Physical constant

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: Planck's constant, the gravitational constant, and 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.

Beginning with 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 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).

Some "constants" are really artifacts of the unit system used, such as mks or cgs. In natural units, some of these supposedly physical constants turn out to be conversion factors.

Constants that are independent of systems of units are typically dimensionless numbers, and are known as fundamental physical constants.

Some believe that if the physical constants had slightly different values, our universe would be so different that intelligent life would probably not have emerged, and that our universe seems to be fine-tuned for intelligent life.

Also see

Scientific constants named after people
Fine-tuned universe

Table of physical constants

Selected physical constants. 2002 CODATA recommended values unless noted otherwise.
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
permeability of vacuum	μ₀	1.2566 370 614... × 10^-6 N·A^-2	a
permittivity of vacuum	ε₀ = 1/(μ₀c²)	8.854 187 817 ... × 10^-12F·m^-1	a
characteristic impedance of vacuum	Z₀ = μ₀c	376.730 313 461... Ω (defined)	a
gravitational constant	G	6.6742(10) × 10^-11m³·kg^-1·s^-2	a
Planck's constant	h	6.626 0693(11) × 10^-34 J·s	a
Dirac's constant	= h / (2π)	1.054 571 68(18) × 10^-34 J·s	a
Planck mass	m_p = ( c / G)^1/2	2.176 45(16) × 10^-8 kg	a
Planck length	l_p= ( G / c³)^1/2	1.616 24(12) × 10^-35 m	a
Planck time	t_p = ( G /c⁵)^1/2	5.391 21(40) × 10^-44 s	a
elementary charge	e	1.602 176 53(14) × 10^-19 C	a
electron rest mass	m_e	9.109 3826(16) × 10^-31 kg	a
proton rest mass	m_p	1.672 621 71(29) × 10^-27 kg	a
neutron rest mass	m_n	1.674 927 28(29) × 10^-27 kg	a
atomic mass constant (unified atomic mass unit)	m_u = 1 u	1.660 538 86(28) × 10^-27 kg	a
Avogadro's number	L, N_A	6.022 1415(10) × 10²³	a
Boltzmann constant	k	1.380 6505(24) × 10^-23 J·K^-1	a
Faraday constant	F	96 485.3383(83)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 of an ideal gas (273.15 K, 100 kPa)		22.710 981(40) × 10^-3 m³ ·mol^-1	a
molar volume of an ideal gas (273.15 K, 101.325 kPa)		22.413 996(39) × 10^-3 m³ ·mol^-1	a
standard atmosphere	atm	101 325 Pa (defined)	a
fine-structure constant	α = μ₀e²c / (2h)	7.297 352 568(24) × 10^-3	a
fine-structure constant	α^-1	137.035 999 11(46)	a
Bohr radius	a₀	0.529 177 2108(18) × 10^-10 m	a
Hartree energy	E_h	4.359 744 17(75) × 10^-18 J	a
Rydberg constant	R_∞	10 973 731.568 525(73) m^-1	a
Bohr magneton	μ_B	927.400 949(80) × 10^-26 J·T^-1	a
electron magnetic moment	μ_e	-928.476 412(80) × 10^-26 J·T^-1	a
Lande g-factor for free electron	g_e	2.002 319 304 386(20)	?
nuclear magneton	μ_N	5.050 783 43(43) × 10^-27 J·T^-1	a
proton magnetic moment	μ_p	1.410 606 71(12) × 10^-26 J·T^-1	a
proton magnetogyric ratio	γ_p	2.675 222 05(23) × 10⁸ s^-1·T^-1	a
magnetic moment of protons in H₂0	μ'_p / μ_B	1.520 993 129(17) × 10^-3	?
proton resonance frequency per field in H₂0	γ'_p / (2π)	42.576 375 (13) MHz·T^-1	?
Stefan-Boltzmann constant	σ	5.670 400(40) × 10^-8 W·m^-2·K^-4	a
first radiation constant	c₁	3.741 771 38(64) × 10^-16 W·m²	a
second radiation constant	c₂	1.438 7752(25) × 10^-2 m·K	a
standard acceleration of free fall on Earth	g_n	9.806 65 m·s^-2 (defined)	a

^aCODATA Internationally recommended values of the Fundamental Physical Constants (at The NIST References on Constants, Units, and Uncertainty )