋅m−2⋅K−4	0	pf
$c_{1}=2\pi hc^{2}$	first radiation constant	3.741771852...×10−16 W⋅m2	0	p
$c_{\text{1L}}=c_{1}/\pi$	first radiation constant for spectral radiance	1.191042972...×10−16 W⋅m2⋅sr−1	0	p
$M({}^{12}{\text{C}})=N_{\text{A}}m({}^{12}{\text{C}})$	molar mass of carbon-12	12.0000000126(37)×10−3 kg⋅mol−1	3.1×10−10	p
$N_{\text{A}}h$	molar Planck constant	3.990312712...×10−10 J⋅Hz−1⋅mol−1	0	p
$c_{2}=hc/k$	second radiation constant	1.438776877...×10−2 m⋅K	0	p
$b$	Wien wavelength displacement law constant	2.897771955...×10−3 m⋅K	0	p
$b'$	Wien frequency displacement law constant	5.878925757...×1010 Hz⋅K−1	0	p
$b_{\text{entropy}}$	Wien entropy displacement law constant	3.002916077...×10−3 m⋅K	0	p

'Group' reflects categorization on the NIST website:

u: universal

d: defined

e: electromagnetic

a: atomic and nuclear

p: physico-chemical

f: frequently used

n: non-SI units

There are some notable omissions in the site's classification: the speed of light (f), vacuum electric permittivity (e), vacuum magnetic permeability (e), hyperfine transition frequency of ¹³³Cs (p).

See also

• Physical constant