Math & Scientific

Calculate Motor Torque from Shaft Power and Speed

Derive torque from mechanical shaft power and RPM, check a 2 kW example, and distinguish electrical input, rated output and stall conditions.

By Uddhav Gopani, FounderPublished 25 September 2026Reviewed 29 September 2026

Calculate Motor Torque from Shaft Power and Speed

Use power and speed from the same operating point

For rotation about a fixed axis, mechanical power is torque multiplied by angular speed: P=Tω. If P is in watts and ω is in radians per second, T is in newton-metres. A motor's shaft power and shaft speed must refer to the same operating condition. Combining a maximum power rating with a speed from another point on a performance curve can produce a torque value the motor never delivers. Start by identifying whether the available power is mechanical output or electrical input, and whether the speed is rated, measured or merely a no-load specification.

Convert RPM to angular speed

One revolution corresponds to 2π radians, and one minute contains 60 seconds. A speed of n revolutions per minute therefore gives ω=2πn/60 radians per second. Substitute this into the power equation to obtain T=60P/(2πn). When power is entered in kilowatts, multiply it by 1,000 first. The resulting convenient form is T≈9549.2966P_kW/n. The often-used coefficient 9550 is rounded. Neither coefficient converts electrical power to shaft power automatically; the formula still requires the mechanical power appropriate to the shaft whose torque is being calculated.

Work a 2 kW and 1,500 RPM example

Suppose a motor delivers 2 kW of mechanical shaft power at 1,500 RPM. Its angular speed is 2π×1,500/60=50π, approximately 157.0796 radians per second. Torque is 2,000/(50π), approximately 12.7324 N·m. Multiplying that torque by the angular speed returns approximately 2,000 W, which is a useful independent check. Using the rounded coefficient 9550 gives 12.7333 N·m, a small rounding difference. Report an appropriate number of digits for the accuracy of the original power and speed data rather than treating the extra calculator digits as measurement precision.

Account for efficiency only when needed

If the given 2 kW is electrical input and the illustrative efficiency at this operating point is 85%, the mechanical output is 0.85×2,000=1,700 W. At the same 1,500 RPM, the corresponding torque is approximately 10.8225 N·m. This is lower than the previous result because the available shaft power is lower. If a datasheet already provides mechanical output power, applying efficiency again would reduce it twice. For an actual motor, obtain the applicable efficiency or output data from its documentation; a single invented percentage is useful for learning the arithmetic, not for characterizing every load condition.

Do not divide by zero at stall

At zero rotational speed, the equation P=Tω gives zero mechanical shaft power for a finite torque. Rearranging it as T=P/ω is then unsuitable for determining stall torque because division by zero is undefined. A motor can exert torque while stationary even though it is doing no rotational mechanical work at that instant. Stall torque, starting torque and the available torque over a speed range require the relevant motor model, control conditions or manufacturer data. They cannot be inferred by inserting zero RPM into a rated running-power calculation.

Keep transmission stages explicit

For an ideal 2:1 speed-reducing transmission, input torque 12.7324 N·m at 1,500 RPM corresponds to output torque 25.4648 N·m at 750 RPM while power remains unchanged. If an illustrative transmission efficiency is 90%, the output torque becomes approximately 22.9183 N·m instead. Distinguish transmission losses from any motor efficiency already applied. Record input and output shafts separately, including which speed and torque belong together. This prevents a common error in which a reduced output speed is combined with a torque measured at the faster input shaft.

Use the torque converter after calculating torque

The linked Torque Converter changes the units of an already known torque. It does not accept motor power and RPM as a motor-sizing model. First perform the P/ω calculation with compatible units, then enter the resulting N·m value if another torque unit is needed. Retain the operating-point assumptions with the converted number. A unit conversion cannot establish whether a particular motor, gearbox or coupling meets startup, thermal or duty-cycle requirements; those depend on the actual equipment data and operating conditions beyond this arithmetic example.

Use the Torque Converter

Open Torque Converter

Source and scope

OpenStax: rotational power and torque