Torque Calculator
Calculate torque from force, lever arm and angle, or solve for the force, wrench length or angle you need, with a live lever diagram. Convert torque units and torque to power at any rpm, all privately in your browser.
τ = r · F · sin θ
P = τ · ω · hp = lbf·ft × rpm / 5252
| Unit | Value |
|---|
How to use the Torque Calculator
- Choose a mode: Torque for force on a lever, Torque ↔ power for engines and motors, or Unit converter.
- Select what to solve for, e.g. Force to find how hard to push a wrench to reach a torque spec.
- Enter the known values with their units; use 90° when you push at right angles to the wrench.
- Read the answer in the highlighted field and on the diagram, and change its unit to convert it.
- Press Copy result to paste the answer and inputs, or check the step-by-step working.
How torque works
Torque is the turning effect of a force: τ = r · F · sin θ. The longer the lever arm r and the more perpendicular the push, the bigger the torque. That is why a breaker bar loosens a seized nut that a short spanner cannot, and why door handles sit far from the hinges. Rearranged, the formula gives the force F = τ / (r sin θ), the lever arm r = τ / (F sin θ) and the angle θ = arcsin(τ / rF).
| Angle θ | sin θ | Share of maximum torque |
|---|---|---|
| 90° | 1.000 | 100% |
| 60° | 0.866 | 86.6% |
| 45° | 0.707 | 70.7% |
| 30° | 0.500 | 50% |
| 0° or 180° | 0 | 0% (pushing along the arm) |
Torque unit conversions
| Unit | In N·m |
|---|---|
| 1 pound-force foot (lbf·ft) | 1.355818 |
| 1 pound-force inch (lbf·in) | 0.1129848 |
| 1 ounce-force inch (ozf·in) | 0.007061552 |
| 1 kilogram-force metre (kgf·m) | 9.80665 |
| 1 kilogram-force centimetre (kgf·cm) | 0.0980665 |
| 1 dyne centimetre (dyn·cm) | 1 × 10⁻⁷ |
Torque and power at a given rpm
An engine or motor's power is its torque multiplied by its angular speed: P = τ · ω, with ω = 2π × rpm / 60 in radians per second. In imperial units this becomes hp = lbf·ft × rpm / 5252. Worked example: 400 N·m at 3,000 rpm gives ω = 314.16 rad/s and P = 125.7 kW, which is 168.5 hp. Going the other way, a 1.5 kW electric motor at 1,450 rpm delivers 1500 / 151.84 = 9.88 N·m on its shaft.
Always follow the manufacturer's torque specification and use a calibrated torque wrench for critical fasteners such as wheel nuts and cylinder-head bolts. To see how gears multiply torque, try the gear ratio calculator, and for engine figures the horsepower calculator.
Frequently asked questions
What is the formula for torque?
Torque is τ = r × F × sin θ, where r is the distance from the pivot to where the force acts (the lever arm), F is the force and θ is the angle between the lever and the force. With r in metres and F in newtons the torque is in newton-metres (N·m).
Why does the angle matter?
Only the part of the force perpendicular to the lever turns it. At 90° sin θ = 1 and you get the full torque; at 30° you get half (sin 30° = 0.5); pushing along the handle (0° or 180°) produces no torque at all.
How much force do I need on a wrench to reach a torque spec?
Divide the torque by the lever length: F = τ / r (at 90°). For 25 N·m with a 20 cm wrench you need 25 / 0.2 = 125 N, about 12.7 kgf or 28.1 lbf. A longer wrench or breaker bar reduces the force in proportion.
How do I convert N·m to lbf·ft?
1 lbf·ft = 1.355818 N·m, so divide N·m by 1.355818 (or multiply by 0.737562). For example 100 N·m = 73.76 lbf·ft. 1 lbf·ft is 12 lbf·in, and 1 kgf·m = 9.80665 N·m.
How are torque and horsepower related?
Power is torque times angular speed: P (W) = τ (N·m) × 2π × rpm / 60. In imperial units hp = lbf·ft × rpm / 5252, which is why torque and horsepower curves on a dyno chart always cross at 5,252 rpm.
Is torque the same as a moment?
In statics, the moment of a force about a point and torque use the same formula and units. Torque is usually used for twisting about an axis (bolts, shafts, engines), moment for bending in beams. Note that N·m of torque is not the same as joules of energy, even though the units match.