Motor Shaft Torque

Calculate steady mechanical shaft torque from delivered shaft power and measured loaded speed.

How this calculation works

Mechanical shaft power is the product of torque and angular speed. Enter the delivered mechanical power in kilowatts and the loaded shaft speed in revolutions per minute at the same steady operating point. The calculator converts speed to radians per second using 2π radians per revolution and 60 seconds per minute, then divides power in watts by that angular speed. Using the exact conversion avoids relying on a rounded torque factor. Electrical input power is not interchangeable with shaft output because the calculation does not account for motor losses or efficiency. Speed must be positive, so this relation cannot determine stall torque. Starting, breakdown and transient torque, as well as shaft or coupling strength, need information beyond these two inputs.

Inputs and units

Mechanical shaft output power (kW): Enter delivered mechanical power, not electrical input
Loaded shaft rotational speed (r/min)

Method and formula

Angular speed ω = 2πn/60 rad/s; shaft torque T = 1000 × shaft power in kW/ω. This uses the exact conversion rather than the rounded factor 9550.

Worked example

Example inputs

Mechanical shaft output power: 15 kW
Loaded shaft rotational speed: 1500 r/min

Calculation steps

Convert 1500 r/min to angular speed: ω = 2π × 1500/60 = 157.079633 rad/s.
Convert mechanical output to watts: 15 × 1000 = 15000 W.
Divide mechanical power by angular speed: torque = 15000/(2π × 1500/60) = 95.492966 N·m.

Example results

Angular speed: 157.0796327 rad/s
Steady shaft torque: 95.49296586 N·m

Assumptions

Power and rotational speed describe the same steady shaft operating point
Mechanical output power is already known or measured

Limitations

Does not predict starting, stall, breakdown or peak transient torque
Does not convert electrical input to shaft power or assess shaft/coupling strength

Sources

ABB: ACS580 Technical eBook: Motor power section: mechanical power equals torque times angular velocity