Horsepower and torque calculator
Power from torque and engine speed, in all three units called horsepower — and the reason every torque and power curve ever plotted crosses at 5252 rpm, which is a fact about the unit rather than about any engine. Nothing you type here leaves your browser — it is worked out on your own device, so there is nothing to send and nothing to log.
There are three horsepowers
They are not variants of one unit. They are three different units that share a name:
- Mechanical, or imperial: 550 foot-pounds a second, which works out at 745.699871582… W
- Metric, written PS in Germany, ch in France, pk in the Netherlands: 75 kilogram-force metres a second, exactly 735.49875 W
- Electrical: defined as exactly 746 W
The first two differ by 1.387%. A car advertised as 150 PS is 147.95 mechanical horsepower — the same car, the same engine, a figure two whole horsepower apart depending which country wrote the brochure.
5252 is not a fact about engines
Every dynamometer plot you have ever seen has the torque and power curves crossing at about 5252 rpm. It is presented as a curious property of internal combustion. It is a property of the units.
A horsepower is defined as 33,000 foot-pounds per minute. A revolution is 2π radians. So
hp = torque × rpm ÷ (33,000 ÷ 2π) = torque × rpm ÷ 5252.113…
Put rpm = 5252.113 into that and the rpm cancels the constant, leaving hp = torque. Exactly. For any torque, on any engine, real or imagined.
It cannot be designed for, it cannot be avoided, and an engine whose curves did not cross there would be an arithmetic mistake rather than an interesting machine.
And in metric units it does not happen at all
Power in kilowatts from torque in newton-metres is Nm × rpm × 2π ÷ 60,000. There is no constant to cancel, so the two curves are simply proportional and never cross in any meaningful sense.
Which is the clearest way to see what the 5252 is: a coincidence manufactured by choosing a unit of power that is 33,000 of one thing per minute, and then measuring rotation in something else.
Nothing here is typed in
The foot (0.3048 m), the pound (0.45359237 kg) and standard gravity (9.80665 m/s²) are exact by definition. Every other number on this page — 745.6999, 735.49875, 5252.113 — is computed from those three each time.
The rounded 5252 that usually gets quoted is out by 0.002%, which is harmless and is still the sort of digit that becomes unexplainable once it has been copied a few times.
What this is not
It is arithmetic on a torque figure you supplied. It does not measure your engine, it is crankshaft power rather than power at the wheels, and it tells you nothing about any engine speed other than the one you typed.
A power curve is a measurement taken on a dynamometer across the whole rev range. One number from one rpm is a single point on it.