Toolbox

Physical constants 39

The fundamental constants (CODATA 2022; the seven that define the SI are exact since 2019), and the standard values of aerospace work.

Universal

Constant	Symbol	Value	Unit	Relative uncertainty	Source
speed of light in vacuum	c	299,792,458	m/s	exact	SI (2019), exact
Planck constant	h	6.62607015 × 10⁻³⁴	J⋅s	exact	SI (2019), exact
reduced Planck constant = h / 2π	ħ	1.0545718176462 × 10⁻³⁴	J⋅s	exact	SI (2019), exact
Newtonian constant of gravitation	G	6.6743 × 10⁻¹¹	m³/(kg·s²)	2.2 × 10⁻⁵	CODATA 2022
vacuum magnetic permeability	μ₀	1.25663706127 × 10⁻⁶	H/m	1.6 × 10⁻¹⁰	CODATA 2022
vacuum electric permittivity = 1 / (μ₀ c²)	ε₀	8.8541878188 × 10⁻¹²	F/m	1.6 × 10⁻¹⁰	CODATA 2022

Electromagnetic

Constant	Symbol	Value	Unit	Relative uncertainty	Source
elementary charge	e	1.602176634 × 10⁻¹⁹	C	exact	SI (2019), exact
magnetic flux quantum = h / 2e	Φ₀	2.0678338484619 × 10⁻¹⁵	Wb	exact	SI (2019), exact
Josephson constant = 2e / h	K_J	4.8359784841698 × 10¹⁴	Hz/V	exact	SI (2019), exact
von Klitzing constant = h / e²	R_K	25,812.8074593045	Ω	exact	SI (2019), exact

Atomic and nuclear

Constant	Symbol	Value	Unit	Relative uncertainty	Source
fine-structure constant = e² / (4π ε₀ ħ c)	α	0.0072973525643		1.6 × 10⁻¹⁰	CODATA 2022
electron mass	mₑ	9.1093837139 × 10⁻³¹	kg	3.1 × 10⁻¹⁰	CODATA 2022
proton mass	mₚ	1.67262192595 × 10⁻²⁷	kg	3.1 × 10⁻¹⁰	CODATA 2022
neutron mass	mₙ	1.67492750056 × 10⁻²⁷	kg	5.1 × 10⁻¹⁰	CODATA 2022
Rydberg constant	R∞	10,973,731.568157	m−1	1.1 × 10⁻¹²	CODATA 2022
Bohr radius	a₀	5.29177210544 × 10⁻¹¹	m	1.6 × 10⁻¹⁰	CODATA 2022

Physico-chemical

Constant	Symbol	Value	Unit	Relative uncertainty	Source
Avogadro constant	N_A	6.02214076 × 10²³	mol⁻¹	exact	SI (2019), exact
Boltzmann constant	k	1.380649 × 10⁻²³	J/K	exact	SI (2019), exact
molar gas constant = N_A k	R	8.31446261815324	J/(K⋅mol)	exact	SI (2019), exact
Faraday constant = N_A e	F	96,485.33212331	C/mol	exact	SI (2019), exact
Stefan–Boltzmann constant = 2π⁵k⁴ / (15h³c²)	σ	5.6703744191844 × 10⁻⁸	W/(m²·K⁴)	exact	SI (2019), exact
atomic mass constant = m(¹²C) / 12	mᵤ	1.66053906892 × 10⁻²⁷	kg	3.1 × 10⁻¹⁰	CODATA 2022
Wien wavelength displacement law constant	b	0.002897771955	m·K	exact	CODATA 2022
electron volt = e × 1 V	eV	1.602176634 × 10⁻¹⁹	J	exact	SI (2019), exact

Adopted values

Constant	Symbol	Value	Unit	Relative uncertainty	Source
standard acceleration of gravity	gₙ	9.80665	m/s2	exact	3rd CGPM (1901)
standard atmosphere	atm	101,325	Pa	exact	10th CGPM (1954)

ICAO standard atmosphere

Constant	Symbol	Value	Unit	Relative uncertainty	Source
sea-level temperature of the standard atmosphere	T₀	288.15	K	exact	ICAO Doc 7488/3
sea-level pressure of the standard atmosphere	p₀	101,325	Pa	exact	ICAO Doc 7488/3
specific gas constant of dry air = R* / M₀	R_air	287.05287	J/(K⋅kg)	exact	ICAO Doc 7488/3
molar mass of dry air	M₀	0.02896442	kg/mol	exact	ICAO Doc 7488/3
ratio of specific heats of air = c_p / c_v	κ	1.4		exact	ICAO Doc 7488/3
temperature gradient of the troposphere	β	-0.0065	K/m	exact	ICAO Doc 7488/3
Earth radius for geopotential altitude	r	6,356,766	m	exact	ICAO Doc 7488/3

Earth (WGS 84)

Constant	Symbol	Value	Unit	Relative uncertainty	Source
Earth's semi-major axis	a	6,378,137	m	exact	NIMA TR8350.2 (WGS 84)
Earth's flattening = 1 / 298.257223563	f	0.00335281066475		exact	NIMA TR8350.2 (WGS 84)
Earth's gravitational constant	GM	3.986004418 × 10¹⁴	m³/s²	exact	NIMA TR8350.2 (WGS 84)
Earth's angular velocity	ω	7.292115 × 10⁻⁵	rad/s	exact	NIMA TR8350.2 (WGS 84)

Astronomy (IAU)

Constant	Symbol	Value	Unit	Relative uncertainty	Source
astronomical unit	au	1.495978707 × 10¹¹	m	exact	IAU 2012 resolution B2
light-year = c × 365.25 days	ly	9.4607304725808 × 10¹⁵	m	exact	IAU

CODATA 2022: the values recommended by the Committee on Data of the International Science Council (published by NIST, 2024). "Exact" values are fixed by definition (the SI since 2019, the CGPM, the ICAO, WGS 84, the IAU).