In science, a physical constant is a physical quantity whose numerical 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.

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.

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^-5 per year for the fine structure constant α and 10^-11 for the gravitational constant G). It is currently disputed [http://xxx.lanl.gov/pdf/physics/0110060 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.

Unless the system of natural units is used, the numerical values of dimensionful physical constants are artifacts of the unit system used, such as SI or cgs; that is, they are essentially conversion factors of human construct.

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.

Constants that are independent of systems of units are typically dimensionless numbers, known as fundamental physical constants, and are truly meaningful parameters of nature, not merely human constructs. The fine-structure constant α is probably the most well-known dimensionless fundamental physical constant. The dimensionless ratios of masses (or other like-dimensioned properties) of fundamental particles are also fundamental physical constants, as are the measure of these properties in terms of natural units.

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

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Quantity	Symbol	Value	Relative Standard Uncertainty
characteristic impedance of vacuum	$Z\_0\; =\; \backslash mu\_0\; c\; \backslash ,$	376.730 313 461... Ω	defined
electric constant (permittivity of free space)	$\backslash epsilon\_0\; =\; 1\; /\; (\; \backslash mu\_0\; c^2\; )\backslash ,$	8.854 187 817... × 10-12F·m-1	defined
magnetic constant (permeability of free space)	$\backslash mu\_0\; \backslash ,$	4π × 10-7 N·A-2 = 1.2566 370 614... × 10-6 N·A-2	defined
Newtonian constant of gravitation	$G\; \backslash ,$	6.6742(10) × 10-11m3·kg-1·s-2	1.5 × 10-4
Planck's constant	$h\; \backslash ,$	6.626 0693(11) × 10-34 J·s	1.7 × 10-7
Dirac's constant	$\backslash hbar\; =\; h\; /\; (2\; \backslash pi)$	1.054 571 68(18) × 10-34 J·s	1.7 × 10-7
speed of light in vacuum	$c\; \backslash ,$	299 792 458 m·s-1	defined

Table of electromagnetic constants

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Quantity	Symbol	Value1 (SI units)	Relative Standard Uncertainty
Bohr magneton	$\backslash mu\_B\; =\; e\; \backslash hbar\; /\; 2\; m\_e$	927.400 949(80) × 10-26 J·T-1	8.6 × 10-8
conductance quantum	$G\_0\; =\; 2\; e^2\; /\; h\; \backslash ,$	7.748 091 733(26) × 10-5 S	3.3 × 10-9
Coulomb's constant	$\backslash kappa\; =\; 1\; /\; 4\backslash pi\backslash epsilon\_0\; \backslash ,$	8.987 742 438 × 109 N·m2C-2	defined
Josephson constant	$K\_J\; =\; 2\; e\; /\; h\; \backslash ,$	483 597.879(41) × 109 Hz· V-1	8.5 × 10-8
magnetic flux quantum	$\backslash phi\_0\; =\; h\; /\; 2\; e\; \backslash ,$	2.067 833 72(18) × 10-15 Wb	8.5 × 10-8
nuclear magneton	$\backslash mu\_N\; =\; e\; \backslash hbar\; /\; 2\; m\_p$	5.050 783 43(43) × 10-27 J·T-1	8.6 × 10-8
resistance quantum	$R\_0\; =\; h\; /\; 2\; e^2\; \backslash ,$	12 906.403 725(43) Ω	3.3 × 10-9
von Klitzing constant	$R\_K\; =\; h\; /\; e^2\; \backslash ,$	25 812.807 449(86) Ω	3.3 × 10-9

Table of atomic and nuclear constants

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Quantity		Symbol	Value1 (SI units)	Relative Standard Uncertainty
Bohr radius		$a\_0\; =\; \backslash alpha\; /\; 4\; \backslash pi\; R\_\backslash infin\; \backslash ,$	0.529 177 2108(18) × 10-10 m	3.3 × 10-9
Fermi coupling constant		$G\_F\; /\; (\backslash hbar\; c)^3$	1.166 39(1) × 10-5 GeV-2	8.6 × 10-6
fine-structure constant		$\backslash alpha\; =\; \backslash mu\_0\; e^2\; c\; /\; (2\; h)\; =\; e^2\; /\; (4\; \backslash pi\; \backslash epsilon\_0\; \backslash hbar\; c)\; \backslash ,$	7.297 352 568(24) × 10-3	3.3 × 10-9
Hartree energy		$E\_h\; =\; 2\; R\_\backslash infin\; h\; c\; \backslash ,$	4.359 744 17(75) × 10-18 J	1.7 × 10-7
quantum of circulation		$h\; /\; 2\; m\_e\; \backslash ,$	3.636 947 550(24) × 10-4 m2 s-1	6.7 × 10-9
Rydberg constant		$R\_\backslash infin\; =\; \backslash alpha^2\; m\_e\; c\; /\; 2\; h\; \backslash ,$	10 973 731.568 525(73) m-1	6.6 × 10-12
Thomson cross section		$(8\; \backslash pi\; /\; 3)r\_e^2$	0.665 245 873(13) × 10-28 m2	2.0 × 10-8
weak mixing angle		$\backslash sin^2\; \backslash theta\_W\; =\; 1\; -\; (m\_W\; /\; m\_Z)^2\; \backslash ,$	0.222 15(76)	3.4 × 10-3

Table of physico-chemical constants

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Quantity		Symbol	Value1 (SI units)	Relative Standard Uncertainty
atomic mass constant (unified atomic mass unit)		$m\_u\; =\; 1\; \backslash \; u\; \backslash ,$	1.660 538 86(28) × 10-27 kg	1.7 × 10-7
Avogadro's number		$N\_A,\; L\; \backslash ,$	6.022 1415(10) × 1023	1.7 × 10-7
Boltzmann constant		$k\; =\; R\; /\; N\_A\; \backslash ,$	1.380 6505(24) × 10-23 J·K-1	1.8 × 10-6
Faraday constant		$F\; =\; N\_A\; e\; \backslash ,$	96 485.3383(83)C·mol-1	8.6 × 10-8
first radiation constant		$c\_1\; =\; 2\; \backslash pi\; h\; c^2\; \backslash ,$	3.741 771 38(64) × 10-16 W·m2	1.7 × 10-7
	for spectral radiance	$c\_\{1L\}\; \backslash ,$	1.191 042 82(20) × 10-16 W · m2 sr-1	1.7 × 10-7
Loschmidt constant	at $T$=273.15 K and $p$=101.325 kPa	$n\_0\; =\; N\_A\; /\; V\_m\; \backslash ,$	2.686 7773(47) × 1025 m-3	1.8 × 10-6
gas constant		$R\; \backslash ,$	8.314 472(15) J·K-1·mol-1	1.7 × 10-6
molar Planck constant		$N\_A\; h\; \backslash ,$	3.990 312 716(27) × 10-10 J · s · mol-1	6.7 × 10-9
molar volume of an ideal gas	at $T$=273.15 K and $p$=100 kPa	$V\_m\; =\; R\; T\; /\; p\; \backslash ,$	22.710 981(40) × 10-3 m3 ·mol-1	1.7 × 10-6
	at $T$=273.15 K and $p$=101.325 kPa		22.413 996(39) × 10-3 m3 ·mol-1	1.7 × 10-6
Sackur-Tetrode constant	at $T$=1 K and $p$=100 kPa	$S\_0\; /\; R\; =\; \backslash frac\{5\}\{2\}$ $+\; \backslash ln\backslash left(2\backslash pi\; m\_u\; k\; T\; /\; h^2)^\{3/2\}\; k\; T\; /\; p\; \backslash right$	-1.151 7047(44)	3.8 × 10-6
	at $T$=1 K and $p$=101.325 kPa		-1.164 8677(44)	3.8 × 10-6
second radiation constant		$c\_2\; =\; h\; c\; /\; k\; \backslash ,$	1.438 7752(25) × 10-2 m·K	1.7 × 10-6
Stefan-Boltzmann constant		$\backslash sigma\; =\; (\backslash pi^2\; /\; 60)\; k^4\; /\; \backslash hbar^3\; c^2$	5.670 400(40) × 10-8 W·m-2·K-4	7.0 × 10-6
Wien displacement law constant		$b\; =\; (h\; c\; /\; k)\; /\; \backslash ,$ 4.965 114 231...	2.897 7685(51) × 10-3 m · K	1.7 × 10-6

Table of adopted values

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Quantity		Symbol	Value (SI units)	Relative Standard Uncertainty
conventional value of Josephson constant2		$K\_\{J-90\}\; \backslash ,$	483 597.9 × 109 Hz · V-1	defined
conventional value of von Klitzing constant3		$R\_\{K-90\}\; \backslash ,$	25 812.807 Ω	defined
molar mass	constant	$M\_u\; =\; M(\backslash ,^\{12\}\backslash mbox\{C\})\; /\; 12$	1 × 10-3 kg · mol-1	defined
	of carbon-12	$M(\backslash ,^\{12\}\backslash mbox\{C\})\; =\; N\_A\; m(\backslash ,^\{12\}\backslash mbox\{C\})$	12 × 10-3 kg · mol−1	defined
standard acceleration of gravity (gee, free fall on Earth)		$g\_n\; \backslash ,\backslash !$	9.806 65 m·s-2	defined
standard atmosphere		$\backslash mbox\{atm\}\; \backslash ,$	101 325 Pa	defined

Notes

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¹The 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.
²This is the value adopted internationally for realizing representations of the volt using the Josephson effect.
³This is the value adopted internationally for realizing representations of the ohm using the quantum Hall effect.

See also

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

Further reading

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

References

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

Measurement | Physical constants

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