Solve torque, RPM, or power
Choose the value to solve. The chosen input stays read-only and is recalculated from the other two values.
Formula at a glance
Power in watts: P = τ × ω. Angular speed: ω = rpm × 2π / 60. Power in kilowatts: kW = N·m × rpm / 9549.2966. Horsepower: hp = lbf·ft × rpm / 5252.1131.
Worked example
Example: 100 N·m at 3000 rpm. ω = 3000 × 2π / 60 = 314.159 rad/s. P = 100 × 314.159 = 31,416 W = 31.416 kW = 42.13 hp.
Unit notes
Available torque input units are N·m, lbf·ft, and lbf·in. Power input units are W, kW, hp, and PS. This calculator reports ideal mechanical shaft power from torque and rotational speed. hp means mechanical horsepower. PS means metric horsepower. 1 hp (mechanical) = 745.6998715822702 W, 1 PS (metric) = 735.49875 W, and 1 kW = 1000 W. kgf·m is not currently available as an input unit. For reference, 1 kgf·m = 9.80665 N·m.
Difference from work, energy & power
Use this calculator when you know rotational speed and torque, such as a motor shaft or rotating machine. For average power from work, force, distance, and time, use the Work Energy Power Calculator.
Related physics tools
Gear Ratio Calculator handles tooth counts, speed ratio, and ideal torque multiplier. Work Energy Power Calculator covers linear work, energy, and average power.
FAQ
How do I calculate power from torque and RPM?
Use P = τ × ω, where angular speed ω = rpm × 2π / 60. In kilowatts, kW = N·m × rpm / 9549.2966.
What is the formula for horsepower from torque and RPM?
For mechanical horsepower, hp = lbf·ft × rpm / 5252.1131. With SI torque, hp = N·m × rpm / 7120.9092.
What is the difference between hp, PS, and kW?
hp is mechanical horsepower, PS is metric horsepower, and kW is kilowatts. 1 hp ≈ 745.7 W, 1 PS ≈ 735.5 W, and 1 kW = 1000 W.
Can I calculate torque from kW and RPM?
Yes. From kW and rpm, torque in N·m = kW × 9549.2966 ÷ rpm. This formula is not defined at 0 rpm.
Can this result be used for motor or shaft design?
No. This is the ideal rotational equation only. It does not check motor ratings, losses, heat, shaft strength, or safety margins.