Torque from power and speed calculator

Enter power in watts, kilowatts, megawatts, mechanical horsepower, or metric horsepower, then provide speed in revolutions per minute or radians per second. The result is torque in newton-metres, with normalized power and angular speed shown alongside it so that every conversion is visible and easy to check. It is useful for motors, gearboxes, pumps, fans, turbines, and other rotating equipment operating at a defined point.

Relate power, speed, and shaft torque correctly

Rotational mechanical power links torque and angular speed through the equation P = T × ω. Rearranging that relationship gives T = P / ω, which is the equation used by this calculator. Power must represent the mechanical power actually transmitted at the shaft, and angular speed must describe that same operating point. When speed is entered in revolutions per minute, the calculator converts it to radians per second using ω = n × 2π / 60 before dividing power in watts by angular speed. Because one watt is one joule per second and a radian is dimensionless, the resulting unit is newton-metre. The familiar shortcut T = 9550 × P(kW) / n(rpm) is an approximation based on the same equation; using the full conversion avoids hiding the constant and works naturally with additional units. A zero speed is rejected because finite power divided by zero angular speed cannot define a finite shaft torque. Zero transmitted power at a positive speed is valid and produces zero torque.

Choose power and speed values from the same operating condition

A meaningful result depends more on input selection than arithmetic. Use output power at the shaft if you need output torque. If only electrical input power is available for a motor, first account for efficiency; otherwise the calculated torque will be higher than the torque actually delivered. Likewise, use loaded running speed rather than synchronous speed, nameplate nominal speed, or no-load speed when sizing around a real duty point. Gear reductions also change the location at which power and speed should be measured. Compute input-shaft torque using input-shaft speed and input power, or output-shaft torque using output speed and power after gearbox losses. The horsepower choices are explicit: hp means mechanical horsepower at exactly 745.6998715822702 watts, while PS means metric horsepower at 735.49875 watts. Keeping these definitions separate prevents a quiet unit error. The calculator reports converted watts and radians per second with the torque, allowing engineers to audit the calculation, compare it with a datasheet, and carry consistent SI values into another design step.

Interpret the result for selection and design

The returned value is steady torque implied by the stated transmitted power and speed. It is not automatically the motor starting torque, pull-out torque, peak transient torque, holding torque, or a guarantee that a component will survive the application. Real selections need allowances for duty cycle, acceleration, shock, service factor, thermal limits, gearbox efficiency, and uncertainty in the operating data. For a conveyor or pump that starts under load, calculate the running point here and then separately evaluate acceleration and breakaway requirements. For variable-speed drives, repeat the calculation at important points on the speed-power curve: constant-power operation makes torque rise as speed falls, whereas a constant-torque region makes power fall with speed. Negative power or speed is outside this calculator's magnitude-based scope, so regenerative direction should be handled with a separate sign convention while using positive magnitudes here. API use costs $0.002 per calculation, and the deterministic arithmetic makes the same input suitable for repeatable design records, automated equipment schedules, and checks embedded in engineering workflows.