Horsepower Calculator
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300 lb-ft at 5,000 rpm is 285.6 hp (213 kW)
At 5,252 rpm, torque in lb-ft and horsepower are the same number, which is why the two curves cross there on a US dyno chart.
How to use the horsepower calculator
- Choose a calculation: horsepower from torque, torque from horsepower, power from work and time, or a unit conversion.
- Enter the values and pick their units: lb-ft or N·m for torque, pounds-force, newtons or kilograms-force for force.
- Read the power in every unit, with the formula used for the main result.
Horsepower formulas
hp = torque (lb-ft) × rpm ÷ 5,252 · kW = torque (N·m) × rpm ÷ 9,549
1 hp (mechanical) = 550 ft·lbf/s = 745.7 W
1 PS (metric hp) = 75 kgf·m/s = 735.5 W · 1 electrical hp = 746 W
James Watt defined the horsepower as 33,000 foot-pounds of work per minute, or 550 per second. Rotating power is torque times angular speed; one revolution is 2π radians, so 33,000 ÷ 2π gives the constant 5,252 for lb-ft and rpm. In SI units, 60,000 ÷ 2π gives 9,549 for newton-meters, rpm and kilowatts. Metric horsepower (PS in Germany, CV in France and Italy) is slightly smaller, at about 0.9863 hp, and electric motors are rated in electrical horsepower of exactly 746 W.
Worked examples
An engine making 300 lb-ft at 5,000 rpm produces 300 × 5,000 ÷ 5,252 = 285.6 hp, or 213 kW. A person carrying 200 lb up a 12 ft flight of stairs in 8 seconds does 2,400 ft·lbf of work, delivering 0.545 hp, about 407 W. A 5 hp motor turning at 1,750 rpm supplies 5 × 5,252 ÷ 1,750 = 15 lb-ft of torque.
Horsepower, kilowatts and metric horsepower
| Mechanical hp | Kilowatts | Metric hp (PS) | Electrical hp |
|---|---|---|---|
| 1 hp | 0.75 kW | 1.01 PS | 1 |
| 5 hp | 3.73 kW | 5.07 PS | 5 |
| 10 hp | 7.46 kW | 10.14 PS | 10 |
| 50 hp | 37.28 kW | 50.69 PS | 49.98 |
| 100 hp | 74.57 kW | 101.39 PS | 99.96 |
| 150 hp | 111.85 kW | 152.08 PS | 149.94 |
| 200 hp | 149.14 kW | 202.77 PS | 199.92 |
| 300 hp | 223.71 kW | 304.16 PS | 299.88 |
| 400 hp | 298.28 kW | 405.55 PS | 399.84 |
| 500 hp | 372.85 kW | 506.93 PS | 499.8 |
Horsepower by torque and rpm
| Torque | 2,000 rpm | 3,000 rpm | 4,000 rpm | 5,252 rpm | 6,000 rpm |
|---|---|---|---|---|---|
| 100 lb-ft | 38 hp | 57 hp | 76 hp | 100 hp | 114 hp |
| 200 lb-ft | 76 hp | 114 hp | 152 hp | 200 hp | 228 hp |
| 300 lb-ft | 114 hp | 171 hp | 228 hp | 300 hp | 343 hp |
| 400 lb-ft | 152 hp | 228 hp | 305 hp | 400 hp | 457 hp |
| 500 lb-ft | 190 hp | 286 hp | 381 hp | 500 hp | 571 hp |
Notice the 5,252 rpm column: there, horsepower equals torque in lb-ft.
Brake, wheel and rated horsepower
Horsepower figures depend on where the power is measured. Brake horsepower (bhp) is measured at the engine's crankshaft on an engine dynamometer, which is what carmakers usually quote. Wheel horsepower comes from a chassis dynamometer and is lower, because the gearbox, driveshaft and differential absorb some power on the way. An electric motor's rating is its continuous shaft output, so a 5 hp motor delivers about 3.73 kW to its load while drawing more than that from the supply. Torque and power are linked only through speed: gearing multiplies torque and divides speed, so it changes the torque at the wheels without changing the power, apart from friction losses.
Tips
- Peak torque and peak power happen at different speeds. Use the torque at the rpm you care about, not the peak figure, when you calculate power.
- Check which horsepower you're reading. European car brochures often quote PS; a 150 PS engine is about 148 hp.
- Motor nameplates show output. An electric motor's horsepower rating is shaft output; the electrical input is higher because of losses.
- Estimating a car's power from a drag strip pass? Use the engine horsepower calculator.
For electrical power, see the Ohm's law calculator and the electricity cost calculator.
Frequently asked questions
How do I calculate horsepower from torque and rpm?
Multiply the torque in lb-ft by the rpm and divide by 5,252. An engine making 300 lb-ft at 5,000 rpm produces 300 × 5,000 ÷ 5,252 ≈ 285.6 hp. In metric units, kW = torque in N·m × rpm ÷ 9,549.
How many watts are in one horsepower?
One mechanical (imperial) horsepower is 550 ft·lbf per second, about 745.7 W. A metric horsepower (PS) is 735.5 W and an electrical horsepower is exactly 746 W. One kilowatt is about 1.341 mechanical horsepower.
Why do torque and horsepower curves cross at 5,252 rpm?
Because hp = lb-ft × rpm ÷ 5,252, the two numbers are equal when the rpm is 5,252. Below that speed the torque figure is larger than the horsepower; above it, horsepower is larger. The constant comes from 33,000 ft·lbf per minute divided by 2π.
How do I convert horsepower to kilowatts?
Multiply mechanical horsepower by 0.7457. A 200 hp engine is about 149.1 kW, and a 1.5 hp pump is about 1.12 kW. To go the other way, multiply kilowatts by 1.341.
What is the difference between hp and PS?
PS (Pferdestärke) is metric horsepower, defined as 75 kilogram-force meters per second, or 735.5 W. It is about 1.4% smaller than mechanical horsepower, so 100 PS is about 98.6 hp, and a 300 hp engine is about 304 PS.