What the inputs mean
- Torque: the twisting force at the crankshaft (or at the wheels, if that is what you measured), in lb-ft or Nm. Switch units at the top of the page.
- Engine speed: the rpm at which that torque was measured. Power is torque at one speed; a torque figure without its rpm cannot give power.
The horsepower formula and the 5252 constant
One mechanical horsepower is 33,000 foot-pounds of work per minute. One turn of the crank at torque T does 2π × T foot-pounds of work, so at a given rpm:
horsepower = torque (lb-ft) × rpm ÷ 5,252
torque = horsepower × 5,252 ÷ rpm
5,252 = 33,000 ÷ (2 × π)
kW = torque (Nm) × rpm ÷ 9,549The metric line is the same physics: 9,549 is 60,000 ÷ (2 × π), which turns rpm into radians per second and watts into kilowatts. The calculator uses the unrounded constants.
Worked example
An engine makes 400 lb-ft at 4,500 rpm:
- 400 × 4,500 ÷ 5,252.1 = 342.7 hp.
- In metric: 400 lb-ft is 542.3 Nm, and 542.3 × 4,500 ÷ 9,549.3 = 255.6 kW, which is 347.5 PS.
Going the other way, 400 hp at 6,000 rpm needs 400 × 5,252.1 ÷ 6,000 = 350.1 lb-ft at that speed.
hp, kW and PS
Three power units are in common use. Mechanical horsepower (hp) is about 745.7 watts. Metric horsepower (PS in German, CV in French, Italian and Spanish, pk in Dutch) is exactly 735.49875 watts, so 1 PS is a little smaller than 1 hp. Kilowatts are the SI unit.
kW = hp × 0.7457 PS = kW ÷ 0.7355100 hp is 74.57 kW or 101.39 PS. 100 kW is 134.10 hp or 135.96 PS.
Why the curves cross at 5,252 rpm
At 5,252 rpm the formula becomes hp = torque, so in lb-ft and hp the two numbers are equal there. On a dyno chart drawn with the same scale for both, the curves cross at that speed. It is a feature of the units, not of the engine. In kW and Nm the equal point is at about 9,549 rpm instead.
Crank figures and wheel figures are different things. If your numbers came from a chassis dyno, the result is wheel power. The wheel horsepower calculator converts between the two with a drivetrain loss you choose.
Questions
How do you convert torque to horsepower?
Multiply torque in lb-ft by rpm and divide by 5,252. For example, 400 lb-ft at 4,500 rpm is 342.7 hp. In metric, kW = Nm × rpm ÷ 9,549.
Why is 5252 used in the horsepower formula?
One horsepower is 33,000 foot-pounds per minute, and one crank turn at torque T does 2π × T foot-pounds of work. 33,000 ÷ 2π = 5,252.1, which is also why hp and lb-ft are equal at 5,252 rpm.
Is PS the same as horsepower?
Almost, but not quite. 1 PS (metric horsepower) is 735.5 W and 1 hp (mechanical) is 745.7 W, so 100 PS is 98.63 hp and 100 hp is 101.39 PS.
How much torque does 400 hp make?
It depends on the rpm. 400 hp at 6,000 rpm means 350.1 lb-ft at that speed. The same 400 hp at 5,252 rpm would be 400 lb-ft.