Power, Torque & RPM
Turn torque and speed into power, or power and speed into torque, for engines, electric motors and bikes. In kW, hp and PS, N·m and lbf·ft, and what a gearbox does to them.
Torque, Speed and Power
Torque is how hard a shaft twists; power is how fast it does work. The same power can come as a strong slow twist or a light fast one: a 7.5 kW motor at 1450 rpm gives about 49 N·m, behind a 5 : 1 gearbox it gives almost five times that at a fifth of the speed.
That is why an engine’s maximum torque and maximum power come at different speeds, and why gears matter: they trade speed for torque while the power passes through, less a few percent of friction.
From Torque to Power, Step by Step
powerKey Relations
With P in watts, T in N·m and ω in rad/s; n is in revolutions per minute.
9549 = 60 000/2π and 5252 = 33 000/2π. At 5252 rpm the torque in lbf·ft and the power in hp are the same number.
The gearbox trades speed for torque; only the efficiency η costs power. For the gear ratio of a gear train, see the Gear train tab.
Sources & Verification
- R. G. Budynas & J. K. Nisbett, Shigley’s Mechanical Engineering Design, 10th ed., McGraw-Hill, 2015 — power transmitted by a rotating shaft, H = Tω.
- A. Thompson & B. N. Taylor, Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 2008 — Appendix B: horsepower (550 ft·lbf/s) = 745.6999 W, metric horsepower = 735.4988 W, lbf·ft = 1.355818 N·m.
Frequently Asked Questions
How do I convert torque to horsepower?
Multiply torque by speed: power = 2π × rpm × torque ÷ 60. With torque in lbf·ft: hp = lbf·ft × rpm ÷ 5252. With torque in N·m: kW = N·m × rpm ÷ 9549. A car engine giving 200 N·m at 4000 rpm makes 83.8 kW, or 112 hp.
How do I calculate the torque of an electric motor?
Divide the power by the speed: torque (N·m) = 9549 × power (kW) ÷ rpm. A 7.5 kW motor at 1450 rpm gives 9549 × 7.5 ÷ 1450 = 49.4 N·m. Behind a 5 : 1 gearbox with 95% efficiency that becomes about 235 N·m at 290 rpm.
How do I convert kW to hp?
Divide by 0.7457: 1 hp (mechanical horsepower) = 745.7 W, so 100 kW = 134.1 hp. European car data often use the metric horsepower PS (or CV), which is 735.5 W: 100 kW = 136 PS. 150 hp is 111.9 kW.
Why do torque and horsepower cross at 5252 rpm?
Because hp = lbf·ft × rpm ÷ 5252: at exactly 5252 rpm the divisor cancels, so the torque in lbf·ft and the power in hp are the same number. On any dyno chart in those units the two curves cross there. In N·m and kW the crossing is at 9549 rpm.
What is the difference between torque and power?
Torque is how hard the shaft twists; power is torque times how fast it turns, the rate of doing work. A diesel engine gives lots of torque at low rpm, a racing engine less torque but at much higher rpm and so more power. Gears trade one for the other but cannot add power.
How much power does a cyclist produce?
A fit cyclist holds about 200 to 300 W for an hour. At 250 W and a cadence of 90 rpm, the pedals carry a torque of 250 × 60 ÷ (2π × 90) = 26.5 N·m, the same as about 15 kg pushing down on a 17.5 cm crank.