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In science, a physical constant is a physical quantity whose value does not change. It can be contrasted with a mathematical constant, which is a fixed value that does not directly involve a physical measurement. Contrary to wide belief, physical constants do not depend on systems of units.

Examples

There are many physical constants in science, some of the most famous being the reduced Planck constant ħ, the gravitational constant G, the speed of light c, the electric constant ε₀, and the elementary charge e. Constants can take many forms: the speed of light in a vacuum signifies a maximum speed limit of the universe; while the fine-structure constant α, which characterizes the interaction between electrons and photons, is dimensionless.

Fundamental Constants

Fundamental physical constants, are basic properties of nature, not depending on our culture. Another civilisation in another Galaxy would find the same values for those constants. All examples above are considered fundamental physical constants, whereas the length of the Eiffel tower or the earths acceleration constant g are not fundamental. While some properties of materials and particles are constant, they do not show up on this page because they are specific to their respective materials or properties alone.

How constant are constants?

Beginning with Paul Dirac in 1937, some scientists have speculated that physical constants may actually decrease in proportion to the age of the universe. Scientific experiments have not yet pinpointed any definite evidence that this is the case, although they have placed upper bounds on the maximum possible relative change per year at very small amounts (roughly 10 per year for the fine structure constant α and 10 for the gravitational constant G). It is currently disputed that any changes in dimensionful physical constants such as G, c, ħ, or ε₀ are operationally meaningless; however, a change in a dimensionless constant such as α is something that would definitely be noticed. If a measurement indicated that a dimensionful physical constant had changed, this would be the result or interpretation of a more fundamental dimensionless constant changing, which is the salient metric.

Anthroposiphic principle

Some people claim that if the physical constants had slightly different values, our universe would be so radically different that intelligent life would probably not have emerged, and that our universe therefore seems to be fine-tuned for intelligent life. The weak anthropic principle simply states that it's only because these fundamental constants acquired their respective values that there was sufficient order and richness in elemental diversity for life to have formed, which subsequently evolved the necessary intelligence toward observing that these constants have taken on the values they have.

Table of universal constants

Quantity	Symbol	Value	Relative Standard Uncertainty
characteristic impedance of vacuum	${\displaystyle Z_{0}=\mu _{0}c\,}$	376.730 313 461... Ω	defined
electric constant (permittivity of free space)	${\displaystyle \epsilon _{0}=1/(\mu _{0}c^{2})\,}$	8.854 187 817... × 10F·m	defined
magnetic constant (permeability of free space)	${\displaystyle \mu _{0}\,}$	4π × 10 N·A = 1.2566 370 614... × 10 N·A	defined
Newtonian constant of gravitation	${\displaystyle G\,}$	6.6742(10) × 10m·kg·s	1.5 × 10
Planck's constant	${\displaystyle h\,}$	6.626 0693(11) × 10 J·s	1.7 × 10
Dirac's constant	${\displaystyle \hbar =h/(2\pi )}$	1.054 571 68(18) × 10 J·s	1.7 × 10
speed of light in vacuum	${\displaystyle c\,}$	299 792 458 m·s	defined

Table of electromagnetic constants

Quantity	Symbol	Value (SI units)	Relative Standard Uncertainty
Bohr magneton	${\displaystyle \mu _{B}=e\hbar /2m_{e}}$	927.400 949(80) × 10 J·T	8.6 × 10
conductance quantum	${\displaystyle G_{0}=2e^{2}/h\,}$	7.748 091 733(26) × 10 S	3.3 × 10
Coulomb's constant	${\displaystyle \kappa =1/4\pi \epsilon _{0}\,}$	8.987 742 438 × 10 N·mC	defined
elementary charge	${\displaystyle e\,}$	1.602 176 53(14) × 10 C	8.5 × 10
Josephson constant	${\displaystyle K_{J}=2e/h\,}$	483 597.879(41) × 10 Hz· V	8.5 × 10
magnetic flux quantum	${\displaystyle \phi _{0}=h/2e\,}$	2.067 833 72(18) × 10 Wb	8.5 × 10
nuclear magneton	${\displaystyle \mu _{N}=e\hbar /2m_{p}}$	5.050 783 43(43) × 10 J·T	8.6 × 10
resistance quantum	${\displaystyle R_{0}=h/2e^{2}\,}$	12 906.403 725(43) Ω	3.3 × 10
von Klitzing constant	${\displaystyle R_{K}=h/e^{2}\,}$	25 812.807 449(86) Ω	3.3 × 10

Table of atomic and nuclear constants

Quantity		Symbol	Value (SI units)	Relative Standard Uncertainty
Bohr radius		${\displaystyle a_{0}=\alpha /4\pi R_{\infty }\,}$	0.529 177 2108(18) × 10 m	3.3 × 10
Fermi coupling constant		${\displaystyle G_{F}/(\hbar c)^{3}}$	1.166 39(1) × 10 GeV	8.6 × 10
fine-structure constant		${\displaystyle \alpha =\mu _{0}e^{2}c/(2h)=e^{2}/(4\pi \epsilon _{0}\hbar c)\,}$	7.297 352 568(24) × 10	3.3 × 10
Hartree energy		${\displaystyle E_{h}=2R_{\infty }hc\,}$	4.359 744 17(75) × 10 J	1.7 × 10
quantum of circulation		${\displaystyle h/2m_{e}\,}$	3.636 947 550(24) × 10 m s	6.7 × 10
Rydberg constant		${\displaystyle R_{\infty }=\alpha ^{2}m_{e}c/2h\,}$	10 973 731.568 525(73) m	6.6 × 10
Thomson cross section		${\displaystyle (8\pi /3)r_{e}^{2}}$	0.665 245 873(13) × 10 m	2.0 × 10
weak mixing angle		${\displaystyle \sin ^{2}\theta _{W}=1-(m_{W}/m_{Z})^{2}\,}$	0.222 15(76)	3.4 × 10

Table of physico-chemical constants

Quantity		Symbol	Value (SI units)	Relative Standard Uncertainty
atomic mass constant (unified atomic mass unit)		${\displaystyle m_{u}=1\ u\,}$	1.660 538 86(28) × 10 kg	1.7 × 10
Avogadro's number		${\displaystyle N_{A},L\,}$	6.022 1415(10) × 10	1.7 × 10
Boltzmann constant		${\displaystyle k=R/N_{A}\,}$	1.380 6505(24) × 10 J·K	1.8 × 10
Faraday constant		${\displaystyle F=N_{A}e\,}$	96 485.3383(83)C·mol	8.6 × 10
first radiation constant		${\displaystyle c_{1}=2\pi hc^{2}\,}$	3.741 771 38(64) × 10 W·m	1.7 × 10
	for spectral radiance	${\displaystyle c_{1L}\,}$	1.191 042 82(20) × 10 W · m sr	1.7 × 10
Loschmidt constant	at ${\displaystyle T}$=273.15 K and ${\displaystyle p}$=101.325 kPa	${\displaystyle n_{0}=N_{A}/V_{m}\,}$	2.686 7773(47) × 10 m	1.8 × 10
gas constant		${\displaystyle R\,}$	8.314 472(15) J·K·mol	1.7 × 10
molar Planck constant		${\displaystyle N_{A}h\,}$	3.990 312 716(27) × 10 J · s · mol	6.7 × 10
molar volume of an ideal gas	at ${\displaystyle T}$=273.15 K and ${\displaystyle p}$=100 kPa	${\displaystyle V_{m}=RT/p\,}$	22.710 981(40) × 10 m ·mol	1.7 × 10
	at ${\displaystyle T}$=273.15 K and ${\displaystyle p}$=101.325 kPa		22.413 996(39) × 10 m ·mol	1.7 × 10
Sackur-Tetrode constant	at ${\displaystyle T}$=1 K and ${\displaystyle p}$=100 kPa	${\displaystyle S_{0}/R={\frac {5}{2}}}$ ${\displaystyle +\ln \left}$	-1.151 7047(44)	3.8 × 10
	at ${\displaystyle T}$=1 K and ${\displaystyle p}$=101.325 kPa		-1.164 8677(44)	3.8 × 10
second radiation constant		${\displaystyle c_{2}=hc/k\,}$	1.438 7752(25) × 10 m·K	1.7 × 10
Stefan-Boltzmann constant		${\displaystyle \sigma =(\pi ^{2}/60)k^{4}/\hbar ^{3}c^{2}}$	5.670 400(40) × 10 W·m·K	7.0 × 10
Wien displacement law constant		${\displaystyle b=(hc/k)/\,}$ 4.965 114 231...	2.897 7685(51) × 10 m · K	1.7 × 10

Table of adopted values

Quantity		Symbol	Value (SI units)	Relative Standard Uncertainty
conventional value of Josephson constant		${\displaystyle K_{J-90}\,}$	483 597.9 × 10 Hz · V	defined
conventional value of von Klitzing constant		${\displaystyle R_{K-90}\,}$	25 812.807 Ω	defined
molar mass	constant	${\displaystyle M_{u}=M(\,^{12}{\mbox{C}})/12}$	1 × 10 kg · mol	defined
	of carbon-12	${\displaystyle M(\,^{12}{\mbox{C}})=N_{A}m(\,^{12}{\mbox{C}})}$	12 × 10 kg · mol	defined
standard acceleration of gravity (gee, free fall on Earth)		${\displaystyle g_{n}\,\!}$	9.806 65 m·s	defined
standard atmosphere		${\displaystyle {\mbox{atm}}\,}$	101 325 Pa	defined

Notes

The values are given in the so-called concise form; the number in brackets is the standard uncertainty, which is the value multiplied by the relative standard uncertainty.
This is the value adopted internationally for realizing representations of the volt using the Josephson effect.
This is the value adopted internationally for realizing representations of the ohm using the quantum Hall effect.

See also

• Astronomical constant
• Scientific constants named after people
• Fine-tuned universe
• Physical law
• CODATA
• atomic units
• Planck units

Further reading

• John D. Barrow, 2002. The Constants of Nature. Pantheon Books.

References

• CODATA Recommendations - 2002 CODATA Internationally recommended values of the Fundamental Physical Constants

• Measurement
• Physical constants