Horsepower calculator

How do I calculate horsepower from torque?

Horsepower = torque (lb-ft) × RPM ÷ 5,252. 300 lb-ft at 5,000 RPM is 300 × 5,000 ÷ 5,252 = 285.6 hp.

Where does 5,252 come from?

One horsepower is 33,000 foot-pounds of work per minute, and one turn is 2π radians: 33,000 ÷ 2π = 5,252.1. That is also why torque and horsepower curves always cross at 5,252 RPM.

How do I convert horsepower to kilowatts?

Multiply by 0.7457: 300 hp is 223.7 kW. Going the other way, 1 kW is 1.341 hp.

How do I convert lb-ft to newton-meters?

Multiply by 1.3558: 300 lb-ft is 406.7 N·m.

Is this wheel horsepower or engine horsepower?

Whatever you put in: engine torque gives engine (brake) horsepower, dyno torque at the wheels gives wheel horsepower, which is lower because of drivetrain losses.

Worked example: 400 N·m at 6,000 RPM in SI units

Power in watts is torque in newton-meters times angular speed in radians per second. At 6,000 RPM the angular speed is 6000 × 2π ÷ 60 = 628.3 rad/s, so power is 400 × 628.3 = 251327 W, or 251.3 kW. Dividing by 745.70 W per horsepower gives 337.0 hp. The route through pound-feet agrees: 400 N·m is 295.0 lb-ft, and 295.0 × 6000 ÷ 5252.1 = 337.0 hp. In reverse, 300 hp at 4,000 RPM means a torque of 393.9 lb-ft.

Which horsepower is it? Mechanical, metric and electric

The NIST conversion tables list several horsepower units. The mechanical horsepower of 550 foot-pounds-force per second is 745.6999 W, the electric horsepower is 746 W, and the metric horsepower (the PS or CV of European specifications) is 735.4988 W. Because the metric unit is smaller, the same engine shows a number 1.4% higher in metric horsepower: 341.7 PS against 337.0 hp for the 400 N·m example. The calculator uses the mechanical horsepower and the lb-ft constant 5,252.

How do I get power in kilowatts straight from N·m?

Power in kW equals torque in N·m times RPM, divided by 9549.3, because 1 RPM is 2π ÷ 60 radians per second and a watt is a newton-meter per second, with 1,000 W to the kilowatt: 60,000 ÷ 2π = 9549.3. For the 400 N·m example at 6,000 RPM that is 400 × 6000 ÷ 9549.3 = 251.3 kW. This constant is the metric counterpart of 5,252, and it is why the curves of N·m and kW cross at 9549 RPM, not at 5,252.

Why does the same power need more torque at low RPM?

Because power is torque times rotational speed, so for a fixed power the torque is inversely proportional to RPM. An engine making 200 hp needs 525 lb-ft at 2,000 RPM, but only 175 lb-ft at 6,000 RPM, a third as much. A slow-turning engine therefore needs a much larger torque than a high-revving one for the same power. Neither number is better on its own: torque is what you feel at a given moment, power is the rate at which work is done.

Common mistakes with horsepower and torque

Using newton-meters with the lb-ft constant: 5,252 only works for lb-ft, and 400 typed as lb-ft at 6,000 RPM would give 457 hp instead of 337. Comparing a metric-horsepower figure with a mechanical one without allowing for the 1.4% difference. Quoting peak torque and peak power as if they occurred at the same speed; the formula links them at each RPM, and the peaks sit at different RPMs. Mixing wheel and engine figures. And forgetting that torque and power are equal numerically at 5,252 RPM only when torque is in lb-ft and power in hp.

Sources and related calculators

Sources: NIST Guide to the SI, Appendix B conversion factors (horsepower of 550 ft·lbf/s = 745.6999 W, electric 746 W, metric 735.4988 W; pound-force foot = 1.355818 N·m); the definition of horsepower as 33,000 foot-pounds per minute. Related: torque calculator, RPM to MPH calculator, quarter mile calculator and power converter.