Motor Torque Calculator
Motor torque is the twisting force a motor delivers at its shaft, and it follows directly from the motor's power output and its rotational speed. Mechanical power equals torque times angular velocity, so rearranging gives torque as power divided by angular velocity. Since motor speeds are quoted in revolutions per minute, the speed must first be converted to radians per second by multiplying by two pi and dividing by sixty. This calculator takes the mechanical power in watts and the rotational speed in revolutions per minute, converts the speed to angular velocity, and returns the shaft torque in newton meters to two decimal places. For a fixed power, torque rises as speed falls, which is why low-speed motors and geared drives produce more torque, and why a gearbox trades speed for turning force. The relationship is the standard one linking power, torque and speed in rotating machinery. Mechanical power conventions and related engineering standards are published by US federal agencies including the National Highway Traffic Safety Administration. Every figure is computed deterministically from the formula, shown in full below, with a worked example that reconciles exactly to the calculator so you can follow and verify each step yourself.
Torque equals power divided by angular velocity: T = P / omega, with omega = 2 pi N / 60. A 1,500 W motor at 1,450 rpm delivers 9.88 N m of torque. Lower speed means more torque for the same power.
Motor torque formula
T = P / omega
omega = 2 pi N / 60
T = torque (N m), P = power (W)
omega = angular velocity (rad/s), N = speed (rpm)
First convert the speed from revolutions per minute to angular velocity in radians per second by multiplying by two pi and dividing by sixty. Then divide the power by that angular velocity to get the torque. For constant power, a lower speed yields a higher torque.
Worked example
A motor outputs 1,500 W of mechanical power while running at 1,450 rpm.
- Convert speed to rad/s: omega = 2 x pi x 1,450 / 60 = 151.8436
- Divide power by angular velocity: 1,500 / 151.8436 = 9.8786
- Round to two decimal places: 9.88
- The shaft torque is 9.88 N m
So the motor delivers about 9.88 N m of torque. These are the calculator's default inputs, so the result above matches the widget exactly.
Motor Torque Calculator: frequently asked questions
How do you calculate motor torque from power and speed?
Convert speed N in rpm to angular velocity omega = 2 pi N / 60 in radians per second, then divide power by omega: T = P / omega. A 1,500 W motor at 1,450 rpm gives omega = 151.84 rad/s and torque = 1,500 / 151.84 = 9.88 N m.
Why does torque rise as speed falls?
Power is the product of torque and angular velocity, so for a fixed power the two are inversely related. A slow-turning shaft must apply more torque to deliver the same power, which is why gear reduction increases torque while reducing speed.
Why convert rpm to radians per second?
The torque-power relationship P = T omega requires angular velocity in radians per second, the SI unit. One revolution is 2 pi radians and one minute is 60 seconds, so omega = 2 pi N / 60 converts rpm to rad/s.
How do I convert torque to horsepower?
First find the power with P = T omega in watts, then divide by 745.7 to get mechanical horsepower. The torque alone does not define power without the speed.
What is the motor torque formula?
Torque equals power divided by angular velocity, T = P / omega, where omega = 2 pi N / 60.
Official sources
- Mechanical power and engineering standards reference: US National Highway Traffic Safety Administration (NHTSA). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.