List_of_physical_constants

List of physical constants

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The constants listed here are known values of physical constants expressed in SI units; that is, physical quantities that are generally believed to be universal in nature and thus are independent of the unit system in which they are measured. Many of these are redundant, in the sense that they obey a known relationship with other physical constants and can be determined from them.

Table of physical constants

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Symbol	Quantity	Value^{[lower-alpha 1]}^{[lower-alpha 2]}	Relative standard uncertainty	Ref
$c$	speed of light in vacuum	299792458 m⋅s⁻¹	0	^[1]
$h$	Planck constant	6.62607015×10⁻³⁴ J⋅Hz⁻¹	0	^[2]
$\hbar =h/2\pi$	reduced Planck constant	1.054571817...×10⁻³⁴ J⋅s	0	^[3]
$\mu _{0}$	vacuum magnetic permeability	1.25663706212(19)×10⁻⁶ N⋅A⁻²	1.5×10⁻¹⁰	^[4]
$Z_{0}=\mu _{0}c$	characteristic impedance of vacuum	376.730313668(57) Ω	1.5×10⁻¹⁰	^[5]
$\varepsilon _{0}=1/\mu _{0}c^{2}$	vacuum electric permittivity	8.8541878128(13)×10⁻¹² F⋅m⁻¹	1.5×10⁻¹⁰	^[6]
$k,k_{\text{B}}$	Boltzmann constant	1.380649×10⁻²³ J⋅K⁻¹	0	^[7]
$G$	Newtonian constant of gravitation	6.67430(15)×10⁻¹¹ m³⋅kg⁻¹⋅s⁻²	2.2×10⁻⁵	^[8]
$k_{\text{e}}=1/4\pi \varepsilon _{0}$	Coulomb constant	8.9875517923(14)×10⁹ N⋅m²⋅C⁻²	1.5×10⁻¹⁰	^[9]
$\Lambda$	cosmological constant	1.089(29)×10⁻⁵² m⁻²	0.027	^[10]
$\sigma =\pi ^{2}k_{\text{B}}^{4}/60\hbar ^{3}c^{2}$	Stefan–Boltzmann constant	5.670374419...×10⁻⁸ W⋅m⁻²⋅K⁻⁴	0	^[11]
$c_{1}=2\pi hc^{2}$	first radiation constant	3.741771852...×10⁻¹⁶ W⋅m²	0	^[12]
$c_{\text{1L}}=2hc^{2}/\mathrm {sr}$	first radiation constant for spectral radiance	1.191042972...×10⁻¹⁶ W⋅m²⋅sr⁻¹	0	^[13]
$c_{2}=hc/k_{\text{B}}$	second radiation constant	1.438776877...×10⁻² m⋅K	0	^[14]
$b$ ^{[lower-alpha 3]}	Wien wavelength displacement law constant	2.897771955...×10⁻³ m⋅K	0	^[15]
$b'$ ^{[lower-alpha 4]}	Wien frequency displacement law constant	5.878925757...×10¹⁰ Hz⋅K⁻¹	0	^[16]
$b_{\text{entropy}}$	Wien entropy displacement law constant	3.002916077...×10⁻³ m⋅K	0	^[17]
$e$	elementary charge	1.602176634×10⁻¹⁹ C	0	^[18]
$G_{0}=2e^{2}/h$	conductance quantum	7.748091729...×10⁻⁵ S	0	^[19]
$G_{0}^{-1}=h/2e^{2}$	inverse conductance quantum	12906.40372... Ω	0	^[20]
$R_{\text{K}}=h/e^{2}$	von Klitzing constant	25812.80745... Ω	0	^[21]
$K_{\text{J}}=2e/h$	Josephson constant	483597.8484...×10⁹ Hz⋅V⁻¹	0	^[22]
$\Phi _{0}=h/2e$	magnetic flux quantum	2.067833848...×10⁻¹⁵ Wb	0	^[23]
$\alpha =e^{2}/4\pi \varepsilon _{0}\hbar c$	fine-structure constant	7.2973525693(11)×10⁻³	1.5×10⁻¹⁰	^[24]
$\alpha ^{-1}$	inverse fine-structure constant	137.035999084(21)	1.5×10⁻¹⁰	^[25]
$m_{\text{e}}$	electron mass	9.1093837015(28)×10⁻³¹ kg	3.0×10⁻¹⁰	^[26]
$m_{\text{p}}$	proton mass	1.67262192369(51)×10⁻²⁷ kg	3.1×10⁻¹⁰	^[27]
$m_{\text{n}}$	neutron mass	1.67492749804(95)×10⁻²⁷ kg	5.7×10⁻¹⁰	^[28]
$m_{\mu }$	muon mass	1.883531627(42)×10⁻²⁸ kg	2.2×10⁻⁸	^[29]
$m_{\tau }$	tau mass	3.16754(21)×10⁻²⁷ kg	6.8×10⁻⁵	^[30]
$m_{\text{t}}$	top quark mass	3.0784(53)×10⁻²⁵ kg	1.7×10⁻³	^[31]
$m_{\text{p}}/m_{\text{e}}$	proton-to-electron mass ratio	1836.15267343(11)	6.0×10⁻¹¹	^[32]
$m_{\text{W}}/m_{\text{Z}}$	W-to-Z mass ratio	0.88153(17)	1.9×10⁻⁴	^[33]
$\sin ^{2}\theta _{\text{W}}=1-(m_{\text{W}}/m_{\text{Z}})^{2}$	weak mixing angle	0.22290(30)	1.3×10⁻³	^[34]
$g_{\text{e}}$	electron g-factor	−2.00231930436256(35)	1.7×10⁻¹³	^[35]
$g_{\mu }$	muon g-factor	−2.0023318418(13)	6.3×10⁻¹⁰	^[36]
$g_{\text{p}}$	proton g-factor	5.5856946893(16)	2.9×10⁻¹⁰	^[37]
$h/2m_{\text{e}}$	quantum of circulation	3.6369475516(11)×10⁻⁴ m²⋅s⁻¹	3.0×10⁻¹⁰	^[38]
$\mu _{\text{B}}=e\hbar /2m_{\text{e}}$	Bohr magneton	9.2740100783(28)×10⁻²⁴ J⋅T⁻¹	3.0×10⁻¹⁰	^[39]
$\mu _{\text{N}}=e\hbar /2m_{\text{p}}$	nuclear magneton	5.0507837461(15)×10⁻²⁷ J⋅T⁻¹	3.1×10⁻¹⁰	^[40]
$r_{\text{e}}=e^{2}k_{\text{e}}/m_{\text{e}}c^{2}$	classical electron radius	2.8179403262(13)×10⁻¹⁵ m	4.5×10⁻¹⁰	^[41]
$\sigma _{\text{e}}=(8\pi /3)r_{\text{e}}^{2}$	Thomson cross section	6.6524587321(60)×10⁻²⁹ m²	9.1×10⁻¹⁰	^[42]
$a_{0}=\hbar ^{2}/k_{\text{e}}m_{\text{e}}e^{2}=r_{\text{e}}/\alpha ^{2}$	Bohr radius	5.29177210903(80)×10⁻¹¹ m	1.5×10⁻¹⁰	^[43]
$E_{\text{h}}=\alpha ^{2}c^{2}m_{\text{e}}$	Hartree energy	4.3597447222071(85)×10⁻¹⁸ J	1.9×10⁻¹²	^[44]
$\mathrm {Ry} =hcR_{\infty }=E_{\text{h}}/2$	Rydberg unit of energy	2.1798723611035(42)×10⁻¹⁸ J	1.9×10⁻¹²	^[45]
$R_{\infty }=\alpha ^{2}m_{\text{e}}c/2h$	Rydberg constant	10973731.568160(21) m⁻¹	1.9×10⁻¹²	^[46]
$G_{\text{F}}/(\hbar c)^{3}$	Fermi coupling constant	1.1663787(6)×10⁻⁵ GeV⁻²	5.1×10⁻⁷	^[47]
$N_{\text{A}},L$	Avogadro constant	6.02214076×10²³ mol⁻¹	0	^[48]
$R=N_{\text{A}}k_{\text{B}}$	molar gas constant	8.31446261815324 J⋅mol⁻¹⋅K⁻¹	0	^[49]
$F=N_{\text{A}}e$	Faraday constant	96485.3321233100184 C⋅mol⁻¹	0	^[50]
$N_{\text{A}}h$	molar Planck constant	3.9903127128934314×10⁻¹⁰ J⋅s⋅mol⁻¹	0	^[51]
$m({}^{12}{\text{C}})$	atomic mass of carbon-12	1.99264687992(60)×10⁻²⁶ kg	3.0×10⁻¹⁰	^[52]
$M({}^{12}{\text{C}})=N_{\text{A}}m({}^{12}{\text{C}})$	molar mass of carbon-12	11.9999999958(36)×10⁻³ kg⋅mol⁻¹	3.0×10⁻¹⁰	^[53]
$m_{\text{u}}=m({}^{12}{\text{C}})/12$	atomic mass constant	1.66053906660(50)×10⁻²⁷ kg	3.0×10⁻¹⁰	^[52]
$M_{\text{u}}=M({}^{12}{\text{C}})/12$	molar mass constant	0.99999999965(30)×10⁻³ kg⋅mol⁻¹	3.0×10⁻¹⁰	^[54]
$V_{\text{m}}({\text{Si}})$	molar volume of silicon	1.205883199(60)×10⁻⁵ m³⋅mol⁻¹	4.9×10⁻⁸	^[55]
$\Delta \nu _{\text{Cs}}$	hyperfine transition frequency of ¹³³Cs	9192631770 Hz	0	^[56]

Uncertainties

While the values of the physical constants are independent of the system of units in use, each uncertainty as stated reflects our lack of knowledge of the corresponding value as expressed in SI units, and is strongly dependent on how those units are defined. For example, the atomic mass constant $m_{\text{u}}$ is exactly known when expressed using the dalton (its value is exactly 1 Da), but the kilogram is not exactly known when using these units, the opposite of when expressing the same quantities using the kilogram.

Technical constants

Some of these constants are of a technical nature and do not give any true physical property, but they are included for convenience. Such a constant gives the correspondence ratio of a technical dimension with its corresponding underlying physical dimension. These include the Boltzmann constant $k_{\text{B}}$ , which gives the correspondence of the dimension temperature to the dimension of energy per degree of freedom, and the Avogadro constant $N_{\text{A}}$ , which gives the correspondence of the dimension of amount of substance with the dimension of count of entities (the latter formally regarded in the SI as being dimensionless). By implication, any product of powers of such constants is also such a constant, such as the molar gas constant $R$ .

Notes

The values are given in the so-called concise form; the number in parentheses is the standard uncertainty and indicates the amount by which the least significant digits of the value are uncertain.
In some instances an exact value has been displayed, calculated from the defining expression, rather than the incomplete decimal expansion as given by the source.
$b={\frac {hc}{k\left(5+W_{0}\left(-5e^{-5}\right)\right)}}$ , where $W_{0}$ is the principal branch of the Lambert W function.
$b'=\left(3+W_{0}\left(-3e^{-3}\right)\right){\frac {k}{h}}$ , where $W_{0}$ is the principal branch of the Lambert W function.

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[1] The values are given in the so-called concise form; the number in parentheses is the standard uncertainty and indicates the amount by which the least significant digits of the value are uncertain.

[2] In some instances an exact value has been displayed, calculated from the defining expression, rather than the incomplete decimal expansion as given by the source.

[17] $b={\frac {hc}{k\left(5+W_{0}\left(-5e^{-5}\right)\right)}}$ , where $W_{0}$ is the principal branch of the Lambert W function.

[19] $b'=\left(3+W_{0}\left(-3e^{-3}\right)\right){\frac {k}{h}}$ , where $W_{0}$ is the principal branch of the Lambert W function.

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