Torque is the turning effect of a force. Push on a wrench, pedal a bicycle or start an engine and you are applying torque — a force multiplied by its distance from the axis of rotation. This calculator handles the everyday versions of the problem: the torque from a given force on a lever (at any angle), the force or lever length needed to reach a torque specification, and the conversion between torque, power and rotational speed used for engines and motors.
How to use the torque calculator
- Choose what you want to find: torque from force and lever arm, the force or lever length needed for a torque, or torque and power from rotational speed.
- Enter the force (lbf, N, kN, kgf or kip) and the lever arm — the distance from the center of the bolt or shaft to where the force is applied.
- Enter the angle between the force and the lever. A square push or pull is 90°.
- For the power options, enter the power (hp, kW, W or metric hp) or the torque, and the speed in rpm.
- Pick the unit to show torque in; the other common units are listed below the result.
Torque formulas
The product r sin θ is the effective lever arm, the perpendicular distance from the pivot to the line of the force. The constant 5,252 is 33,000 ft·lbf/min per horsepower divided by 2π.
Worked examples
50 lbf on an 18 in wrench at 90° (the default)
τ = 50 lbf × 18 in × sin 90° = 900 lb·in = 75 lb·ft. In SI units, 222.41 N × 0.4572 m = 101.69 N·m.
Push at 60° instead and the effective lever arm shrinks to 18 × 0.866 = 15.6 in, giving 64.95 lb·ft.
Meeting a torque spec. A lug nut specification of 80 lb·ft with a 12 in wrench needs 80 lbf of force; with an 18 in breaker bar it needs only 53.3 lbf. Doubling the lever length halves the effort.
Engine torque from power. A 300 hp engine at 4,500 rpm: ω = 2π × 4,500 ÷ 60 = 471.24 rad/s, and τ = 223,710 W ÷ 471.24 = 474.7 N·m, or 300 × 5,252 ÷ 4,500 = 350.1 lb·ft. Running the same calculation backwards, 400 lb·ft at 3,000 rpm delivers 228.5 hp.
Typical torque values
| Application | Typical torque |
|---|---|
| Bicycle stem and handlebar bolts | 4–6 N·m (35–53 lb·in) |
| Cyclist pushing 400 N on a 170 mm crank | 68 N·m (50 lb·ft) |
| Passenger car lug nuts | 100–140 N·m (75–100 lb·ft) |
| Cordless drill, high-torque setting | 40–100 N·m (30–75 lb·ft) |
| Midsize gasoline engine, peak | 250–400 N·m (185–295 lb·ft) |
Always use the manufacturer’s specification for fasteners; these ranges only show the scale.
Getting accurate fastener torque
A torque wrench reads correctly only when force is applied at its handle mark; an extension that lengthens the lever changes the effective torque, while one that sits on the axis (a socket extension) does not. Specifications state whether threads should be clean and dry or lubricated: oil or anti-seize reduces friction, so the same torque reading clamps the joint much harder and can stretch the bolt.
To pass torque through gears and see how it multiplies, use the gear ratio calculator. The torque converter switches between N·m, lb·ft, lb·in and kgf·m, and the work calculator covers force times distance along a path.
These are estimates. Follow the equipment manufacturer's torque specifications and use a calibrated torque wrench for safety-critical fasteners such as wheels, brakes and structural connections.
Frequently asked questions
What is the formula for torque?
τ = F × r × sin θ, where F is the force, r the distance from the pivot to where the force acts, and θ the angle between the force and the lever. Pushing squarely (90°) with 50 lbf on an 18 in wrench gives 50 × 1.5 ft = 75 lb·ft, or about 101.7 N·m.
How do I convert horsepower and rpm to torque?
Torque (lb·ft) = hp × 5,252 ÷ rpm. In SI units, τ (N·m) = P (W) ÷ ω (rad/s), with ω = 2π × rpm ÷ 60. A 300 hp engine at 4,500 rpm produces about 350 lb·ft (475 N·m) at that speed.
Why do torque and horsepower curves cross at 5,252 rpm?
Because hp = torque (lb·ft) × rpm ÷ 5,252. At exactly 5,252 rpm the two numbers are equal, so on any dyno chart that uses lb·ft and hp the curves cross there. In kW and N·m the crossing point is different.
Does pushing at an angle reduce torque?
Yes. Only the part of the force perpendicular to the lever produces torque. Pushing at 60° instead of 90° gives sin 60° = 0.866, or 13.4% less torque — 64.95 lb·ft instead of 75 lb·ft in the wrench example.
What is the difference between torque and work?
Both multiply a force by a distance and can be expressed in N·m, but torque uses the perpendicular distance to a pivot and describes a turning effect, while work uses the distance moved along the force and describes energy. That is why torque is usually written as N·m or lb·ft and energy as joules or ft·lbf.