What torque is
Torque is the turning effect of a force. Pushing on a door near its hinges barely moves it, while the same push at the handle swings it open easily. What matters is the force and its distance from the axis of rotation, called the lever arm. Torque is measured in newton-meters (N·m) or, in the US, pound-feet (lb·ft).
The formulas
- Torque = force × lever arm × sin(angle)
- Power = torque × angular speed = torque × rpm × 2π ÷ 60
- In US units: horsepower = lb·ft × rpm ÷ 5,252
The angle is between the force and the arm. At 90°, a perpendicular push, sin(90°) = 1 and all of the force produces torque. At 30°, only half of it does.
Worked example
You push with 50 lbf at the end of a wrench, 12 inches from the bolt, at a right angle.
- Torque = 50 lbf × 1 ft × sin(90°) = 50 lb·ft, or 67.8 N·m.
- If an engine delivered that torque at 3,000 rpm, its power would be 50 × 3,000 ÷ 5,252 = 28.6 hp (21.3 kW).
- Pushing at 45° instead, you would only get 35.4 lb·ft from the same effort.
Torque units
| Unit | In N·m |
|---|---|
| 1 N·m | 1 |
| 1 lb·ft | 1.356 |
| 1 lb·in | 0.113 |
| 1 kgf·m | 9.807 |
Watch the difference between lb·ft and lb·in: torque wrenches for bicycles and small engines are often graduated in lb·in, twelve times smaller than lb·ft.
Torque and horsepower
Engine specifications give both torque and power. Torque tells you how hard the engine twists; power tells you how fast it can do work, which is torque multiplied by rotation speed. Because of the constant 5,252 in the US formula, torque and horsepower curves always cross at 5,252 rpm when drawn on the same scale.
Practical uses
- Tightening bolts: wheel lug nuts on cars typically take 80 to 100 lb·ft. Using the right torque prevents both loose wheels and stretched studs.
- Choosing a lever: doubling the length of a wrench or a breaker bar doubles the torque for the same effort.
- Gears: a gearbox trades speed for torque. Combine this calculator with the gear ratio calculator to see the torque at the wheels.
Torque and moment
In physics textbooks the same quantity is often called the moment of a force. It is a vector, perpendicular to both the force and the lever arm, but for everyday problems its magnitude, computed here, is what you need.