Physical Constants

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A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement.

There are many physical constants in science, some of the most widely recognized being the speed of light in vacuum c, the gravitational constant G, Planck's constant h, the electric constant ε0, and the elementary charge e. Physical constants can take many dimensional forms: the speed of light signifies a maximum speed limit of the universe and is expressed dimensionally as length divided by time; while the fine-structure constant α, which characterizes the strength of the electromagnetic interaction, is dimensionless.

Table of universal constants

Quantity Symbol Value Relative Standard Uncertainty
speed of light in vacuum c \, 299 792 458 m·s−1 defined
Newtonian constant of gravitation G \, \small G = \left(6.67428 \pm 0.00067 \right) \times 10^{-11} \ \mbox{m}^3 \ \mbox{kg}^{-1} \ \mbox{s}^{-2}. 1.0 × 10−4
Planck constant h \, 6.626 068 96(33) × 10−34 J·s 5.0 × 10−8
reduced Planck constant \hbar = h / (2 \pi) 3.313 034 48π-1 × 10−34 J·s = 1.054 571 628(53) × 10−34 J·s 5.0 × 10−8

Table of Other Accepted & Useful Constants

Quantity Symbol Value<ref name="concise" /> (SI units) Relative Standard Uncertainty
Stefan-Boltzmann constant \sigma = (\pi^2 / 60) k^4 / \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) /   \, 4.965 114 231... 2.897 768 5(51) × 10−3 m·K 1.7 × 10−6
atomic mass unit (unified atomic mass unit) m_u = 1 \ u \, 1.660 538 86(28) × 10−27 kg 1.7 × 10−7
Avogadro's number N_A, L \, 6.022 141 5(10) × 1023 mol−1 1.7 × 10−7
Boltzmann constant k = R / N_A \, 1.380 650 388 238 137 546 253 272 195 613 5(24) × 10−23 J·K−1 1.8 × 10−6
Faraday constant F = N_A e \, 96 485.337 716 389 95(83)C·mol−1 8.6 × 10−8
Bohr radius a_0 = \alpha / 4 \pi R_\infin \, 0.529 177 2108(18) × 10−10 m 3.3 × 10−9
classical electron radius r_e = e^2 / 4\pi\epsilon_0 m_e c^2\, 2.817 940 299 579 513 654 416 052 301 942(58) × 10−15 m 2.1 × 10−9
electron mass m_e \, 9.109 382 15(45) × 10−31 kg 5.0 × 10−8
Fermi coupling constant G_F / (\hbar c)^3 1.166 39(1) × 10−5 GeV−2 8.6 × 10−6
fine-structure constant \alpha = \mu_0 e^2 c / (2 h) = e^2 / (4 \pi \epsilon_0 \hbar c) \, 7.297 352 537 6(50) × 10−3 6.8 × 10−10
Hartree energy E_h = 2 R_\infin h c \, 4.359 744 17(75) × 10−18 J 1.7 × 10−7
proton mass m_p \, 1.672 621 637(83) × 10−27 kg 5.0 × 10−8
quantum of circulation h / 2 m_e \, 3.636 947 550(24) × 10−4 m² s−1 6.7 × 10−9
Rydberg constant R_\infin = \alpha^2 m_e c / 2 h \, 10 973 731.568 525(73) m−1 6.6 × 10−12
Thomson Cross section (8 \pi / 3)r_e^2 6.652 458 73(13) × 10−292.0 × 10−8
Weinberg angle \sin^2 \theta_W = 1 - (m_W / m_Z)^2 \, 0.222 15(76)</td>

<td>3.4 × 10−3

Table of electromagnetic constants

Quantity Symbol Value<ref name="concise">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.</ref> (SI units) Relative Standard Uncertainty
magnetic constant (vacuum permeability)  \mu_0 \, 4π × 10−7 N·A−2 = 1.256 637 061... × 10−6 N·A−2 defined
electric constant (vacuum permittivity)  \epsilon_0 = 1/(\mu_0 c^2) \, 2.781 625 140 134 046 080 435 224 912 12π-1 × 10-11 F·m−1 = 8.854 187 817... × 10−12 F·m−1 defined
characteristic impedance of vacuum Z_0 = \mu_0 c \, 119.916 983 2π Ω = 376.730 313 461... Ω defined
Coulomb's constant \kappa = 1 / 4\pi\epsilon_0 \, 8.987 551 787 368 176 4 × 109 N·m²·C−2 defined
elementary charge e
\,

1.602 176 487(40) × 10−19 C 2.5 × 10−8
Bohr magneton \mu_B = e \hbar / 2 m_e 927.400 915(23) × 10−26 J·T−1 2.5 × 10−8
conductance quantum G_0 = 2 e^2 / h \, 7.748 091 717 914 392 775 819 594 884 104 2(53) × 10−5 S 6.8 × 10−10
inverse conductance quantum G_0^{-1} = h / 2 e^2 \, 12 906.403 749 556 760 396 515 369 018 534(88) Ω 6.8 × 10−10
Josephson constant K_J = 2 e / h \, 4.835 978 91(12) × 1014 Hz·V−1 2.5 × 10−8
magnetic flux quantum \phi_0 = h / 2 e \, 2.067 833 667(52) × 10−15 Wb 2.5 × 10−8
nuclear magneton \mu_N = e \hbar / 2 m_p 5.050 783 43(43) × 10−27 J·T−1 8.6 × 10−8
von Klitzing constant R_K = h / e^2 \, 25 812.807 499 113 520 793 030 738 037 068(18) Ω 6.8 × 10−10

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