How to use the torque and power calculator
Choose what to find in the first box: power from torque and speed, torque from power and speed, or speed from power and torque. Then fill in the other two. The field for the quantity you are finding is ignored, so whatever is left in it doesn't matter.
Choose your units. Power can be in kilowatts, watts, mechanical horsepower (hp) or metric horsepower (PS). Torque can be in newton-meters, pound-feet or kilogram-force meters. Speed is in revolutions per minute. The answer leads with the unit selected for it and lists the others underneath, so choosing hp before you find power puts horsepower first.
The torque, power and speed formula
Power is torque times angular speed: P = T × ω. With torque in N·m and ω in radians per second, power comes out in watts. One revolution is 2π radians and a minute is 60 seconds, so ω = 2π × rpm ÷ 60.
Rearranged, T = P ÷ ω and ω = P ÷ T. In everyday units this gives two shortcuts: kW = N·m × rpm ÷ 9,549, and hp = lb-ft × rpm ÷ 5,252.
The unit factors come from their definitions. 1 lb-ft is about 1.355818 N·m and 1 kgf·m is exactly 9.80665 N·m. 1 hp is 550 ft·lbf per second, about 745.6999 W. 1 PS is 75 kgf·m per second, exactly 735.49875 W.
Worked examples: power, torque and speed
Power from torque: a shaft carries 100 N·m at 3,000 rpm. Its angular speed is 2π × 3,000 ÷ 60 = 314.159 rad/s, so P = 100 × 314.159 = 31,415.9 W. The calculator shows 31.4159 kW, which is 42.1295 hp or 42.7138 PS. The shortcut gives 73.7562 lb-ft × 3,000 ÷ 5,252 ≈ 42.13 hp.
Torque from power: a 7.5 kW motor is rated at 1,450 rpm. Choose Torque, enter Power 7.5 kW and Speed 1,450. T = 7,500 W ÷ 151.844 rad/s = 49.3929 N·m, which is 36.4303 lb-ft or 5.03668 kgf·m.
Speed from power and torque: 30 kW delivered at 100 N·m means ω = 30,000 ÷ 100 = 300 rad/s, which the calculator shows as 2,864.79 rpm.
Why horsepower and torque curves cross at 5,252 rpm
One horsepower is 550 ft·lbf per second, which is 33,000 ft·lbf per minute. A torque of T lb-ft turning at n rpm does T × 2π × n ft·lbf of work each minute, so hp = T × 2π × n ÷ 33,000 = T × n ÷ 5,252.11. At 5,252 rpm the divisor cancels, and the horsepower number equals the lb-ft number.
So on a dyno chart that plots horsepower and lb-ft on the same scale, the two curves always cross at 5,252 rpm. Below it the torque number is larger, and above it the horsepower number is. This is a property of the units, not of the engine. Plot kW against N·m and the curves cross at 9,549 rpm instead. PS against kgf·m cross at 716 rpm.
The calculator confirms it: 300 lb-ft at 5,252 rpm gives 299.994 hp. The small gap is there because the exact crossing point is 5,252.11 rpm.
Limits: which horsepower, and where it is measured
The formula is exact, so the answer is only as good as the figures you give it. The torque and speed must be measured at the same moment, on the same shaft. Some points to watch:
- Peak torque and peak power happen at different speeds. Multiplying peak torque by the rpm of peak power overstates the power.
- Horsepower comes in several sizes. Mechanical hp, about 745.7 W, is the usual unit for engines in the US and UK. Metric hp (PS, also written CV or ch) is 735.5 W, about 1.4% smaller. Electric motors rated in hp use 746 W.
- Engine power is quoted at the crankshaft. Power at the wheels is lower, because the gearbox and drivetrain lose some on the way.
- Through a gearbox, power stays almost the same while torque and speed trade places: halve the speed and the torque roughly doubles, less the gear losses.
- An electric motor's rated torque applies at its rated speed. Its starting torque can be quite different.