Torque and power: what is the difference?

The engines and motors here are “simplified teaching models”. They are not real products, and the numbers are rough shapes, not real specifications.

Torque is the turning force, power is the speed of work

When you turn a screw, the strength of the twist is torque. Its unit is the newton metre (N·m): how hard you push, and how far from the axle. Power is how much work is done each second. With the same force, the faster something turns, the faster the work goes.

For a turning shaft, the two are linked by a multiplication:

power = torque × angular speed (radians per second)

With revolutions per minute (rpm), power in kW = torque in N·m × rpm ÷ 9549.3. The 9549.3 is 30000 ÷ π, rounded; many sources round it to 9550. This site’s program checked the formula, including that power is zero at zero speed (torque-and-power/engine.test.ts).

Why do the peaks fall at different speeds?

The torque of a petrol engine is largest at a middling speed, then falls as air has a harder time getting in and friction grows. But power is torque times speed. While the speed keeps rising, the product can keep rising even after torque has started to fall. So the power peak comes at a higher speed than the torque peak.

The formula shows why. At the power peak, the drop in torque and the rise in speed exactly balance, which can only happen on the falling side of the torque curve, to the right of its peak. This site’s model also checked that, for its three fictional machines, the power peak comes at a higher speed than the torque peak (same test).

As a general tendency: a diesel engine gives large torque from low speeds. An electric motor, in theory, gives its maximum torque from standstill, keeps roughly the same torque up to some speed, and beyond that power stays about constant while torque falls. These are general trends and differ a lot between machines. Real motors also have limits from current and heat.

Gears trade force for speed

A gearbox is not a magic torque-maker. What it gains in torque, it loses in speed. Without losses, torque times speed, that is, power, stays the same. Roughly, wheel torque = engine torque × gear ratio × final ratio × efficiency.

For example (made-up numbers): engine 150 N·m at 3000 rpm, gear ratio 3.5, final ratio 4.0, efficiency 0.9, tyre radius 0.30 m. Wheel torque is 1890 N·m, the force on the road is 6300 N, and the speed is about 6.73 m/s (about 24 km/h). Engine power is about 47.1 kW and power at the wheels (force × speed) is about 42.4 kW, which is exactly 47.1 × 0.9. This site’s program checked these values, and that force × speed equals engine power × efficiency in every gear (torque-and-power/engine.test.ts).

A low gear for a hill gives up speed to get a bigger force.

Horsepower, PS, kW, hp: many units

There is not just one “horsepower”.

• PS (metric horsepower): 75 kgf·m of work per second. With standard gravity, 75 × 9.80665 = 735.49875 W. PS comes from the German word Pferdestärke, “horse strength”.
• hp (mechanical horsepower): 550 foot-pounds-force per second (33,000 per minute), about 745.7 W. There are other definitions too, such as the electrical horsepower (746 W) and the boiler horsepower.
• kW (kilowatt): the unit of the International System of Units (SI). The watt was listed as the SI unit of power by the 11th General Conference on Weights and Measures in 1960.

PS and hp differ by about 1.4%. 100 PS is about 73.55 kW, or about 98.6 hp: the same “100” in different units is a different power. This site’s program checked the PS and hp conversions (torque-and-power/engine.test.ts).

Torque, too, was often given in kgf·m. Multiply by 9.80665 (about 9.8) to get N·m.

Car catalogues in Japan are said to give kW first today, with PS in brackets. We could not confirm when or under which rule that changed, so we give no date.

Watt, and where “horsepower” comes from

The watt is named after James Watt, who improved the steam engine. He did not name it himself: the engineer William Siemens is said to have proposed it as a unit name in 1882.

The horsepower, on the other hand, is said to have been set by Watt in the 1780s, using the work of a horse as a yardstick to sell his steam engines as replacements for the horses that drove mills and the like. One horsepower is 33,000 foot-pounds-force per minute. How he arrived at that number is told in several versions. Stories of a horse walking in a circle are passed down, but the details are legend. And it is a defined unit, not the real strength of one horse.

Which one matters more?

Neither wins. Power is torque times speed, and both are things to look at for the job you have in mind. Pulling away and climbing hills lean on torque; keeping up a high speed leans on power.

All numbers here are simplified examples for teaching, not specifications of real machines.