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[edit]

Symbol Quantity Value[a][b] Relative
standard
uncertainty
Ref
Newtonian constant of gravitation 6.67430(15)×10−11 m3⋅kg−1⋅s−2 2.2×10−5 [1]
speed of light in vacuum 299792458 m⋅s−1 0 [2]
Planck constant 6.62607015×10−34 J⋅Hz−1 0 [3]
reduced Planck constant 1.054571817...×10−34 J⋅s 0 [4]
vacuum magnetic permeability 1.25663706212(19)×10−6 N⋅A−2 1.5×10−10 [5]
characteristic impedance of vacuum 376.730313668(57) Ω 1.5×10−10 [6]
vacuum electric permittivity 8.8541878128(13)×10−12 F⋅m−1 1.5×10−10 [7]
Coulomb constant 8.9875517923(14)×109 N⋅m2⋅C−2 1.5×10−10 [8]
Boltzmann constant 1.380649×10−23 J⋅K−1 0 [9]
Stefan–Boltzmann constant 5.670374419...×10−8 W⋅m−2⋅K−4 0 [10]
first radiation constant 3.741771852...×10−16 W⋅m2 0 [11]
first radiation constant for spectral radiance 1.1910429723971884140794892×10−16 W⋅m2⋅sr−1 0 [12]
second radiation constant 1.438776877...×10−2 m⋅K 0 [13]
[c] Wien wavelength displacement law constant 2.897771955...×10−3 m⋅K 0 [14]
[d] Wien frequency displacement law constant 5.878925757...×1010 Hz⋅K−1 0 [15]
Wien entropy displacement law constant 3.002916077...×10−3 m⋅K 0 [16]
elementary charge 1.602176634×10−19 C 0 [17]
conductance quantum 7.748091729...×10−5 S 0 [18]
inverse conductance quantum 12906.40372... Ω 0 [19]
von Klitzing constant 25812.80745... Ω 0 [20]
Josephson constant 483597.8484...×109 Hz⋅V−1 0 [21]
magnetic flux quantum 2.067833848...×10−15 Wb 0 [22]
fine-structure constant 7.2973525693(11)×10−3 1.5×10−10 [23]
inverse fine-structure constant 137.035999084(21) 1.5×10−10 [24]
electron mass 9.1093837015(28)×10−31 kg 3.0×10−10 [25]
proton mass 1.67262192369(51)×10−27 kg 3.1×10−10 [26]
neutron mass 1.67492749804(95)×10−27 kg 5.7×10−10 [27]
muon mass 1.883531627(42)×10−28 kg 2.2×10−8 [28]
tau mass 3.16754(21)×10−27 kg 6.8×10−5 [29]
top quark mass 3.0784(53)×10−25 kg 1.7×10−3 [30]
proton-to-electron mass ratio 1836.15267343(11) 6.0×10−11 [31]
W-to-Z mass ratio 0.88153(17) 1.9×10−4 [32]
weak mixing angle 0.22290(30) 1.3×10−3 [33]
electron g-factor −2.00231930436256(35) 1.7×10−13 [34]
muon g-factor −2.0023318418(13) 6.3×10−10 [35]
proton g-factor 5.5856946893(16) 2.9×10−10 [36]
quantum of circulation 3.6369475516(11)×10−4 m2⋅s−1 3.0×10−10 [37]
Bohr magneton 9.2740100783(28)×10−24 J⋅T−1 3.0×10−10 [38]
nuclear magneton 5.0507837461(15)×10−27 J⋅T−1 3.1×10−10 [39]
classical electron radius 2.8179403262(13)×10−15 m 4.5×10−10 [40]
Thomson cross section 6.6524587321(60)×10−29 m2 9.1×10−10 [41]
Bohr radius 5.29177210903(80)×10−11 m 1.5×10−10 [42]
Hartree energy 4.3597447222071(85)×10−18 J 1.9×10−12 [43]
Rydberg unit of energy 2.1798723611035(42)×10−18 J 1.9×10−12 [44]
Rydberg constant 10973731.568160(21) m−1 1.9×10−12 [45]
Fermi coupling constant 1.1663787(6)×10−5 GeV−2 5.1×10−7 [46]
Avogadro constant 6.02214076×1023 mol−1 0 [47]
molar gas constant 8.31446261815324 J⋅mol−1⋅K−1 0 [48]
Faraday constant 96485.3321233100184 C⋅mol−1 0 [49]
molar Planck constant 3.9903127128934314×10−10 J⋅s⋅mol−1 0 [50]
atomic mass of carbon-12 1.99264687992(60)×10−26 kg 3.0×10−10 [51]
molar mass of carbon-12 11.9999999958(36)×10−3 kg⋅mol−1 3.0×10−10 [52]
atomic mass constant 1.66053906660(50)×10−27 kg 3.0×10−10 [53]
molar mass constant 0.99999999965(30)×10−3 kg⋅mol−1 3.0×10−10 [54]
molar volume of silicon 1.205883199(60)×10−5 m3⋅mol−1 4.9×10−8 [55]
hyperfine transition frequency of 133Cs 9192631770 Hz 0 [56]

Uncertainties[edit]

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 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[edit]

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 , which gives the correspondence of the dimension temperature to the dimension of energy per degree of freedom, and the Avogadro constant , 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 .

See also[edit]

Notes[edit]

  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.
  3. ^ , where is the principal branch of the Lambert W function.
  4. ^ , where is the principal branch of the Lambert W function.

References[edit]

  1. ^ "2018 CODATA Value: Newtonian constant of gravitation". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  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 2021-04-28.
  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: vacuum magnetic permeability". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  6. ^ "2018 CODATA Value: characteristic impedance of vacuum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-10-31.
  7. ^ "2018 CODATA Value: vacuum electric permittivity". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  8. ^ "vacuum electric permittivity". NIST.gov. NIST. Retrieved 2 June 2022.
  9. ^ "2018 CODATA Value: Boltzmann constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  10. ^ "2018 CODATA Value: Stefan–Boltzmann constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  11. ^ "2018 CODATA Value: first radiation constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  12. ^ "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.
  13. ^ "2018 CODATA Value: second radiation constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  14. ^ "2018 CODATA Value: Wien wavelength displacement law constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  15. ^ "2018 CODATA Value: Wien frequency displacement law constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  16. ^ 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.
  17. ^ "2018 CODATA Value: elementary charge". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  18. ^ "2018 CODATA Value: conductance quantum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  19. ^ "2018 CODATA Value: inverse of conductance quantum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  20. ^ "2018 CODATA Value: von Klitzing constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  21. ^ "2018 CODATA Value: Josephson constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  22. ^ "2018 CODATA Value: magnetic flux quantum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  23. ^ "2018 CODATA Value: fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  24. ^ "2018 CODATA Value: inverse fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  25. ^ "2018 CODATA Value: electron mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  26. ^ "2018 CODATA Value: proton mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  27. ^ "2018 CODATA Value: neutron mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-08-23.
  28. ^ "2018 CODATA Value: muon mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  29. ^ "2018 CODATA Value: tau mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  30. ^ "t-quark mass". pdglive.lbl.gov. Particle Data Group. Retrieved 9 July 2022. t-quark mass (direct measurements): 172.69(30) GeV/c2
  31. ^ "2018 CODATA Value: proton-electron mass ratio". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  32. ^ "2018 CODATA Value: W to Z mass ratio". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-12-21.
  33. ^ "2018 CODATA Value: weak mixing angle". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  34. ^ "2018 CODATA Value: electron g factor". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2020-03-13.
  35. ^ "2018 CODATA Value: muon g factor". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  36. ^ "2018 CODATA Value: proton g factor". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-03-08.
  37. ^ "2018 CODATA Value: quantum of circulation". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  38. ^ "2018 CODATA Value: Bohr magneton". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  39. ^ "2018 CODATA Value: nuclear magneton". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  40. ^ "2018 CODATA Value: classical electron radius". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  41. ^ "2018 CODATA Value: Thomson cross section". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  42. ^ "2018 CODATA Value: Bohr radius". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  43. ^ "2018 CODATA Value: Hartree energy". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  44. ^ "Rydberg constant times hc in J". NIST.gov. NIST. Retrieved 23 June 2022.
  45. ^ "2018 CODATA Value: Rydberg constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  46. ^ "2018 CODATA Value: Fermi coupling constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  47. ^ "2018 CODATA Value: Avogadro constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  48. ^ "2018 CODATA Value: molar gas constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  49. ^ "2018 CODATA Value: Faraday constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  50. ^ "2018 CODATA Value: molar Planck constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  51. ^ "atomic mass constant". NIST.gov. NIST. Retrieved 5 June 2022.
  52. ^ "2018 CODATA Value: molar mass of carbon-12". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  53. ^ "2018 CODATA Value: atomic mass constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  54. ^ "2018 CODATA Value: molar mass constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  55. ^ "2018 CODATA Value: molar volume of silicon". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-06-23.
  56. ^ "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.