Motor Torque, Power & Speed Calculator
Find motor torque from power and rpm (T = 9,549 × kW ÷ rpm), or power or speed from the other two, or torque from volts, amps, power factor and efficiency — in N·m, lb·ft, kgf·cm and more, with a gearbox, pulley line pull, synchronous speed and slip, and a torque-versus-speed table.
How it works
P = T × ω, with ω = 2π × rpm ÷ 60 · T (N·m) = 9,549 × P (kW) ÷ rpm · T (lb·ft) = 5,252 × hp ÷ rpm · electrical input: DC P = V × I; 1-phase P = V × I × PF; 3-phase P = √3 × V × I × PF; shaft power = input × efficiency · gearbox: T_out = T_in × ratio × η, rpm_out = rpm_in ÷ ratio · synchronous speed n_s = 120 f ÷ poles, slip = (n_s − n) ÷ n_s · drum pull F = T_out ÷ r
Power is torque times angular speed, so a motor’s nameplate power and rpm fix its rated torque. The constants 9,549 (metric) and 5,252 (imperial) simply bundle the conversion from rpm to radians per second. Pick what you know: power and speed give torque, torque and speed give power, and power and torque give speed. If you only have electrical data, enter the voltage, current, power factor and efficiency; the calculator finds the input power (√3 × V × I × PF for three-phase), the shaft power after losses and then the torque. The relationship explains why high-speed motors are small for their power and why a gearbox is the usual way to get torque: reducing speed ten-fold multiplies torque ten-fold, less the few percent lost to friction. Under More options you can add the pole count and supply frequency to get the synchronous speed and slip of an AC induction motor, and a pulley or drum diameter to turn the output torque into a rope or belt pull and a line speed. The table shows how the torque would change at other speeds for the same power — the constant-power curve above a motor’s base speed.
Worked example
A 7.5 kW motor at 1,450 rpm: ω = 2π × 1,450 ÷ 60 = 151.84 rad/s, so T = 7,500 ÷ 151.84 = 49.4 N·m (36.4 lb·ft, 504 kgf·cm). Through a 10:1 gearbox at 95% efficiency the output is 469 N·m at 145 rpm. On a 4-pole, 50 Hz supply the synchronous speed is 1,500 rpm, so the slip is 3.3%. From electrical data, a three-phase motor drawing 14 A at 400 V with PF 0.85 and 90% efficiency takes 8.24 kW and delivers 7.42 kW to the shaft — 48.9 N·m at 1,450 rpm.
Frequently asked questions
Is starting torque the same?
No — induction motors deliver 1.5–3× rated torque at start (locked rotor), while their rated torque applies at full-load speed. Servo and stepper motors have their own curves.
Why do electric cars quote torque at 0 rpm?
Permanent-magnet and induction traction motors produce maximum torque from standstill up to a base speed, then torque falls as constant power takes over — the curve shown in the table.
How do I get torque from amps and volts?
Work out the electrical input (√3 × V × I × PF for three-phase, V × I × PF for single-phase, V × I for DC), multiply by the motor efficiency to get shaft power, then divide by the angular speed. Choose “Torque from volts, amps and speed” to do this in one step.
What are synchronous speed and slip?
An AC induction motor’s magnetic field turns at 120 × frequency ÷ poles — 1,500 rpm for 4 poles at 50 Hz, 1,800 rpm at 60 Hz. The rotor runs a little slower; that shortfall, the slip, is usually 1–5% at full load.
Where does 5,252 come from?
One horsepower is 33,000 lb·ft per minute, and one revolution is 2π radians, so 33,000 ÷ 2π = 5,252. That is also why horsepower and lb·ft curves always cross at 5,252 rpm on a dyno chart.
How do I convert N·m to kgf·cm or lb·ft?
Multiply N·m by 10.197 for kgf·cm, by 0.7376 for lb·ft and by 8.851 for lb·in. You can also type the torque in any of these units with the unit menu next to the torque box.
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This calculator is for educational purposes. Double-check important results before acting on them.