In science, a physical constant is a physical quantity whose numerical value is fixed. It can be constrasted with a mathematical constant, which is a fixed number that does not directly involve a physical measurement.
There are many physical constants in science, some of the most famous being: Planck's constant, the gravitational constant, and Avogadro's constant (better known as Avogadro's number). Constants can take many forms: the Planck length represents a fundamental physical distance; the speed of light in a vacuum signifies a maximum speed limit of the universe; and the fine-structure constant, which characterizes the interaction between electrons and photons, is dimensionless.
Below is a list of physical constants:
| Quantity | Symbol | Value | Ref. |
|---|---|---|---|
| speed of light in vacuum | c | 299 792 458 m·s-1 (defined) | a |
| permeability of vacuum | μ0 | 4π × 10-7 N A-2 (defined) | a |
| 12.566 370 614... × 10-7 N A-2 | a | ||
| permittivity of vacuum | ε0 = 1/(μ0c2) | 8.854 187 817 ... × 10-12 F·m-1 | a |
| characteristic impedance of vacuum | Z0 = μ0c | 376.730 313 461... Ω (defined) | a |
| gravitational constant | G | 6.672 59(85) × 10-11 m3·kg-1·s-2 | ? |
| Planck's constant | h | 6.626 068 76(52) × 10-34 J·s | a |
| Dirac's constant | 1.054 571 596(82) × 10-34 J·s | a | |
| Planck mass | mp = ( |
2.1767(16) × 10-8 kg | a |
| Planck length | lp= ( |
1.6160(12) × 10-35 m | a |
| Planck time | tp = ( |
5.3906(40) × 10-44 s | a |
| elementary charge | e | 1.602 176 462(63) × 10-19 C | a |
| electron rest mass | me | 9.109 381 88(72) × 10-31 kg | a |
| proton rest mass | mp | 1.672 621 58(13) × 10-27 kg | a |
| neutron rest mass | mn | 1.674 927 16(13) × 10-27 kg | a |
| atomic mass constant, (unified atomic mass unit) | mu = 1 u | 1.660 538 73(13) × 10-27 kg | a |
| Avogadro's number | L, NA | 6.022 141 99(47) × 1023 | a |
| Boltzmann constant | k | 1.380 6503(24) × 10-23 J·K-1 | a |
| Faraday constant | F | 9.648 534 15(39) × 104 C·mol-1 | a |
| gas constant | R | 8.314 472(15) J·K-1·mol-1 | a |
| zero of the Celsius scale | 273.15 K (defined) | ? | |
| molar volume, ideal gas, p = 1 bar, θ = 00C | 22.710 981(40) L·mol-1 | a | |
| standard atmosphere | atm | 101 325 Pa (defined) | a |
| fine-structure constant | α = μ0e2c / (2h) | 7.297 352 533(27) × 10-3 | a |
| α-1 | 137.035 999 76(50) | a | |
| Bohr radius | a0 | 5.291 772 083(19) × 10-11 m | a |
| Hartree energy | Eh | 4.359 743 81(34) × 10-18 J | a |
| Rydberg constant | R∞ | 1.097 373 156 8549(83) × 107 m-1 | a |
| Bohr magneton | μB | 9.274 008 99(37) × 10-24 J·T-1 | a |
| electron magnetic moment | μe | -9.284 763 62(37) × 10-24 J·T-1 | a |
| Lande g-factor for free electron | ge | 2.002 319 304 386(20) | ? |
| nuclear magneton | μN | 5.050 786 6(17) × 10-27 J·T-1 | ? |
| proton magnetic moment | μp | 1.410 607 61(47) × 10-26 J·T-1 | ? |
| proton magnetogyric ratio | γp | 2.675 221 28(81) × 108 s-1·T-1 | ? |
| magnetic moment of protons in H20, μ'p | μ'p / μB | 1.520 993 129(17) × 10-3 | ? |
| proton resonance frequency per field in H20 | γ'p / (2π) | 42.576 375 (13) M·Hz·T-1 | ? |
| Stefan-Boltzmann constant | σ | 5.670 400(40) × 10-8 W·m-2·K-4 | a |
| first radiation constant | c1 | 3.741 774 9(22) × 10-16 W·m2 | ? |
| second radiation constant | c2 | 1.438 769 (12) × 10-2 m·K | ? |
| standard acceleration of free fall | gn | 9.80665 m·s-2 (defined) | ? |
Some "constants" are really artifacts of the unit system used, like mks or cgs. In natural units, some of these supposedly physical constants turn out to be mere conversion factors.
aPeter J. Mohr and Barry N. Taylor, "CODATA Recommended Values of the Fundamental Physical Constants: 1998," Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000.[[1]References