How it works
Power is the rate of doing work, and for a rotating shaft it equals torque times angular speed. One horsepower is defined as 33,000 foot-pounds per minute, and one revolution is 2π radians, so with torque in pound-feet and speed in RPM, hp = torque × RPM × 2π ÷ 33,000 = torque × RPM ÷ 5,252.
The relation holds at any single operating point. It says nothing about a whole engine’s power curve, and a motor’s rated horsepower applies only near its rated speed.
Worked example
A motor producing 100 lb·ft of torque at 3,000 RPM:
- Power = torque × RPM ÷ 5,252 = 100 lb·ft × 3,000 ÷ 5,252 = 57.12 hp
- In kilowatts = 57.12 hp × 0.7457 = 42.59 kW
| Input | Value |
|---|---|
| Find | Horsepower from torque |
| Speed | 3000 RPM |
| Torque (find horsepower) | 100 lb·ft |
| Power (find torque) | 50 hp |
| Result | Value |
|---|---|
| Power | 57.12 hp |
| Torque | 100 lb·ft |
Assumptions and limits
- Mechanical horsepower (550 ft·lb/s), not metric horsepower.
- Shaft power at the speed given; losses in belts, gears, or a load are not included.
- For electric motors, electrical input power also depends on efficiency and power factor.
Common questions
Why do torque and horsepower cross at 5,252 RPM?
At that speed the formula reduces to hp = torque, because the constant equals the RPM where the two numbers are equal.
How many kilowatts is a horsepower?
One mechanical horsepower is about 0.7457 kW.
Is this the same for metric?
Switch to Metric to see kilowatts and newton-meters. The relation is the same, with power = torque × angular speed.
How do I get torque at the shaft of a geared drive?
Torque changes inversely with speed through a gear, belt, or chain, ignoring losses; see the pulley and sprocket RPM calculator.
Sources
- Definition of horsepower: 550 ft·lb/s = 33,000 ft·lb/min; power = torque × angular speed.
- Equal to torque at 5,252 RPM; 1 hp = 745.7 W.
Updated 2026-09-30