Subject overview

SI Units & Physical Constants

Explore the seven SI base units, all 22 derived units with special names, useful unit relationships and key physical constants.

The International System of Units (SI) uses seven base units. Products and powers of these units describe other physical quantities. There are infinitely many possible combinations; the tables below cover all 22 derived units with special names and a selection of common relationships.

The seven SI base units

Quantity	Typical symbol	Unit	Unit symbol
Time	$t$	second	$\mathrm{s}$
Length	$l$	metre	$\mathrm{m}$
Mass	$m$	kilogram	$\mathrm{kg}$
Electric current	$I$	ampere	$\mathrm{A}$
Thermodynamic temperature	$T$	kelvin	$\mathrm{K}$
Amount of substance	$n$	mole	$\mathrm{mol}$
Luminous intensity	$I_v$	candela	$\mathrm{cd}$

Derived units with special names

Here, [F] means “the SI unit of force”, rather than its numerical value or dimension. Quantity symbols depend on context: F can denote force, while the upright unit symbol F denotes farad.

Quantity	Unit name	Unit relationship
Plane angle	radian	$[\theta] = \mathrm{rad} = \frac{\mathrm{m}}{\mathrm{m}} = 1$
Solid angle	steradian	$[\Omega] = \mathrm{sr} = \frac{\mathrm{m}^2}{\mathrm{m}^2} = 1$
Frequency	hertz	$[f] = \mathrm{Hz} = \mathrm{s^{-1}}$
Force	newton	$[F] = \mathrm{N} = \frac{\mathrm{kg}\,\mathrm{m}}{\mathrm{s}^2}$
Pressure, stress	pascal	$[p] = \mathrm{Pa} = \frac{\mathrm{N}}{\mathrm{m}^2} = \frac{\mathrm{kg}}{\mathrm{m}\,\mathrm{s}^2}$
Energy, work, heat	joule	$[E] = \mathrm{J} = \mathrm{N\,m} = \frac{\mathrm{kg}\,\mathrm{m}^2}{\mathrm{s}^2}$
Power	watt	$[P] = \mathrm{W} = \frac{\mathrm{J}}{\mathrm{s}} = \frac{\mathrm{kg}\,\mathrm{m}^2}{\mathrm{s}^3}$
Electric charge	coulomb	$[Q] = \mathrm{C} = \mathrm{A\,s}$
Electric potential difference	volt	$[U] = \mathrm{V} = \frac{\mathrm{W}}{\mathrm{A}} = \frac{\mathrm{kg}\,\mathrm{m}^2}{\mathrm{s}^3\,\mathrm{A}}$
Capacitance	farad	$[C] = \mathrm{F} = \frac{\mathrm{C}}{\mathrm{V}} = \frac{\mathrm{s}^4\,\mathrm{A}^2}{\mathrm{kg}\,\mathrm{m}^2}$
Electric resistance	ohm	$[R] = \Omega = \frac{\mathrm{V}}{\mathrm{A}} = \frac{\mathrm{kg}\,\mathrm{m}^2}{\mathrm{s}^3\,\mathrm{A}^2}$
Electric conductance	siemens	$[G] = \mathrm{S} = \frac{\mathrm{A}}{\mathrm{V}} = \frac{\mathrm{s}^3\,\mathrm{A}^2}{\mathrm{kg}\,\mathrm{m}^2}$
Magnetic flux	weber	$[\Phi] = \mathrm{Wb} = \mathrm{V\,s} = \frac{\mathrm{kg}\,\mathrm{m}^2}{\mathrm{s}^2\,\mathrm{A}}$
Magnetic flux density	tesla	$[B] = \mathrm{T} = \frac{\mathrm{Wb}}{\mathrm{m}^2} = \frac{\mathrm{kg}}{\mathrm{s}^2\,\mathrm{A}}$
Inductance	henry	$[L] = \mathrm{H} = \frac{\mathrm{Wb}}{\mathrm{A}} = \frac{\mathrm{kg}\,\mathrm{m}^2}{\mathrm{s}^2\,\mathrm{A}^2}$
Celsius temperature	degree Celsius	$[t] = {}^\circ\mathrm{C}$
Luminous flux	lumen	$[\Phi_v] = \mathrm{lm} = \mathrm{cd\,sr}$
Illuminance	lux	$[E_v] = \mathrm{lx} = \frac{lm}{\mathrm{m}^2} = \frac{\mathrm{cd}\,\mathrm{sr}}{\mathrm{m}^2}$
Activity of a radionuclide	becquerel	$[A] = \mathrm{Bq} = \mathrm{s^{-1}}$
Absorbed dose	gray	$[D] = \mathrm{Gy} = \frac{\mathrm{J}}{\mathrm{kg}} = \frac{\mathrm{m}^2}{\mathrm{s}^2}$
Dose equivalent	sievert	$[H] = \mathrm{Sv} = \frac{\mathrm{J}}{\mathrm{kg}} = \frac{\mathrm{m}^2}{\mathrm{s}^2}$
Catalytic activity	katal	$[z] = \mathrm{kat} = \frac{\mathrm{mol}}{\mathrm{s}}$

Radian and steradian have unit one; their names preserve the distinction between plane and solid angle. Lumen and lux retain sr to show that distinction. Hertz and becquerel also share the same base-unit expression but describe different quantities.

A temperature interval of 1 °C equals an interval of 1 K. Temperature readings have an offset:

\frac{t}{\mathrm{{}^\circ C}} = \frac{T}{\mathrm{K}} - 273.15

Common unit relationships

Quantity	SI unit
Area	$[A] = \mathrm{m^2}$
Volume	$[V] = \mathrm{m^3}$
Velocity	$[v] = \frac{\mathrm{m}}{\mathrm{s}}$
Acceleration	$[a] = \frac{\mathrm{m}}{\mathrm{s}^2}$
Density	$[\rho] = \frac{\mathrm{kg}}{\mathrm{m}^3}$
Momentum	$[p] = \mathrm{N\,s} = \frac{\mathrm{kg}\,\mathrm{m}}{\mathrm{s}}$
Torque	$[M] = \mathrm{N\,m} = \frac{\mathrm{kg}\,\mathrm{m}^2}{\mathrm{s}^2}$
Dynamic viscosity	$[\eta] = \mathrm{Pa\,s} = \frac{\mathrm{kg}}{\mathrm{m}\,\mathrm{s}}$
Specific heat capacity	$[c] = \frac{\mathrm{J}}{\mathrm{kg}\,\mathrm{K}} = \frac{\mathrm{m}^2}{\mathrm{s}^2\,\mathrm{K}}$
Thermal conductivity	$[\lambda] = \frac{\mathrm{W}}{\mathrm{m}\,\mathrm{K}} = \frac{\mathrm{kg}\,\mathrm{m}}{\mathrm{s}^3\,\mathrm{K}}$

Torque and energy share the same base-unit expression. Torque is conventionally written in N·m rather than J to keep the quantities distinct. Matching units is a necessary check on an equation, but does not by itself prove the physics is correct.

Physical constants

The first seven constants define the SI through fixed, exact numerical values. Other constants can be measured or derived. Parentheses indicate the standard uncertainty in the final digits: 6.674 30(15) means 6.674 30 ± 0.000 15.

Constant	Value in SI units	Status
Caesium-133 hyperfine transition frequency	$\Delta\nu_{Cs} = 9\,192\,631\,770\;\mathrm{Hz}$	Exact; unperturbed ground-state transition.
Speed of light in vacuum	$c = 299\,792\,458\;\mathrm{m\,s^{-1}}$	Exact.
Planck constant	$h = 6.626\,070\,15 \times 10^{-34}\;\mathrm{J\,s}$	Exact.
Elementary charge	$e = 1.602\,176\,634 \times 10^{-19}\;\mathrm{C}$	Exact.
Boltzmann constant	$k = 1.380\,649 \times 10^{-23}\;\mathrm{J\,K^{-1}}$	Exact.
Avogadro constant	$N_A = 6.022\,140\,76 \times 10^{23}\;\mathrm{mol^{-1}}$	Exact.
Luminous efficacy	$K_{cd} = 683\;\mathrm{lm\,W^{-1}}$	Exact; monochromatic radiation of frequency 540 × 10¹² Hz.
Newtonian constant of gravitation	$G = 6.674\,30(15) \times 10^{-11}\;\mathrm{m^3\,kg^{-1}\,\mathrm{s}^{-2}}$	Measured; CODATA 2022.
Electron mass	$m_e = 9.109\,383\,7139(28) \times 10^{-31}\;\mathrm{kg}$	Measured; CODATA 2022.
Proton mass	$m_p = 1.672\,621\,925\,95(52) \times 10^{-27}\;\mathrm{kg}$	Measured; CODATA 2022.
Molar gas constant	$R = N_\mathrm{A} k \approx 8.314\,462\,618\;\mathrm{J\,mol^{-1}\,\mathrm{K}^{-1}}$	Exact product; displayed decimal rounded.

Gravitational acceleration g depends on location and is not the gravitational constant G. The calculators use 9.81 m/s² as a default approximation for g; it is not an exact SI defining value.

Sources

Unit definitions and relationships: BIPM, SI Brochure, 9th edition, version 4.01 (2026). Defining values: BIPM defining constants. Measured and derived constants: NIST, CODATA 2022 recommended values.