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.

SI Derived Units Reference

Email me this result

Get this tool's output sent to your inbox, plus one useful tool a week. No spam, unsubscribe any time.

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.

Notes and examples

The gray and the sievert both reduce to m²·s⁻² (joules per kilogram) yet measure different things — absorbed dose versus biologically weighted dose equivalent — which is why radiation-safety standards keep them strictly separate. The radian and steradian are dimensionless (they reduce to the number 1) but their names make clear that a plane or solid angle is meant. Tracing any derived unit back to base units, as the right-hand column does, is a fast way to check the dimensional consistency of a physics formula.