Last updated: 2026-06-15

Torque from Power

An engine's spec sheet quotes both torque and power, and they are not independent — once you know how fast the shaft turns, each fixes the other. The link is one tidy equation, and this calculator solves it in any direction: torque from power and rpm, power from torque and speed, or the speed that ties a given pair together.

The relationship

The power delivered by a rotating shaft is its torque times its angular speed:

Rearranged, that gives whichever quantity you are missing:

It is the rotational echo of the straight-line rule, power equals force times velocity — with torque playing the role of force and angular speed the role of velocity.

Mind the units

The clean form $P = \tau\omega$ only holds when $\omega$ is in radians per second. Engine speeds come in revolutions per minute, so convert first: one revolution is $2\pi$ radians and one minute is 60 seconds, hence

Skip this and the answer is off by a factor of about 0.105. The calculator converts automatically, so you can type rpm straight in.

Worked example

A motor rated at $P = 100\ \text{kW}$ runs at $3000\ \text{rpm}$. First the speed in SI units,

then the torque,

Torque versus power in an engine

Torque is the twist the engine makes right now; power is how fast it can do work, which is that twist multiplied by how quickly the crankshaft spins. An engine can peak its torque low in the rev range yet keep making more power higher up, because rising speed more than offsets the gently falling torque — until it does not, and power peaks too. As a rule of thumb, torque is the shove you feel out of a corner, while power sets the top speed.