List of physical constants explained

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

Symbol	Quantity	Value	Relativestandarduncertainty	Ref
c	speed of light in vacuum
h	Planck constant
\hbar=h/2\pi	reduced Planck constant
k,kB	Boltzmann constant
G	Newtonian constant of gravitation
Λ	cosmological constant			[1] [2]
\sigma=\pi2 4 k B /60\hbar3c2	Stefan–Boltzmann constant
c1=2\pihc2	first radiation constant
c1L=2hc2/sr	first radiation constant for spectral radiance
c2=hc/kB	second radiation constant
b	Wien wavelength displacement law constant
b'	Wien frequency displacement law constant
bentropy	Wien entropy displacement law constant			[3]
e	elementary charge
G0=2e2/h	conductance quantum
-1 G 0 =h/2e2	inverse conductance quantum
RK=h/e2	von Klitzing constant
KJ=2e/h	Josephson constant
\Phi0=h/2e	magnetic flux quantum
\alpha=e2/4\pi\varepsilon0\hbarc	fine-structure constant
\alpha-1	inverse fine-structure constant
\mu0=4\pi\alpha\hbar/e2c	vacuum magnetic permeability
Z0=4\pi\alpha\hbar/e2	characteristic impedance of vacuum
\varepsilon0=e2/4\pi\alpha\hbarc	vacuum electric permittivity
me	electron mass
m\mu	muon mass
m\tau	tau mass
mp	proton mass
mn	neutron mass
mp/me	proton-to-electron mass ratio
mW/mZ	W-to-Z mass ratio
\sin2\thetaW =1-(mW/mZ)2	sine-square weak mixing angle			[4]
ge	electron g-factor
g\mu	muon g-factor
gp	proton g-factor
h/2me	quantum of circulation
\muB=e\hbar/2me	Bohr magneton
\muN=e\hbar/2mp	nuclear magneton
re=\alpha\hbar/mec	classical electron radius
\sigmae=(8\pi/ 2 3)r e	Thomson cross section
a0=\hbar/\alphamec	Bohr radius
Rinfin=\alpha2mec/2h	Rydberg constant
Ry=Rinfinhc=Eh/2	Rydberg unit of energy
Eh=\alpha2mec2	Hartree energy
GF/(\hbarc)3	Fermi coupling constant
NA	Avogadro constant
R=NAkB	molar gas constant
F=NAe	Faraday constant
NAh	molar Planck constant
M({}12C)=NAm({}12C)	molar mass of carbon-12
mu=m({}12C)/12	atomic mass constant
Mu=M({}12C)/12	molar mass constant
Vm(Si)	molar volume of silicon
\Delta\nuCs	hyperfine transition frequency of 133Cs

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

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

, 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

• List of mathematical constants
• Mathematical constant
• Physical constant
• List of particles

Notes and References

1. Planck Collaboration. 2020. Planck 2018 results. VI. Cosmological parameters (page 17: Λ =).. Astronomy & Astrophysics. 641. A6. 10.1051/0004-6361/201833910. 1807.06209. 2020A&A...641A...6P . 119335614.
2. 1 . Workman . R L . Burkert . V D . Crede . V . Klempt . E . Thoma . U . Tiator . L . Agashe . K . Aielli . G . Allanach . B C . Amsler . C . Antonelli . M . Aschenauer . E C . Asner . D M . Baer . H . Banerjee . Sw . Barnett . R M . Baudis . L . Bauer . C W . Beatty . J J . Belousov . V I . Beringer . J . Bettini . A . Biebel . O . Black . K M . Blucher . E . Bonventre . R . Bryzgalov . V V . Buchmuller . O . Bychkov . M A . Cahn . R N . Carena . M . Ceccucci . A . Cerri . A . Chivukula . R Sekhar . Cowan . G . Cranmer . K . Cremonesi . O . D'Ambrosio . G . Damour . T . de Florian . D . de Gouvêa . A . DeGrand . T . de Jong . P . Demers . S . Dobrescu . B A . D'Onofrio . M . Doser . M . Dreiner . H K . Eerola . P . Egede . U . Eidelman . S . El-Khadra . A X . Ellis . J . Eno . S C . Erler . J . Ezhela . V V . Fetscher . W . Fields . B D . Freitas . A . Gallagher . H . Gershtein . Y . Gherghetta . T . Gonzalez-Garcia . M C . Goodman . M . Grab . C . Gritsan . A V . Grojean . C . Groom . D E . Grünewald . M . Gurtu . A . Gutsche . T . Haber . H E . Hamel . Matthieu . Hanhart . C . Hashimoto . S . Hayato . Y . Hebecker . A . Heinemeyer . S . Hernández-Rey . J J . Hikasa . K . Hisano . J . Höcker . A . Holder . J . Hsu . L . Huston . J . Hyodo . T . Ianni . Al . Kado . M . Karliner . M . Katz . U F . Kenzie . M . Khoze . V A . Klein . S R . Krauss . F . Kreps . M . Križan . P . Krusche . B . Kwon . Y . Lahav . O . Laiho . J . Lellouch . L P . Lesgourgues . J . Liddle . A R . Ligeti . Z . Lin . C-J . Lippmann . C . Liss . T M . Littenberg . L . Lourenço . C . Lugovsky . K S . Lugovsky . S B . Lusiani . A . Makida . Y . Maltoni . F . Mannel . T . Manohar . A V . Marciano . W J . Masoni . A . Matthews . J . Meißner . U-G . Melzer-Pellmann . I-A . Mikhasenko . M . Miller . D J . Milstead . D . Mitchell . R E . Mönig . K . Molaro . P . Moortgat . F . Moskovic . M . Nakamura . K . Narain . M . Nason . P . Navas . S . Nelles . A . Neubert . M . Nevski . P . Nir . Y . Olive . K A . Patrignani . C . Peacock . J A . Petrov . V A . Pianori . E . Pich . A . Piepke . A . Pietropaolo . F . Pomarol . A . Pordes . S . Profumo . S . Quadt . A . Rabbertz . K . Rademacker . J . Raffelt . G . Ramsey-Musolf . M . Ratcliff . B N . Richardson . P . Ringwald . A . Robinson . D J . Roesler . S . Rolli . S . Romaniouk . A . Rosenberg . L J . Rosner . J L . Rybka . G . Ryskin . M G . Ryutin . R A . Sakai . Y . Sarkar . S . Sauli . F . Schneider . O . Schönert . S . Scholberg . K . Schwartz . A J . Schwiening . J . Scott . D . Sefkow . F . Seljak . U . Sharma . V . Sharpe . S R . Shiltsev . V . Signorelli . G . Silari . M . Simon . F . Sjöstrand . T . Skands . P . Skwarnicki . T . Smoot . G F . Soffer . A . Sozzi . M S . Spanier . S . Spiering . C . Stahl . A . Stone . S L . Sumino . Y . Syphers . M J . Takahashi . F . Tanabashi . M . Tanaka . J . Taševský . M . Terao . K . Terashi . K . Terning . J . Thorne . R S . Titov . M . Tkachenko . N P . Tovey . D R . Trabelsi . K . Urquijo . P . Valencia . G . Van de Water . R . Varelas . N . Venanzoni . G . Verde . L . Vivarelli . I . Vogel . P . Vogelsang . W . Vorobyev . V . Wakely . S P . Walkowiak . W . Walter . C W . Wands . D . Weinberg . D H . Weinberg . E J . Wermes . N . White . M . Wiencke . L R . Willocq . S . Wohl . C G . Woody . C L . Yao . W-M . Yokoyama . M . Yoshida . R . Zanderighi . G . Zeller . G P . Zenin . O V . Zhu . R-Y . Zhu . Shi-Lin . Zimmermann . F . Zyla . P A . Review of Particle Physics. 2. Astrophysical Constants and Parameters (2023 revision) . Progress of Theoretical and Experimental Physics . 8 August 2022 . 2022 . 8 . 2 . 10.1093/ptep/ptac097 . 31 May 2024.
3. Delgado-Bonal A . Entropy of radiation: the unseen side of light . Scientific Reports . 7 . 1 . 1642 . May 2017 . 28490790 . 5432030 . 10.1038/s41598-017-01622-6 . 2017NatSR...7.1642D .
4. 1 . Workman . R L . Burkert . V D . Crede . V . Klempt . E . Thoma . U . Tiator . L . Agashe . K . Aielli . G . Allanach . B C . Amsler . C . Antonelli . M . Aschenauer . E C . Asner . D M . Baer . H . Banerjee . Sw . Barnett . R M . Baudis . L . Bauer . C W . Beatty . J J . Belousov . V I . Beringer . J . Bettini . A . Biebel . O . Black . K M . Blucher . E . Bonventre . R . Bryzgalov . V V . Buchmuller . O . Bychkov . M A . Cahn . R N . Carena . M . Ceccucci . A . Cerri . A . Chivukula . R Sekhar . Cowan . G . Cranmer . K . Cremonesi . O . D'Ambrosio . G . Damour . T . de Florian . D . de Gouvêa . A . DeGrand . T . de Jong . P . Demers . S . Dobrescu . B A . D'Onofrio . M . Doser . M . Dreiner . H K . Eerola . P . Egede . U . Eidelman . S . El-Khadra . A X . Ellis . J . Eno . S C . Erler . J . Ezhela . V V . Fetscher . W . Fields . B D . Freitas . A . Gallagher . H . Gershtein . Y . Gherghetta . T . Gonzalez-Garcia . M C . Goodman . M . Grab . C . Gritsan . A V . Grojean . C . Groom . D E . Grünewald . M . Gurtu . A . Gutsche . T . Haber . H E . Hamel . Matthieu . Hanhart . C . Hashimoto . S . Hayato . Y . Hebecker . A . Heinemeyer . S . Hernández-Rey . J J . Hikasa . K . Hisano . J . Höcker . A . Holder . J . Hsu . L . Huston . J . Hyodo . T . Ianni . Al . Kado . M . Karliner . M . Katz . U F . Kenzie . M . Khoze . V A . Klein . S R . Krauss . F . Kreps . M . Križan . P . Krusche . B . Kwon . Y . Lahav . O . Laiho . J . Lellouch . L P . Lesgourgues . J . Liddle . A R . Ligeti . Z . Lin . C-J . Lippmann . C . Liss . T M . Littenberg . L . Lourenço . C . Lugovsky . K S . Lugovsky . S B . Lusiani . A . Makida . Y . Maltoni . F . Mannel . T . Manohar . A V . Marciano . W J . Masoni . A . Matthews . J . Meißner . U-G . Melzer-Pellmann . I-A . Mikhasenko . M . Miller . D J . Milstead . D . Mitchell . R E . Mönig . K . Molaro . P . Moortgat . F . Moskovic . M . Nakamura . K . Narain . M . Nason . P . Navas . S . Nelles . A . Neubert . M . Nevski . P . Nir . Y . Olive . K A . Patrignani . C . Peacock . J A . Petrov . V A . Pianori . E . Pich . A . Piepke . A . Pietropaolo . F . Pomarol . A . Pordes . S . Profumo . S . Quadt . A . Rabbertz . K . Rademacker . J . Raffelt . G . Ramsey-Musolf . M . Ratcliff . B N . Richardson . P . Ringwald . A . Robinson . D J . Roesler . S . Rolli . S . Romaniouk . A . Rosenberg . L J . Rosner . J L . Rybka . G . Ryskin . M G . Ryutin . R A . Sakai . Y . Sarkar . S . Sauli . F . Schneider . O . Schönert . S . Scholberg . K . Schwartz . A J . Schwiening . J . Scott . D . Sefkow . F . Seljak . U . Sharma . V . Sharpe . S R . Shiltsev . V . Signorelli . G . Silari . M . Simon . F . Sjöstrand . T . Skands . P . Skwarnicki . T . Smoot . G F . Soffer . A . Sozzi . M S . Spanier . S . Spiering . C . Stahl . A . Stone . S L . Sumino . Y . Syphers . M J . Takahashi . F . Tanabashi . M . Tanaka . J . Taševský . M . Terao . K . Terashi . K . Terning . J . Thorne . R S . Titov . M . Tkachenko . N P . Tovey . D R . Trabelsi . K . Urquijo . P . Valencia . G . Van de Water . R . Varelas . N . Venanzoni . G . Verde . L . Vivarelli . I . Vogel . P . Vogelsang . W . Vorobyev . V . Wakely . S P . Walkowiak . W . Walter . C W . Wands . D . Weinberg . D H . Weinberg . E J . Wermes . N . White . M . Wiencke . L R . Willocq . S . Wohl . C G . Woody . C L . Yao . W-M . Yokoyama . M . Yoshida . R . Zanderighi . G . Zeller . G P . Zenin . O V . Zhu . R-Y . Zhu . Shi-Lin . Zimmermann . F . Zyla . P A . Review of Particle Physics. 1. Physical Constants (2023 revision) . Progress of Theoretical and Experimental Physics . 8 August 2022 . 2022 . 8 . 1 . 10.1093/ptep/ptac097 . 31 May 2024.