Physics Constants

Comprehensive reference of fundamental physical constants with precise values, symbols, and units

Constant Name	Symbol	Value	Unit	Category	Description
Speed of Light in Vacuum	c	299,792,458	m/s	fundamental	Maximum speed at which all conventional matter and information can travel
Planck Constant	h	6.62607015 × 10⁻³⁴	J⋅s	fundamental	Relates the energy of a photon to its frequency
Reduced Planck Constant	ℏ	1.054571817 × 10⁻³⁴	J⋅s	fundamental	Planck constant divided by 2π, commonly used in quantum mechanics
Gravitational Constant	G	6.67430 × 10⁻¹¹ ±0.00015 × 10⁻¹¹	m³⋅kg⁻¹⋅s⁻²	fundamental	Universal constant of gravitation
Elementary Charge	e	1.602176634 × 10⁻¹⁹	C	fundamental	Electric charge carried by a single proton or electron
Boltzmann Constant	k	1.380649 × 10⁻²³	J/K	fundamental	Relates average kinetic energy of particles to temperature
Avogadro Constant	N_A	6.02214076 × 10²³	mol⁻¹	fundamental	Number of particles in one mole of substance
Fine Structure Constant	α	7.2973525693 × 10⁻³ ±0.0000000011 × 10⁻³	dimensionless	fundamental	Coupling constant characterizing the strength of electromagnetic interaction
Magnetic Flux Quantum	Φ_0	2.067833848 × 10⁻¹⁵	Wb	fundamental	Quantum of magnetic flux
Conductance Quantum	G_0	7.748091729 × 10⁻⁵	S	fundamental	Quantum of electrical conductance
Electron Mass	m_e	9.1093837015 × 10⁻³¹ ±0.0000000028 × 10⁻³¹	kg	atomic	Rest mass of an electron
Proton Mass	m_p	1.67262192369 × 10⁻²⁷ ±0.00000000051 × 10⁻²⁷	kg	atomic	Rest mass of a proton
Neutron Mass	m_n	1.67492749804 × 10⁻²⁷ ±0.00000000095 × 10⁻²⁷	kg	atomic	Rest mass of a neutron
Bohr Radius	a_0	5.29177210903 × 10⁻¹¹ ±0.00000000080 × 10⁻¹¹	m	atomic	Radius of the first Bohr orbit of hydrogen atom
Rydberg Constant	R_∞	1.0973731568160 × 10⁷ ±0.000000000021 × 10⁷	m⁻¹	atomic	Wavenumber of the lowest-energy photon capable of ionizing hydrogen
Hartree Energy	E_h	4.3597447222071 × 10⁻¹⁸ ±0.0000000000085 × 10⁻¹⁸	J	atomic	Atomic unit of energy
Bohr Magneton	μ_B	9.2740100783 × 10⁻²⁴ ±0.0000000028 × 10⁻²⁴	J/T	atomic	Magnetic moment of an electron due to its orbital or spin angular momentum
Nuclear Magneton	μ_N	5.0507837461 × 10⁻²⁷ ±0.0000000015 × 10⁻²⁷	J/T	atomic	Magnetic moment of a nucleon
Compton Wavelength	λ_C	2.42631023867 × 10⁻¹² ±0.00000000073 × 10⁻¹²	m	atomic	Wavelength of a photon whose energy equals the rest mass energy of an electron
Classical Electron Radius	r_e	2.8179403262 × 10⁻¹⁵ ±0.0000000013 × 10⁻¹⁵	m	atomic	Radius of an electron if its mass were entirely due to its electrostatic energy
Thomson Cross Section	σ_e	6.6524587321 × 10⁻²⁹ ±0.0000000060 × 10⁻²⁹	m²	atomic	Scattering cross section for Thomson scattering
Vacuum Permittivity	ε_0	8.8541878128 × 10⁻¹² ±0.0000000013 × 10⁻¹²	F/m	electromagnetic	Electric constant, permittivity of free space
Vacuum Permeability	μ_0	1.25663706212 × 10⁻⁶ ±0.00000000019 × 10⁻⁶	N/A²	electromagnetic	Magnetic constant, permeability of free space
Coulomb Constant	k_e	8.9875517923 × 10⁹ ±0.0000000014 × 10⁹	N⋅m²/C²	electromagnetic	Electrostatic force constant
Characteristic Impedance of Vacuum	Z_0	376.730313668 ±0.000000057	Ω	electromagnetic	Impedance of free space
Magnetic Constant	μ_0	4π × 10⁻⁷	H/m	electromagnetic	Magnetic permeability of free space
Electric Constant	ε_0	8.8541878128 × 10⁻¹² ±0.0000000013 × 10⁻¹²	F/m	electromagnetic	Electric permittivity of free space
Josephson Constant	K_J	483597.8484 × 10⁹ ±0.0000019 × 10⁹	Hz/V	electromagnetic	Frequency-voltage ratio in Josephson effect
von Klitzing Constant	R_K	25812.80745 ±0.00018	Ω	electromagnetic	Quantum Hall resistance
Stefan-Boltzmann Constant	σ	5.670374419 × 10⁻⁸ ±0.000000081 × 10⁻⁸	W⋅m⁻²⋅K⁻⁴	thermodynamic	Relates total energy radiated by a black body to its temperature
First Radiation Constant	c_1	3.741771852 × 10⁻¹⁶ ±0.000000057 × 10⁻¹⁶	W⋅m²	thermodynamic	Used in Planck's law of black body radiation
Second Radiation Constant	c_2	1.438776877 × 10⁻² ±0.000000022 × 10⁻²	m⋅K	thermodynamic	Used in Wien's displacement law
Gas Constant	R	8.314462618 ±0.000000075	J⋅mol⁻¹⋅K⁻¹	thermodynamic	Universal gas constant
Faraday Constant	F	96485.33212 ±0.00000059	C/mol	thermodynamic	Electric charge of one mole of electrons
Molar Gas Constant	R	8.314462618 ±0.000000075	J⋅mol⁻¹⋅K⁻¹	thermodynamic	Universal gas constant per mole
Loschmidt Constant	n_0	2.686780111 × 10²⁵ ±0.000000024 × 10²⁵	m⁻³	thermodynamic	Number density of particles in an ideal gas at standard temperature and pressure
Sackur-Tetrode Constant	S_0/R	-1.15170753706 ±0.00000000045	dimensionless	thermodynamic	Entropy constant for monatomic ideal gas
Astronomical Unit	au	1.495978707 × 10¹¹ ±0.000000000 × 10¹¹	m	astronomical	Average distance between Earth and Sun
Parsec	pc	3.08567758149 × 10¹⁶ ±0.00000000037 × 10¹⁶	m	astronomical	Distance at which 1 au subtends an angle of 1 arcsecond
Light Year	ly	9.4607304725808 × 10¹⁵ ±0.0000000000000 × 10¹⁵	m	astronomical	Distance light travels in one Julian year
Solar Mass	M_☉	1.98847 × 10³⁰ ±0.00007 × 10³⁰	kg	astronomical	Mass of the Sun
Solar Radius	R_☉	6.957 × 10⁸ ±0.001 × 10⁸	m	astronomical	Radius of the Sun
Solar Luminosity	L_☉	3.828 × 10²⁶ ±0.001 × 10²⁶	W	astronomical	Total power output of the Sun
Earth Mass	M_⊕	5.9722 × 10²⁴ ±0.0006 × 10²⁴	kg	astronomical	Mass of the Earth
Earth Radius	R_⊕	6.3781 × 10⁶ ±0.0001 × 10⁶	m	astronomical	Equatorial radius of the Earth
Hubble Constant	H_0	70.0 ±2.0	km⋅s⁻¹⋅Mpc⁻¹	astronomical	Rate of expansion of the universe
Cosmic Microwave Background Temperature	T_CMB	2.72548 ±0.00057	K	astronomical	Temperature of the cosmic microwave background radiation
Quantum of Circulation	h/m_e	7.2738951036 × 10⁻⁴ ±0.0000000022 × 10⁻⁴	m²/s	quantum	Quantum of circulation for electrons
Quantum of Magnetic Flux	h/2e	2.067833848 × 10⁻¹⁵	Wb	quantum	Quantum of magnetic flux in superconductors
Quantum of Conductance	2e²/h	7.748091729 × 10⁻⁵	S	quantum	Quantum of electrical conductance
Quantum of Resistance	h/e²	25812.80745 ±0.00018	Ω	quantum	Quantum of electrical resistance
Quantum of Action	h	6.62607015 × 10⁻³⁴	J⋅s	quantum	Fundamental quantum of action
Nuclear Magneton	μ_N	5.0507837461 × 10⁻²⁷ ±0.0000000015 × 10⁻²⁷	J/T	nuclear	Magnetic moment of a nucleon
Fermi Coupling Constant	G_F	1.1663787 × 10⁻⁵ ±0.0000006 × 10⁻⁵	GeV⁻²	nuclear	Weak interaction coupling constant
Strong Coupling Constant	α_s	0.1184 ±0.0007	dimensionless	nuclear	Strong interaction coupling constant at Z mass
Weak Mixing Angle	θ_W	0.22290 ±0.00030	rad	nuclear	Weinberg angle in electroweak theory
Neutron Lifetime	τ_n	879.4 ±0.6	s	nuclear	Mean lifetime of a free neutron
Bohr Magneton	μ_B	9.2740100783 × 10⁻²⁴ ±0.0000000028 × 10⁻²⁴	J/T	solid-state	Magnetic moment of an electron due to its orbital or spin angular momentum
Nuclear Magneton	μ_N	5.0507837461 × 10⁻²⁷ ±0.0000000015 × 10⁻²⁷	J/T	solid-state	Magnetic moment of a nucleon
Fermi Energy	E_F	Variable Material dependent	J	solid-state	Energy of the highest occupied state in a Fermi gas at absolute zero
Fermi Temperature	T_F	Variable Material dependent	K	solid-state	Temperature equivalent of Fermi energy
Debye Temperature	θ_D	Variable Material dependent	K	solid-state	Characteristic temperature in Debye model of specific heat
Dynamic Viscosity of Water	μ_water	1.002 × 10⁻³ ±0.001 × 10⁻³	Pa⋅s	fluid	Dynamic viscosity of water at 20°C
Kinematic Viscosity of Water	ν_water	1.004 × 10⁻⁶ ±0.001 × 10⁻⁶	m²/s	fluid	Kinematic viscosity of water at 20°C
Surface Tension of Water	γ_water	72.8 × 10⁻³ ±0.1 × 10⁻³	N/m	fluid	Surface tension of water at 20°C
Density of Water	ρ_water	998.2 ±0.1	kg/m³	fluid	Density of water at 20°C
Speed of Sound in Water	c_water	1482 ±1	m/s	fluid	Speed of sound in water at 20°C
Refractive Index of Air	n_air	1.000293 ±0.000001	dimensionless	optics	Refractive index of air at standard conditions
Refractive Index of Water	n_water	1.333 ±0.001	dimensionless	optics	Refractive index of water at 20°C
Refractive Index of Glass	n_glass	1.5 ±0.1	dimensionless	optics	Typical refractive index of crown glass
Critical Angle for Water-Air	θ_c	48.6 ±0.1	°	optics	Critical angle for total internal reflection from water to air
Brewster Angle for Glass-Air	θ_B	56.3 ±0.1	°	optics	Brewster angle for glass-air interface
Speed of Sound in Air	c_air	343 ±1	m/s	acoustics	Speed of sound in air at 20°C
Characteristic Acoustic Impedance of Air	Z_air	415 ±1	Pa⋅s/m	acoustics	Acoustic impedance of air at 20°C
Threshold of Hearing	I_0	1 × 10⁻¹²	W/m²	acoustics	Reference intensity for sound level measurements
Reference Sound Pressure	p_0	2 × 10⁻⁵	Pa	acoustics	Reference pressure for sound level measurements
Resonant Frequency of Middle Ear	f_res	1000 ±100	Hz	acoustics	Typical resonant frequency of human middle ear
Young's Modulus of Steel	E_steel	200 × 10⁹ ±10 × 10⁹	Pa	materials	Young's modulus of typical steel
Young's Modulus of Aluminum	E_Al	70 × 10⁹ ±5 × 10⁹	Pa	materials	Young's modulus of aluminum
Thermal Conductivity of Copper	k_Cu	401 ±1	W⋅m⁻¹⋅K⁻¹	materials	Thermal conductivity of copper at 20°C
Thermal Conductivity of Aluminum	k_Al	237 ±1	W⋅m⁻¹⋅K⁻¹	materials	Thermal conductivity of aluminum at 20°C
Coefficient of Thermal Expansion of Steel	α_steel	12 × 10⁻⁶ ±1 × 10⁻⁶	K⁻¹	materials	Linear thermal expansion coefficient of steel
Atmospheric Pressure	P_atm	101325 ±1	Pa	environmental	Standard atmospheric pressure at sea level
Density of Air	ρ_air	1.225 ±0.001	kg/m³	environmental	Density of air at sea level and 15°C
Gravitational Acceleration	g	9.80665 ±0.00001	m/s²	environmental	Standard gravitational acceleration at sea level
Solar Constant	S	1361 ±1	W/m²	environmental	Solar irradiance at Earth's distance from the Sun
Earth's Magnetic Field	B_earth	5 × 10⁻⁵ ±1 × 10⁻⁵	T	environmental	Typical Earth's magnetic field strength at surface

Showing 87 of 87 constants

About These Constants

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Most constants are measured values with associated uncertainties. Constants marked as "exact" are defined values used to establish the International System of Units (SI).

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Physics Constants

About These Constants

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