What is a derived unit?

A derived unit is formed from products and powers of the seven SI base units. The 22 listed here are special because the CGPM gave them their own names and symbols, such as the newton for force instead of the unwieldy kilogram metre per second squared.

Why do the gray and sievert share the same base units?

Both reduce to joules per kilogram (metre squared per second squared), but they measure physically different things: the gray is absorbed radiation dose while the sievert is the biologically weighted dose equivalent. They are kept distinct to avoid dangerous confusion in radiation safety.

Are the radian and steradian units?

They are dimensionless derived units. A radian is metre per metre and a steradian is metre squared per metre squared, so both reduce to the pure number one, but their names usefully signal that an angle or solid angle is being expressed.

What does coherent mean for these units?

Coherent means each derived unit is formed from base units with no extra numerical factor. One newton is exactly one kilogram metre per second squared, so equations using coherent SI units never need conversion constants between them.

Is degree Celsius an SI unit?

Yes. Degree Celsius is a named derived unit equal in size to the kelvin, offset so that 0 degrees Celsius equals 273.15 kelvin. It is accepted for expressing temperatures and temperature differences within the SI.

What is the SI Derived Units Reference?

Complete list of the 22 named SI derived units with their special names, symbols, expressions in other SI units, and expressions in the seven base units. Filter by force, energy, pressure, and more. Runs in your browser. It runs free in your browser on Gera Tools, with nothing uploaded.

SI Derived Units Reference

Name: SI Derived Units Reference
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

While the SI rests on seven base units, most everyday physics is written in derived units. Twenty-two of these were given special names and symbols by the CGPM so that quantities like force, energy, and pressure read cleanly. This reference lists all of them with both their compact and base-unit expressions.

How it works

Filter the table by unit name, symbol, or measured quantity. Each row shows two equivalent expressions:

newton  (N)  = kg·m·s⁻²
pascal  (Pa) = N/m²  = kg·m⁻¹·s⁻²
joule   (J)  = N·m   = kg·m²·s⁻²
watt    (W)  = J/s   = kg·m²·s⁻³

The “in other units” column expresses the unit in terms of more familiar derived units, while the “in base units” column reduces it all the way down to the seven base units. Every one of these is a coherent unit, meaning it is built from base units with a numerical factor of exactly one — no conversion constants creep into equations written purely in SI.

All 22 named SI derived units at a glance

Name	Symbol	Quantity	In other SI units
hertz	Hz	frequency	s⁻¹
radian	rad	plane angle	m/m = 1
steradian	sr	solid angle	m²/m² = 1
newton	N	force	kg·m·s⁻²
pascal	Pa	pressure	N/m²
joule	J	energy, work	N·m
watt	W	power	J/s
coulomb	C	electric charge	A·s
volt	V	electric potential	W/A
farad	F	capacitance	C/V
ohm	Ω	resistance	V/A
siemens	S	conductance	A/V
weber	Wb	magnetic flux	V·s
tesla	T	magnetic flux density	Wb/m²
henry	H	inductance	Wb/A
degree Celsius	°C	temperature	K − 273.15
lumen	lm	luminous flux	cd·sr
lux	lx	illuminance	lm/m²
becquerel	Bq	radioactivity	s⁻¹
gray	Gy	absorbed dose	J/kg
sievert	Sv	dose equivalent	J/kg
katal	kat	catalytic activity	mol/s

Notable cases that trip people up

Gray versus sievert — Both reduce to joules per kilogram (m²·s⁻²) but measure physically different things: the gray measures raw absorbed radiation energy, while the sievert weights that energy by the biological effectiveness of the radiation type. Using gray when sievert is meant (or vice versa) in a radiation-safety context is a meaningful error, which is why they are kept as separate named units despite identical base-unit expressions.

Becquerel versus hertz — Both reduce to s⁻¹ but mean very different things. One becquerel is one radioactive decay per second; one hertz is one cycle of a periodic phenomenon per second. Context determines which is appropriate.

Radian and steradian — Dimensionless units that reduce to the number one, but their names signal that a plane angle or solid angle is expressed. This allows equations to communicate intent clearly: an angular velocity in rad/s is obviously an angle rate; the same number in plain s⁻¹ would be ambiguous.

Katal — Added to the SI in 1999 to give catalytic activity a coherent unit. One katal is one mole of substrate converted per second. Before the katal, enzyme activity was often reported in international units (IU), which remain in common use in clinical laboratory practice.

Why trace to base units?

Reducing a derived unit to base units is the most reliable way to check dimensional consistency in a formula. If two sides of an equation reduce to the same combination of m, kg, s, A, K, mol, and cd, the equation is dimensionally consistent. If they differ, there is an error — either a missing factor, a wrong unit, or a misidentified quantity. This technique, dimensional analysis, works for any physical equation in any system of units.