136 motor cells — 2.2 kW at 1800 rpm is 11.7 N·m
Every pairing of 17 rated outputs and 8 synchronous speeds, worked out as newton metres. There is no table to memorise — power is torque times angular velocity, so dividing power by angular velocity gives torque. The familiar 9550 factor is just 60000 divided by 2π.
Torque is power divided by angular velocity
The output of a turning shaft is torque times angular velocity. Angular velocity is the speed expressed in radians per second, ω = 2π × n ÷ 60, so torque is P × 60 ÷ (2π × n). The catalogue shortcut T = 9550 × P(kW) ÷ n(rpm) is exactly that formula, and 9550 is 60000 ÷ 2π = 9549.3 rounded up. Knowing where the number came from beats memorising it: mixed units stop being a trap.
Poles and mains frequency fix the speed
The synchronous speed of an induction motor is not a choice: it is 120 × frequency ÷ poles. The same four-pole motor therefore turns at 1800 rpm on 60 Hz and 1500 rpm on 50 Hz — Korea, the United States and eastern Japan run 60 Hz, while Europe, China and India run 50 Hz. Same power, speeds in a 6 : 5 ratio, so the torques land in a 5 : 6 ratio. In service the rotor lags by the slip, which is why the nameplate reads something like 1746 rpm.
There are two horsepowers and they differ
Metric horsepower (PS) is 735.49875 W and mechanical horsepower (hp) is 745.699872 W. The 1.4 % gap looks small, but a 75 kW motor is 102 PS and 101 hp — mix the two while comparing catalogues and you pick the wrong frame size. German, Japanese and Korean data sheets use PS, North America uses hp. Converting both to kilowatts before comparing is the safe move.
A gearbox divides speed and multiplies torque
Put a reduction ratio i in the path and the output shaft turns at 1/i of the speed while the torque grows i-fold. Power does not grow — it shrinks by the efficiency η, so the torque is i × η times the input. The figures here assume η = 0.95, typical of a helical gearbox. A worm drive falls to 0.5–0.8 and delivers far less. More torque never means more energy: the same power is simply traded for slower, heavier turning.
Current needs voltage, power factor and efficiency too
For a three-phase induction motor the current is I = P ÷ (√3 × V × cosφ × η). Rated output is what leaves the shaft, so the electrical input is larger by the efficiency, and only the working share of that counts through the power factor. Supply voltage differs by country, so the same motor draws 1.7 times as much at 220 V as at 380 V. The power factor and efficiency used here are representative values by frame size; the nameplate carries the real ones and should be read first.
At a glance
Torque
0.1 kW100 W
0.2 kW200 W
0.4 kW400 W
0.75 kW750 W
1.5 kW1500 W
2.2 kW2200 W
3.7 kW3700 W
5.5 kW5500 W
7.5 kW7500 W
11 kW11000 W
15 kW15000 W
22 kW22000 W
30 kW30000 W
37 kW37000 W
45 kW45000 W
55 kW55000 W
75 kW75000 W
Worth knowing
- Torque (N·m) is power (W) divided by angular velocity (rad/s), and that velocity is 2π × rpm ÷ 60.
- The 9550 in T = 9550 × P(kW) ÷ n(rpm) is 60000 ÷ 2π rounded up.
- At constant power, doubling the speed halves the torque — they are inversely proportional.
- Metric horsepower (PS) is 735.49875 W and mechanical horsepower (hp) is 745.699872 W: different numbers.
Related tables
Common questions
Q. How do I work out motor torque?
Divide the output by the angular velocity. That velocity is 2π × rpm ÷ 60, so torque (N·m) = power (W) × 60 ÷ (2π × rpm), which tidies up to T = 9550 × P(kW) ÷ n(rpm). The 9550 is 60000 ÷ 2π = 9549.3 rounded up — nothing to memorise.
Q. Does the same motor really run differently on 50 Hz and 60 Hz?
Yes. Synchronous speed is 120 × frequency ÷ poles, so a four-pole motor turns 1800 rpm on 60 Hz and 1500 rpm on 50 Hz. At equal power the slower 50 Hz case carries 6/5 of the torque.
Q. Are PS and hp the same horsepower?
No. Metric horsepower (PS) is 735.49875 W and mechanical horsepower (hp) is 745.699872 W, a gap of 1.4 %. A 75 kW motor is 102 PS but 101 hp.