Quick answer: 1 kW is 1.341 mechanical horsepower, so a 100 kW engine makes 134.1 hp (136.0 PS); 400 N·m at 3,000 rpm is 400 × 3,000 ÷ 9,549 = 125.7 kW, or 168.5 hp.
How it's calculated
Mechanical horsepower is defined as 550 foot-pounds-force per second, exactly 745.699872 W. Metric horsepower (PS, CV, ch) is 75 kilogram-force metres per second, exactly 735.49875 W. Electric horsepower, used for motor ratings, is 746 W. The factors are from NIST Special Publication 811.
Power is torque times rotational speed: P = T × 2π × rpm ÷ 60. With torque in lb·ft this becomes hp = T × rpm ÷ 5,252; with torque in N·m it becomes kW = T × rpm ÷ 9,549.
That is why torque and horsepower curves in lb·ft and hp always cross at 5,252 rpm. Use the torque at the same rpm as the power you want; peak torque and peak power usually come at different speeds.
Worked examples
- 100 kW to hp: 100 ÷ 0.745700 = 134.10 hp
- 400 N·m at 3,000 rpm: 400 × 3,000 ÷ 9,549.3 = 125.66 kW = 168.5 hp
- 300 lb·ft at 5,252 rpm: 300 × 5,252 ÷ 5,252.1 = 300.0 hp
Horsepower and kilowatts
| Unit | Watts | kW |
|---|---|---|
| 1 hp (mechanical) | 745.700 | 0.745700 |
| 1 PS (metric hp) | 735.499 | 0.735499 |
| 1 electric hp | 746 | 0.746 |
| 1 kW | 1,000 | 1 = 1.341 hp = 1.360 PS |
Frequently asked questions
How many hp is 1 kW?
1 kW = 1.341 mechanical horsepower = 1.360 metric horsepower (PS).
What is the difference between hp and PS?
PS (Pferdestärke) is metric horsepower, 735.5 W. Mechanical hp is 745.7 W, so a figure in PS is about 1.4% higher than the same power in hp.
Why 5,252?
It is 33,000 ÷ 2π: one horsepower is 33,000 ft·lbf per minute and one revolution turns 2π radians. At 5,252 rpm torque in lb·ft and power in hp are the same number.
How do I get horsepower from torque and rpm?
With lb·ft, hp = torque × rpm ÷ 5,252. With N·m, kW = torque × rpm ÷ 9,549. So 400 N·m at 3,000 rpm is about 126 kW, or 168.5 hp.
What is brake horsepower (bhp)?
Power measured at the engine's crankshaft, before the gearbox and drivetrain take their share. Horsepower at the wheels, from a chassis dyno, always comes out lower.
How many kW is a 200 hp car?
About 149 kW.