Use this free horsepower calculator to find the rotational shaft power produced at a specified torque and engine or motor speed. Enter torque in newton-meters (N·m) and rotational speed in revolutions per minute (RPM). The calculator converts angular speed to radians per second, multiplies it by torque, and displays mechanical horsepower (hp), metric horsepower (PS), kilowatts (kW) and watts. The different horsepower units are labeled separately because they are not identical. The result is a point on a torque-versus-RPM curve, not a prediction of maximum engine power.
## How to calculate horsepower from torque and RPM. Mechanical shaft power is torque multiplied by angular velocity. For rotational speed N measured in RPM, the angular velocity is 2πN/60 radians per second. Therefore power in watts is P = torque (N·m) × RPM × 2π/60. To display kilowatts, divide watts by 1,000. At 300 N·m and 5,000 RPM, P = 300 × 5,000 × 2π/60 ≈ 157,079.63 W, or 157.08 kW. Multiplying torque by RPM without the angular-velocity factor gives the wrong power. The component assumes torque and speed are measured at the same shaft.
## Mechanical horsepower versus metric horsepower (PS). The word horsepower does not name a single universal quantity. Mechanical, or imperial, horsepower is defined as 550 foot-pounds-force per second, approximately 745.6998716 watts per hp. Metric horsepower (PS, also called pk or CV in some countries) is exactly 735.49875 watts per PS. The same 157.08 kW output is approximately 210.65 mechanical hp or 213.57 metric PS. The numerical PS figure is higher because each metric horsepower represents slightly less power. This calculator displays both so a European PS rating cannot silently be compared to an American mechanical hp rating as though they were the same unit.
## Worked automotive example: torque at 5,000 RPM. Imagine an engine delivering 300 N·m of crankshaft torque at exactly 5,000 RPM. The angular velocity is 5,000 × 2π/60 ≈ 523.599 radians per second. Multiply 300 N·m by 523.599 radians per second to obtain 157,079.63 watts. Dividing by the mechanical horsepower conversion gives 210.65 hp; dividing by the metric horsepower conversion gives 213.57 PS. These values are rounded for display. They do not tell you the engine's peak output at another RPM or what power reaches the wheels after drivetrain losses.
Shaft power from torque and rotational speed
Angular speed (rad/s) = RPM × 2π ÷ 60
Mechanical shaft power (W) = Torque (N·m) × Angular speed (rad/s)
Power (kW) = Power (W) ÷ 1,000
Mechanical horsepower (hp) = Power (W) ÷ 745.6998715822702
Metric horsepower (PS) = Power (W) ÷ 735.49875
These formulas calculate mechanical power from torque and speed at one operating point. The two horsepower units have different definitions. Inputs must be nonnegative and finite, and this tool does not model losses, engine torque curves or efficiency.
A motor produces 300 newton-meters of torque at a measured speed of 5,000 revolutions per minute.
Result: 157.08 kW, or 210.65 mechanical hp and 213.57 metric PS.
Multiply torque in newton-meters by RPM and 2π/60 to get watts. Divide by approximately 745.6998716 for mechanical hp, or by 735.49875 for metric PS.
At this single operating point, shaft power is about 157.08 kW, 210.65 mechanical hp or 213.57 metric PS.
Mechanical horsepower is about 745.7 watts; metric horsepower (PS) is exactly 735.49875 watts. The same motor therefore has a slightly higher numerical PS rating.
Mechanical kilowatts = torque (N·m) × RPM × 2π ÷ 60,000. A 200 N·m shaft at 3,000 RPM produces approximately 62.83 kW.
Only if the torque remains unchanged. Real engines often develop different torque at different rotational speeds.
No. It calculates theoretical power at the shaft for the entered torque and speed; it does not subtract transmission, axle or tire losses.
Not from one torque/RPM point. Peak power requires comparing multiple points along an engine's measured torque curve.
Mechanical shaft power is zero because the product of torque and angular velocity is zero.