Engine Horsepower Calculator

power = torque × 2π × rpm ÷ 60

torque

Crankshaft torque at that engine speed, in N·m

rpm

Engine speed, in revolutions per minute

Use it when a dyno sheet or a workshop manual gives you torque and you want the power figure, or when the two numbers you have are in different units from the ones the brochure quotes. It is also the way to check a suspicious claim: a peak power figure at an rpm where the torque curve has already fallen away cannot be right, and running the numbers backwards tells you what torque that power implies.

1. A 2.0 litre turbo at its torque peak: 400 N·m at 4,000 rpm

   1. Angular velocity: 2π × 4,000 ÷ 60 = 418.879 rad/s
   2. Power in watts: 400 × 418.879 = 167,552 W
   3. Horsepower: 167,552 ÷ 745.6999 = 224.7 hp
   4. Kilowatts: 167,552 ÷ 1,000 = 167.6 kW
   5. Metric horsepower: 167,552 ÷ 735.49875 = 227.8 PS

   224.7 hp against 227.8 PS for one engine. The two differ by 1.4% because the horsepower and the metric horsepower are defined from different weights — 550 foot-pounds per second against 75 kilogram-force metres per second — and this is the only place a reader sees them side by side.

2. A diesel at 1,000 N·m, turning slowly

   1. Angular velocity: 2π × 100 ÷ 60 = 10.472 rad/s
   2. Power in watts: 1,000 × 10.472 = 10,472 W
   3. Horsepower: 10,472 ÷ 745.6999 = 14.0 hp
   4. Kilowatts: 10,472 ÷ 1,000 = 10.5 kW
   5. Metric horsepower: 10,472 ÷ 735.49875 = 14.2 PS

   Enormous torque and almost no power, because power is torque multiplied by speed and there is very little speed here. This is the arithmetic behind a tractor, a ship engine and a starter motor: the torque figure that impresses at the crankshaft is worth nothing until it is multiplied by rpm.

This is a conversion, not a measurement: it takes a torque figure on trust and turns it into power. On a real engine the torque at a given rpm depends on throttle position, boost, temperature, fuel and how the engine was loaded, so an engine rated at 400 N·m on a dyno may deliver noticeably less in a hot engine bay. Crank horsepower, which is what this page computes, is not wheel horsepower — drivetrain losses take 10–15% of it on the way to the road, and more on four-wheel drive. The three units are exact conversions of one another and none of them is more correct than the others, but manufacturers quote the one that flatters the car most, which is why the same engine is a 300 in one market and a 304 in another. Nothing here knows about the shape of a torque curve, so a single point gives a single answer and not the engine's power band.

Why are there three different horsepower figures?

Because horsepower is not one unit. Mechanical horsepower is 550 foot-pounds per second and equals 745.6999 W; metric horsepower, written PS, is 75 kilogram-force metres per second and equals 735.49875 W. The two land 1.4% apart, so 300 hp is 304 PS for the same engine. Kilowatts are the SI unit and the one the figure is really measured in before being converted.

How is torque to power converted?

Multiply the torque in newton metres by the engine speed in radians per second. The rpm has to be turned into radians per second first: 2π × rpm ÷ 60. So 400 N·m at 4,000 rpm is 400 × 418.879 = 167,552 W, or 224.7 hp. Older books use the shortcut hp = lb-ft × rpm ÷ 5252, which is the same relationship with the unit conversions already folded in.

Is this brake horsepower or wheel horsepower?

Brake horsepower — power at the crankshaft, which is what a manufacturer quotes and what an engine dyno measures. A chassis dyno measures at the wheels and will always read lower: 10–15% lower on a two-wheel-drive car, more on a four-wheel-drive one. If you are comparing a published figure against a dyno run, check which end of the drivetrain each one was taken at.

What torque should I enter?

The torque the engine makes at the rpm you entered, not the peak torque. A torque figure is only meaningful together with the speed it was measured at, and the peak torque and the peak power happen at different rpm on every real engine. Entering peak torque alongside peak-power rpm produces a number that is higher than the engine can actually make.

Why is the power so low at low rpm?

Because power is torque multiplied by speed, so at low speed even a huge torque is multiplied by very little. 1,000 N·m at 100 rpm is only 14 hp, while a modest 200 N·m at 6,000 rpm is 168 hp. That is also why an engine's power rises with rpm until the torque curve falls faster than the speed rises — the peak power point is where those two curves cross.

• NIST Guide to the SI, Special Publication 811 — US National Institute of Standards and Technology
• The International System of Units (SI Brochure) — Bureau International des Poids et Mesures