Horsepower and Torque Calculator
Enter a power figure in any of the three units to get the other two. Add the rpm it was measured at and you also get the torque.
Power
186.4kW
- Horsepower
- 250 hp
- Kilowatts
- 186.4 kW
- Metric horsepower
- 253.5 PS
- Torque at 5,500 rpm
- 238.7 lb-ft
- In newton metres
- 323.7 Nm
- At 5,500 rpm, 250 hp is 238.7 lb-ft of torque. The same engine at half those revs would need twice the torque for the same power.
- Power is torque times rotational speed, and that is the whole relationship. It is why horsepower and torque curves always cross at 5,252 rpm on an imperial chart — not a property of any engine, just where the conversion constant lands.
- Torque is the twist available. Power is how quickly you can keep applying it. Torque gets a load moving; power is what carries speed.
- PS and hp are close but not equal — PS is metric horsepower, defined in kilogram-metres, and runs about 1.4% higher for the same engine.
About power and torque
Power is quoted in three units and they are all close enough to be confused. Horsepower is the imperial unit, kilowatts are the SI unit, and PS — metric horsepower, sometimes written CV or pk — is defined in kilogram-metres and runs about 1.4% higher than hp for the same engine. European manufacturers usually quote PS, which is why a car sold as 250 PS is around 247 hp.
Torque and power are not two properties of an engine. They are the same measurement expressed at a rotational speed: power is torque multiplied by revolutions. Torque is the twist available at the crank; power is how quickly that twist can keep being applied.
That relationship explains the thing everyone notices about dyno charts. On an imperial chart the horsepower and torque curves always cross at exactly 5,252 rpm, on every engine ever built. It is not a property of engines — it is where the conversion constant between pound-feet and horsepower happens to land, and on a metric chart in kW and Nm the crossing does not appear at all.
Torque is what gets a load moving and power is what carries speed. It is why a tractor has enormous torque and modest power, and why a motorcycle engine can have very little torque and a great deal of power.
What it works out
- Horsepower, kilowatts and PS between each other
- Torque in pound-feet and newton metres
- Torque from power and engine speed
- Why the curves cross at 5,252 rpm
The formula
Torque (lb-ft) = Power (hp) × 5252 ÷ RPM kW = hp × 0.7457
250 hp is 186.4 kW, or 253.5 PS. The unit conversions are plain multiplication; nothing about the engine changes.
Torque needs the engine speed, because torque and power are the same thing measured at different revs. At 5,500 rpm, 250 hp is 238.7 lb-ft — or 323.7 Nm.
The 5,252 is the whole explanation for the crossover on a dyno chart. One horsepower is 33,000 foot-pounds per minute, and one revolution moves a one-foot lever through 2π feet, so 33,000 divided by 2π is 5,252. Whenever the rpm equals 5,252 the two numbers are necessarily identical, which is why every imperial chart crosses there and no metric one does.
Below 5,252 rpm the torque figure is always the larger of the two, and above it the power figure is. That is arithmetic rather than engineering.
- Power
- In hp, kW or PS. PS is metric horsepower and about 1.4% larger than hp.
- RPM
- The engine speed the figure was measured at. Peak power and peak torque occur at different revs.
- 5252
- 33,000 foot-pounds per minute divided by 2π — a unit conversion, not a property of engines.
A worked example
An engine making 250 hp at 5,500 rpm.
That works out to 186.4 kW.
- Horsepower
- 250 hp
- Kilowatts
- 186.4 kW
- Metric horsepower
- 253.5 PS
- Torque at 5,500 rpm
- 238.7 lb-ft
- In newton metres
- 323.7 Nm
Questions
How do I convert horsepower to kilowatts?
Multiply by 0.7457. 250 hp is 186.4 kW. Going the other way, divide by the same figure, or multiply kW by 1.341.
What is the difference between hp and PS?
PS is metric horsepower, defined in kilogram-metres rather than foot-pounds, and it is about 1.4% smaller as a unit — so the same engine scores higher in PS. 250 hp is 253.5 PS.
How do I work out torque from horsepower?
Multiply the horsepower by 5,252 and divide by the rpm. 250 hp at 5,500 rpm is 238.7 lb-ft, or 323.7 Nm.
Why do horsepower and torque cross at 5,252 rpm?
Because that is where the conversion constant puts them. One horsepower is 33,000 foot-pounds per minute and one revolution of a one-foot lever is 2π feet, so 33,000 ÷ 2π = 5,252. At that engine speed the two numbers are identical by definition, on any engine.
Is torque or horsepower more important?
They measure the same thing at different rotational speeds, so the question is really about where in the rev range an engine is strong. Torque low down makes a car feel effortless in traffic; power high up is what produces speed.
Why does a diesel have more torque but less power?
Diesels typically have a long stroke and a rev limit well below a petrol engine's. The long stroke gives leverage, hence torque; the low rev ceiling caps the power, since power is torque times revs.
Is the quoted power at the engine or the wheels?
Manufacturers quote at the crank. A rolling road measures at the wheels, which is typically ten to fifteen per cent lower for a manual and more for an automatic or four-wheel drive, because of losses in the transmission.
What is brake horsepower?
Power measured at the crankshaft with a brake dynamometer, which is what manufacturers quote. In practice "bhp" and "hp" are used interchangeably in ordinary conversation.