Torque and Power Calculator
Convert between torque, rotational speed, and mechanical power for motors, engines, and drivetrain components. Use it when sizing a motor or verifying shaft power output at a given RPM and efficiency.
About this calculator
In rotating machinery, power is the rate at which torque does work over an angular displacement. The fundamental relationship is P = (T × ω × η) / 1000, where T is torque in Nm, ω is angular velocity in rad/s (converted from RPM as ω = 2π × N / 60), η is mechanical efficiency as a decimal, and P is power in kW. Rearranging gives torque from power: T = (P × 1000) / (ω × η). The 2π / 60 factor converts RPM into radians per second, since one full revolution equals 2π radians. Efficiency accounts for frictional and mechanical losses between the input shaft and the useful output, and is expressed as a percentage (e.g. 90% → 0.90). Understanding this relationship is essential for motor selection, gearbox design, and energy audits.
How to use
Suppose an electric motor produces 150 Nm of torque at 1450 RPM with 92% mechanical efficiency, and you want to find the output power. Step 1: Convert speed — ω = 2π × 1450 / 60 = 151.84 rad/s. Step 2: Apply the formula — P = (150 × 151.84 × 0.92) / 1000 = (20,952) / 1000 ≈ 20.95 kW. So the motor delivers approximately 20.95 kW of useful mechanical power. If you instead know the power and need torque, enter P = 20.95 kW and the calculator rearranges to T = (20,950) / (151.84 × 0.92) ≈ 150 Nm.
Frequently asked questions
What is the relationship between torque, RPM, and horsepower in a motor?
Torque and RPM together determine mechanical power output. Power in kW equals torque (Nm) multiplied by angular velocity (2π × RPM / 60), divided by 1000. To convert kW to horsepower, multiply by 1.341. For example, a motor producing 100 Nm at 1000 RPM outputs about 10.47 kW or roughly 14 HP before accounting for efficiency losses.
How does mechanical efficiency affect the power output of a rotating shaft?
Mechanical efficiency represents the fraction of input power that becomes useful output, with losses arising from friction in bearings, gears, and seals. An efficiency of 85% means 15% of the input power is dissipated as heat. When calculating output power, the formula multiplies the ideal power by η (e.g. 0.85), so a higher efficiency directly increases usable output. Selecting well-lubricated, precision-grade components keeps efficiency close to 95–98% in well-designed systems.
When should I use the torque-to-power formula versus looking up a motor datasheet?
Use the formula when you need to verify a datasheet figure, estimate shaft power under non-rated conditions, or design a custom drive system where exact efficiency must be factored in. Datasheets typically list rated power at a specific RPM and load point; real operating conditions often differ. The formula lets you interpolate or extrapolate performance and check whether a motor is over- or under-powered for your application.