Motors and transformers
Shaft torque from power and speed
- where
- shaft torque (N·m)
- mechanical output power (W)
- actual shaft speed (rpm)
Explain this equation
Gives the torque at a motor shaft from its mechanical output power and shaft speed. Use it when matching a motor to a load or checking a gearbox or coupling rating.
P_out is the mechanical power at the shaft, entered in watts. n is the actual shaft speed in rpm. T is the torque in newton-metres.
Power equals torque times angular speed in radians per second. Converting rpm to rad/s multiplies by 2π/60, and the reciprocal, 60/(2π), is about 9.55. Working with power in kW makes that 9550, so the 1000 underneath converts the watts you enter into kW.
7.5 kW at 1500 rpm gives about 48 N·m. Halve the speed at the same power and the torque doubles, which is why slow-speed motors and gearboxes are big.
Watch out: use shaft output, not electrical input, and actual shaft speed, not synchronous speed. 9550 is rounded, and the formula cannot give starting torque at zero speed.
Power combines turning force with rotational speed. For a given output power, a slower rotating shaft requires a greater torque.
Use mechanical output kW and actual shaft speed. If only electrical input is known, account for motor efficiency before calculating torque.
Enter your values to see the result.
Common mistake
Do not use watts in a formula expecting kW or use synchronous speed instead of shaft speed.
Limits
Steady rotation, n > 0. The constant 9550 is rounded. The equation cannot predict starting torque at zero speed; use the motor/drive torque-speed data.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.