The formula
P (kW) = M (N·m) × n (rpm) × 2π ÷ 60,000
Where it comes from
Torque is the twisting force the engine produces and power is the rate at which it does work. An engine with a lot of torque low down and one with little torque high up can make the same power, and that is the whole difference between a diesel that pulls from the bottom and a high-revving petrol engine you have to wring out. The formula is the usual mechanical power one, with angular velocity in radians per second; the sixty thousand in the denominator is the sixty seconds of a minute times the thousand watts of a kilowatt.
How to work it out by hand
- Convert the engine speed to radians per second: rpm × 2π ÷ 60
- Multiply the torque in newton metres by that angular velocity
- Divide by a thousand to get kilowatts
- Multiply by 1.36 if you want metric horsepower
What is worth knowing
Leave torque at zero and enter power to solve for torque, or the other way round. Metric horsepower is 735.5 watts and imperial horsepower 745.7, so the two figures do not match: an engine of a hundred metric hp is 98.6 imperial hp. The kgf·m still turns up in older spec sheets and is simply the newton metre divided by 9.80665. One useful fact: at 9,549 rpm the torque in N·m and the power in kW are numerically equal, because that is where the factor is exactly one.