Horsepower from torque:
turning a torque figure and engine speed into power

Why torque and speed combine to give power

Torque is a turning force; power is the rate at which work is done. An engine that delivers 200 N·m while spinning at 3,000 revolutions each minute does more work per second than one that delivers the same torque at 1,500 rpm. Power rises with both, so multiplying them is the natural step.

Doing the units properly: one revolution is 2π radians, and there are 60 seconds in a minute. Torque × rpm × 2π ÷ 60 gives watts. Dividing by 1,000 converts to kilowatts, and the constant that falls out of 60,000 ÷ 2π is about 9,549.3.

The formula with a worked case

The answer in kilowatts is the SI result. Horsepower comes from converting, as the next section shows. The calculation does not, by itself, tell you the peak power of an engine; it gives power at that one speed.

Converting to horsepower and PS

The difference between hp and PS is small but real, about 1.4%. Always check which one a source is using, because brochures differ across markets.

If your torque is in pound-feet instead, use hp = lb-ft × rpm ÷ 5,252. For 147.5 lb-ft (which is 200 N·m) at 3,000 rpm that gives 84.3 hp, consistent with the metric calculation.

Peak torque and peak power are at different speeds

A torque figure is only meaningful with the rpm at which it applies. Most engines produce their highest torque at a middle speed and then torque falls off while rpm keeps climbing. Because power is torque times speed, the power peak sits at a higher rpm than the torque peak.

• A diesel with 350 N·m at 1,800 rpm gives about 66 kW at that point.
• A petrol engine with 200 N·m at 3,000 rpm gives about 63 kW; the same engine may reach 90 kW or more near 6,000 rpm even though torque there is lower.
• Electric motors deliver near-flat torque from zero speed, so their power rises almost in step with rpm up to the base speed.

When you see a spec sheet with two peaks, the claimed power and the claimed torque are different points on the same curve, and the formula applies to every point on it.

Using the number sensibly

The formula gives power at the shaft where the torque was measured. Power at the wheels is lower because of drivetrain losses, typically 10% to 20% depending on the transmission and drive layout. A dyno result at the wheels can therefore be well below the engine's rated figure even when nothing is wrong.

Rated power also follows a test standard, with specific fuel, temperature and accessories. A quoted 62.83 kW from the formula is a power estimate for the stated torque, not a certified rating.

A second worked case: an electric motor

The relation is not limited to engines. A small electric motor rated at 40 N·m and 1,500 rpm delivers 40 × 1500 ÷ 9,549.3 = 6.28 kW, about 8.4 hp. Many motor nameplates list kW and rpm but not torque, so you can rearrange: torque = 9,549 × kW ÷ rpm.

A 5.5 kW motor running at 1,440 rpm therefore delivers 9549.3 × 5.5 ÷ 1440 = 36.5 N·m at full load. Using a gearbox with a 4:1 ratio would give about 146 N·m at 360 rpm, less friction losses. That is how a modest motor drives a conveyor or a pump that needs high torque.

How gearing changes the picture

A gearbox changes torque and speed but not power, apart from losses. If the engine produces 62.83 kW at 3,000 rpm and the gearing reduces speed to 1,000 rpm at the wheels, torque at that shaft is about three times higher, near 600 N·m before losses. The product of torque and speed, which is power, stays roughly the same.

This is why a vehicle in a low gear can pull a heavy load: the engine's power is unchanged, but it is exchanged for more force at a lower speed.

Reading a spec sheet critically

Spec sheets list peak power and peak torque with the rpm at which each occurs. Use the formula to check them against each other. If a sheet says 200 N·m at 3,000 rpm and 90 kW at 6,000 rpm, the torque at 6,000 rpm must be 9549.3 × 90 ÷ 6000 = 143 N·m, which is lower than the peak, consistent with a torque curve that falls off.

If a sheet claims a power figure that would require a torque higher than the stated peak at that rpm, one of the numbers is wrong or from a different test. This quick cross-check is a useful tool when comparing figures from different sources, such as a brochure and a dyno chart.

Related quantities worth knowing

Once power is known, you can estimate acceleration and fuel use. Dividing power by mass gives power-to-weight, a more useful comparison than power alone: 84 hp in a 1,000 kg car is 84 hp per tonne. Brake specific fuel consumption relates fuel flow to power produced.

A general physics magnitude tool can help with related conversions and unit checks, but the core relation for this topic is simply torque times speed, with the right constant for your units.