Horsepower explained: hp, PS, kW and how torque fits in

One mechanical horsepower is about 745.7 watts. Metric horsepower (PS, CV or pk) is slightly smaller at 735.5 W, so 100 PS is about 98.6 hp, and one kilowatt is about 1.34 hp. Horsepower measures power, the rate of doing work, and for an engine it is torque multiplied by rotational speed: in common units, hp = torque in lb-ft × rpm ÷ 5,252. The horsepower calculator converts between all of these and works out power from torque and rpm.

Where horsepower comes from

James Watt needed a way to sell steam engines to people who used horses. After observing horses turning mill wheels, he and Matthew Boulton settled in the 1780s on a figure of 33,000 foot-pounds of work per minute, or 550 foot-pounds per second, as one horsepower. The number was a marketing yardstick rather than a precise measurement of a horse, but it stuck. Converted to SI units, 550 ft·lbf/s is about 745.7 W, the factor the US National Institute of Standards and Technology lists for horsepower.

hp, PS, kW and electrical hp

Several "horsepowers" are still in use, which causes real confusion when comparing cars:

• Mechanical horsepower (hp, bhp): 745.7 W, used in the UK and US.
• Metric horsepower (PS in German, CV in French, Spanish and Italian, pk in Dutch): defined as lifting 75 kg by one metre in one second, 735.49875 W, about 98.6% of a mechanical horsepower. A car rated at 150 PS has about 148 hp.
• Electrical horsepower: exactly 746 W, used for electric motors.
• Kilowatt (kW): the SI unit, used in official EU vehicle documents; 1 kW ≈ 1.341 hp.

Electric cars are increasingly quoted in kW, which also links power to energy use: a motor delivering 100 kW for one hour does 100 kWh of work, as What is a kilowatt-hour, and how do you work out what an appliance costs? explains. The watts to amps calculator handles the electrical side of motor ratings.

Horsepower, torque and rpm

Torque is twisting force; power is how quickly that force does work. An engine producing a given torque produces more power the faster it spins. The relationship is power = torque × angular speed, which in everyday units becomes:

• hp = lb-ft × rpm ÷ 5,252
• kW = N·m × rpm ÷ 9,549

The 5,252 is 33,000 divided by 2π, and 9,549 is 60,000 divided by 2π. So 200 lb-ft at 3,000 rpm is about 114 hp, and the same 200 lb-ft at 6,000 rpm is about 228 hp. A side effect is that when horsepower and lb-ft are plotted on the same chart, the two curves always cross at 5,252 rpm. In metric, 300 N·m at 4,000 rpm is about 126 kW, or 169 hp. The torque converter switches between N·m, lb-ft and other torque units, and Torque units explained: N·m, lb-ft, lb-in and kgf·m goes into them in detail.

Reading engine specifications

Manufacturers quote peak power and peak torque, usually at different engine speeds, so multiplying the two headline numbers does not give anything meaningful. Brake horsepower (bhp) is measured at the engine's crankshaft. Wheel horsepower, measured on a rolling-road dynamometer, is lower because the gearbox, driveshafts and tyres absorb some of the power; the loss is often quoted as 10 to 20% but depends on the drivetrain. For comparing two cars, make sure both figures are the same kind: PS against PS, or bhp against bhp.

It also helps to know what each number tells you on the road. Peak power largely sets top speed and how quickly a car can accelerate at high revs, while the shape of the torque curve decides how strongly it pulls from low engine speeds without a downshift. Two engines with the same peak horsepower can feel very different if one makes its torque low down and the other only near the redline. Gearing multiplies torque at the wheels too, which is why a car feels strongest in first gear even though the engine itself produces the same torque in every gear.

Converting quickly

For rough mental conversions: kW × 1.34 ≈ hp, hp × 0.746 ≈ kW, and PS × 0.986 ≈ hp. A 1.5 kW kitchen appliance is about 2 hp; a 200 hp car is about 149 kW. Human power is easier to feel in watts: the cycling power calculator shows how many watts it takes to ride at a given speed, a useful reminder of how much one horsepower really is.