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 rotational force produced at the shaft of an electric motor. The fundamental relationship τ = P/ω connects torque to mechanical power output and angular velocity. This equation is the starting point for sizing motors, selecting gear ratios, and verifying that a motor can handle a given load.
In practice, motor selection involves balancing torque, speed, power, efficiency, and physical size. A motor rated at 5 horsepower produces very different torques depending on its speed — a 1750 RPM motor produces four times the torque of the same power at 7000 RPM. Understanding this tradeoff is essential for mechanical design.
This calculator computes shaft torque from either direct power input or from electrical voltage and current with efficiency factored in. It provides results in multiple unit systems (N·m, lb·ft, oz·in), generates speed-torque tables at constant power, and includes NEMA frame size references for quick motor selection. Check the example with realistic values before reporting.
Converting between power, torque, and speed involves the factor 2π/60 for RPM-to-rad/s conversion and efficiency corrections that are easy to mishandle. Unit conversions between N·m, lb·ft, and oz·in add another source of errors. This calculator handles all conversions instantly and provides comparison tables that help you evaluate motor options across different speed ranges.
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.
Power = Torque × Angular velocity (P = τω). At constant power, torque and speed are inversely proportional — higher speed means less torque and vice versa.
Efficiency determines how much electrical input becomes useful mechanical output. The rest is lost as heat in windings, bearings, and magnetic losses. Higher efficiency means less cooling needed and lower operating costs.
Rated torque is the continuous torque at rated speed and power. Stall torque is the maximum torque at zero speed — typically 2-5× rated torque for short durations, but the motor overheats if stalled continuously.
1 mechanical horsepower = 745.7 watts. A 5 HP motor delivers about 3730 W of mechanical power at rated efficiency.
NEMA frame sizes standardize motor mounting dimensions. The frame number indicates shaft height and mounting bolt patterns, making it easy to swap motors of the same frame size.
Yes, by adding a gear reduction. A 10:1 gear ratio multiplies torque by 10 while dividing speed by 10 (minus gear losses). This is exactly what the gear-ratio calculator helps with.