Calculate motor torque from power and speed using τ = P/ω. Includes efficiency, unit conversions (N·m, lb·ft, oz·in), speed-torque tables, and NEMA frame reference.
Motor torque is the twisting force available at an electric motor shaft. The core relationship τ = P/ω ties torque to mechanical power and angular speed, which is why the same horsepower rating can produce different torque values at different RPM.
That matters when you are matching a motor to a load. A slow motor can deliver much more torque than a fast one at the same power, and efficiency changes the electrical input required to get that mechanical output.
This calculator turns power and speed into shaft torque, or electrical input plus efficiency into mechanical output torque. It also shows the result in N·m, lb·ft, and oz·in, and includes speed-torque tables for motor selection.
Power, torque, RPM, and efficiency are linked, but the conversions are easy to mix up when you are checking a motor by hand. This calculator keeps the RPM-to-rad/s step, the efficiency loss, and the output unit conversions together so the result is easier to compare against the load.
Torque: τ = P / ω Angular Velocity: ω = 2πn / 60 Combined: τ = 60P / (2πn) Power from electrical: P_mech = V × I × η Unit Conversions: 1 N·m = 0.7376 lb·ft 1 N·m = 141.612 oz·in 1 HP = 745.7 W
Result: 20.35 N·m
A 5 HP motor (3730 W) at 1750 RPM: ω = 2π × 1750/60 = 183.3 rad/s, so τ = 3730/183.3 = 20.35 N·m (15.01 lb·ft). At 90% efficiency, electrical input is 4144 W with 414 W lost as heat.
The relationship τ = P/ω is a direct consequence of the definition of power in rotational systems. Just as linear power is force times velocity (P = Fv), rotational power is torque times angular velocity (P = τω). This means a motor's torque output is completely determined by its power and speed.
Motor manufacturers specify ratings at particular operating points — for example, "5 HP at 1750 RPM" means the motor delivers 3730 W of mechanical power at 1750 RPM, which corresponds to 20.35 N·m of torque. Operating at different speeds changes the available torque.
Motor losses fall into several categories: copper losses (I²R heating in windings), iron losses (hysteresis and eddy currents in the core), mechanical losses (bearing friction, windage), and stray losses. Premium efficiency (IE3/IE4) motors minimize these through better materials, tighter tolerances, and optimized electromagnetic design.
The cost of efficiency matters: a 90% efficient 10 HP motor running 8000 hours/year wastes about 6,000 kWh annually. Upgrading to 95% efficiency saves 3,000 kWh/year — often paying for itself within 2-3 years through reduced electricity bills.
Different motor types have different torque-speed curves. AC induction motors have relatively constant torque up to rated speed, then torque drops. DC motors can produce high torque at low speeds. Stepper motors have high holding torque but torque drops rapidly with speed (torque rolloff). Understanding these characteristics is critical for matching motors to applications.
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Power equals torque multiplied by angular speed, so torque and speed move in opposite directions at constant power.
Efficiency tells you how much electrical input becomes useful shaft power. The rest becomes heat, which affects cooling, wiring, and operating cost.
Rated torque is the continuous output near the motor’s design point. Stall torque is the maximum low-speed torque and is usually only safe for short bursts.
One mechanical horsepower is 745.7 watts. That lets you compare motor nameplate ratings with electrical power in a consistent way.
A NEMA frame size standardizes mounting dimensions such as shaft height and bolt pattern, which makes replacement and interchange easier.
Yes. A gearbox trades speed for torque, so a reduction ratio can increase output torque while lowering RPM.