List of physical constants

Table of physical constants

Symbol	Quantity	Value[1]	Relative standard uncertainty	Group
${\displaystyle c}$	speed of light in vacuum	299792458 m/s[2]	0	ud
${\displaystyle h}$	Planck constant	6.62607015×10^−34 J⋅s[3]	0	ud   f
${\displaystyle \hbar =h/2\pi }$	reduced Planck constant	1.054571817...×10^−34 J⋅s[4]	0	ud   f
${\displaystyle G}$	Newtonian constant of gravitation	6.67430(15)×10^−11 m^3⋅kg^−1⋅s^−2[5]	2.2×10^−5	u    f
${\displaystyle \varepsilon _{0}=1/\mu _{0}c^{2}}$	vacuum electric permittivity	8.8541878128(13)×10^−12 F⋅m^−1[6]	1.5×10^−10	u    f
${\displaystyle \mu _{0}}$	vacuum magnetic permeability	1.25663706212(19)×10^−6 N⋅A^−2[7]	1.5×10^−10	u    f
${\displaystyle Z_{0}=\mu _{0}c}$	characteristic impedance of vacuum	376.730313668(57) Ω[8]	1.5×10^−10	u
${\displaystyle e,q_{\text{e}}}$	elementary charge	1.602176634×10^−19 C[9]	0	de  f
${\displaystyle \Delta \nu _{\text{Cs}}}$	hyperfine transition frequency of ^133Cs	9192631770 Hz[10]	0	d
${\displaystyle N_{\text{A}},L}$	Avogadro constant	6.02214076×10^23 mol^−1[11]	0	d  pf
${\displaystyle k,k_{\text{B}}}$	Boltzmann constant	1.380649×10^−23 J⋅K^−1[12]	0	d  pf
${\displaystyle G_{0}=2e^{2}/h}$	conductance quantum	7.748091729...×10^−5 S[13]	0	e  f
${\displaystyle K_{\mathrm {J} }=2e/h}$	Josephson constant	483597.8484...×10^9 Hz⋅V^−1[14]	0	e  f
${\displaystyle R_{\mathrm {K} }=h/e^{2}}$	von Klitzing constant	25812.80745... Ω[15]	0	e  f
${\displaystyle \Phi _{0}=h/2e}$	magnetic flux quantum	2.067833848...×10^−15 Wb[16]	0	e  f
${\displaystyle G_{0}^{-1}=h/2e^{2}}$	inverse conductance quantum	12906.40372... Ω[17]	0	e
${\displaystyle \mu _{\mathrm {B} }=e\hbar /2m_{\mathrm {e} }}$	Bohr magneton	9.2740100783(28)×10^−24 J⋅T^−1[18]	3.0×10^−10	e
${\displaystyle \mu _{\mathrm {N} }=e\hbar /2m_{\mathrm {p} }}$	nuclear magneton	5.0507837461(15)×10^−27 J⋅T^−1[19]	3.1×10^−10	e
${\displaystyle \alpha =e^{2}/4\pi \varepsilon _{0}\hbar c}$	fine-structure constant	7.2973525693(11)×10^−3[20]	1.5×10^−10	a f
${\displaystyle \alpha ^{-1}}$	inverse fine-structure constant	137.035999084(21)[21]	1.5×10^−10	a f
${\displaystyle m_{\mathrm {e} }}$	electron mass	9.1093837015(28)×10^−31 kg[22]	3.0×10^−10	a f
${\displaystyle m_{\mathrm {p} }}$	proton mass	1.67262192369(51)×10^−27 kg[23]	3.1×10^−10	a f
${\displaystyle m_{\mathrm {n} }}$	neutron mass	1.67492749804(95)×10^−27 kg[24]	5.7×10^−10	a
${\displaystyle a_{0}=\hbar /\alpha m_{\text{e}}c}$	Bohr radius	5.29177210903(80)×10^−11 m[25]	1.5×10^−10	a
${\displaystyle r_{\mathrm {e} }=e^{2}/4\pi \varepsilon _{0}m_{\mathrm {e} }c^{2}}$	classical electron radius	2.8179403262(13)×10^−15 m[26]	4.5×10^−10	a
${\displaystyle g_{\mathrm {e} }}$	electron g-factor	−2.00231930436256(35)[27]	1.7×10^−13	a
${\displaystyle G_{\mathrm {F} }/(\hbar c)^{3}}$	Fermi coupling constant	1.1663787(6)×10^−5 GeV^−2[28]	5.1×10^−7	a
${\displaystyle E_{\mathrm {h} }=2R_{\infty }hc}$	Hartree energy	4.3597447222071(85)×10^−18 J[29]	1.9×10^−12	a
${\displaystyle h/2m_{\mathrm {e} }}$	quantum of circulation	3.6369475516(11)×10^−4 m^2⋅s^−1[30]	3.0×10^−10	a
${\displaystyle R_{\infty }=\alpha ^{2}m_{\mathrm {e} }c/2h}$	Rydberg constant	10973731.568160(21) m^−1[31]	1.9×10^−12	a
${\displaystyle \sigma _{\text{e}}=(8\pi /3)r_{\mathrm {e} }^{2}}$	Thomson cross section	6.6524587321(60)×10^−29 m^2[32]	9.1×10^−10	a
${\displaystyle m_{\mathrm {W} }/m_{\mathrm {Z} }}$	W-to-Z mass ratio	0.88153(17)[33]	1.9×10^−4
${\displaystyle \sin ^{2}\theta _{\mathrm {W} }=1-(m_{\mathrm {W} }/m_{\mathrm {Z} })^{2}}$	weak mixing angle	0.22290(30)[34]	1.3×10^−3	a
${\displaystyle m_{\text{u}}=1\,{\text{Da}}}$	atomic mass constant	1.66053906660(50)×10^−27 kg[35]	3.0×10^−10	pf
${\displaystyle F=N_{\text{A}}e}$	Faraday constant	96485.33212... C⋅mol^−1[36]	0	pf
${\displaystyle R=N_{\text{A}}k_{\text{B}}}$	molar gas constant	8.314462618... J⋅mol^−1⋅K^−1[37]	0	pf
${\displaystyle M_{\text{u}}=M({}^{12}{\text{C}})/12}$	molar mass constant	0.99999999965(30)×10^−3 kg⋅mol^−1[38]	3.0×10^−10	pf
${\displaystyle \sigma =\pi ^{2}k^{4}/60\hbar ^{3}c^{2}}$	Stefan–Boltzmann constant	5.670374419...×10^−8 W⋅m^−2⋅K^−4[39]	0	pf
${\displaystyle c_{1}=2\pi hc^{2}}$	first radiation constant	3.741771852...×10^−16 W⋅m^2[40]	0	p
${\displaystyle c_{\text{1L}}=c_{1}/\pi }$	first radiation constant for spectral radiance	1.191042972...×10^−16 W⋅m^2⋅sr^−1[41]	0	p
${\displaystyle M({}^{12}{\text{C}})=N_{\text{A}}m({}^{12}{\text{C}})}$	molar mass of carbon-12	11.9999999958(36)×10^−3 kg⋅mol^−1[42]	3.0×10^−10	p
${\displaystyle N_{\text{A}}h}$	molar Planck constant	3.990312712...×10^−10 J⋅Hz^−1⋅mol^−1[43]	0	p
${\displaystyle c_{2}=hc/k}$	second radiation constant	1.438776877...×10^−2 m⋅K[44]	0	p
${\displaystyle b}$	Wien wavelength displacement law constant	2.897771955...×10^−3 m⋅K[45]	0	p
${\displaystyle b'}$	Wien frequency displacement law constant	5.878925757...×10^10 Hz⋅K^−1[46]	0	p
${\displaystyle b_{\text{entropy}}}$	Wien entropy displacement law constant	3.002916077...×10^−3 m⋅K[47]	0	p

'Group' reflects categorization on the NIST website:[48]

u: universal

d: defined

e: elecromagnetic

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

References

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. "2018 CODATA Value: speed of light in vacuum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
3. "2018 CODATA Value: Planck constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
4. "2018 CODATA Value: reduced Planck constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-08-28.
5. "2018 CODATA Value: Newtonian constant of gravitation". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
6. "2018 CODATA Value: vacuum electric permittivity". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
7. "2018 CODATA Value: vacuum magnetic permeability". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
8. "2018 CODATA Value: characteristic impedance of vacuum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-10-31.
9. "2018 CODATA Value: elementary charge". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
10. "2018 CODATA Value: hyperfine transition frequency of Cs-133". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-08-18.
11. "2018 CODATA Value: Avogadro constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
12. "2018 CODATA Value: Boltzmann constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
13. "2018 CODATA Value: conductance quantum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
14. "2018 CODATA Value: Josephson constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
15. "2018 CODATA Value: von Klitzing constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
16. "2018 CODATA Value: magnetic flux quantum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
17. "2018 CODATA Value: inverse of conductance quantum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
18. "2018 CODATA Value: Bohr magneton". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
19. "2018 CODATA Value: nuclear magneton". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
20. "2018 CODATA Value: fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
21. "2018 CODATA Value: inverse fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
22. "2018 CODATA Value: electron mass in u". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
23. "2018 CODATA Value: proton mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
24. "2018 CODATA Value: neutron mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-08-23.
25. "2018 CODATA Value: Bohr radius". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
26. "2018 CODATA Value: classical electron radius". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
27. "2018 CODATA Value: electron g factor". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2020-03-13.
28. "2018 CODATA Value: Fermi coupling constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
29. "2018 CODATA Value: Hartree energy". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
30. "2018 CODATA Value: quantum of circulation". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
31. "2018 CODATA Value: Rydberg constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
32. "2018 CODATA Value: Thomson cross section". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
33. "2018 CODATA Value: W to Z mass ratio". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-12-21.
34. "2018 CODATA Value: weak mixing angle". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
35. "2018 CODATA Value: atomic mass constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
36. "2018 CODATA Value: Faraday constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
37. "2018 CODATA Value: molar gas constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
38. "2018 CODATA Value: molar mass constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
39. "2018 CODATA Value: Stefan–Boltzmann constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
40. "2018 CODATA Value: first radiation constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
41. "2018 CODATA Value: first radiation constant for spectral radiance". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
42. "2018 CODATA Value: molar mass of carbon-12". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
43. "2018 CODATA Value: molar Planck constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
44. "2018 CODATA Value: second radiation constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
45. "2018 CODATA Value: Wien wavelength displacement law constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
46. "2018 CODATA Value: Wien frequency displacement law constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
47. Delgado-Bonal A (May 2017). "Entropy of radiation: the unseen side of light". Scientific Reports. 7 (1): 1642. Bibcode:2017NatSR...7.1642D. doi:10.1038/s41598-017-01622-6. PMC 5432030. PMID 28490790.
48. "Fundamental Physical Constants from NIST".