Torque Calculator
Torque from force, lever length and angle — with the power at a given speed.
Results update as you type.
About this calculator
Torque is the rotational equivalent of force — the twisting effect a force has about a pivot. It is τ = F × r × sin(θ), where F is the applied force, r is the lever arm (distance from the pivot) and θ is the angle between the force and the arm. Only the component of force perpendicular to the lever produces rotation, so torque is greatest when the force is applied at a right angle (θ = 90°), reducing to the familiar τ = F × r. The SI unit is the newton-metre (N·m); this calculator also converts to pound-feet (1 N·m ≈ 0.7376 lb·ft).
As a worked example, pushing with 100 N at the end of a 0.5 m wrench, perpendicular to the handle, produces τ = 100 × 0.5 × sin(90°) = 50 N·m. Angle the same push at 30° to the handle and it drops to 100 × 0.5 × 0.5 = 25 N·m, because only half the force now acts crossways. This is why a longer wrench or a straight-on pull loosens a stubborn bolt more easily — you multiply either the lever arm or the effective force.
If you enter a rotational speed, the calculator also returns the mechanical power, P = τ × ω, where the angular speed ω = rpm × 2π / 60 in radians per second. The same torque delivers more power the faster it turns, which is the link between an engine’s torque and its horsepower. Torque calculations are essential for tightening fasteners to spec, sizing motors and gearboxes, designing levers and wrenches, and analysing any rotating machinery.
Frequently asked questions
What is the torque formula?
Torque equals force times lever length times the sine of the angle between them, τ = F × r × sin(θ). It is measured in newton-metres (N·m).
Why does the angle matter?
Only the component of force perpendicular to the lever produces rotation. At 90° all the force is effective; at 0° (straight along the arm) the torque is zero.
How do torque and power relate?
Mechanical power is torque times angular speed, P = τ × ω, where ω = rpm × 2π / 60. The same torque delivers more power the faster it spins.
What is the difference between torque and force?
Force is a straight-line push or pull in newtons; torque is its turning effect about a pivot, in newton-metres, and depends on both the force and how far from the pivot it acts. The same force gives more torque on a longer lever arm.
How do I convert newton-metres to pound-feet?
Multiply N·m by 0.7376. So 50 N·m is about 36.9 lb·ft. The calculator shows both units, which is handy since torque specs are quoted in N·m in most of the world and lb·ft in the US.
How do I get more torque on a bolt?
Increase the lever arm or the force, or apply the force at a right angle. A wrench twice as long, or a straight-on pull instead of an angled one, both multiply the torque for the same effort — which is why breaker bars work.
Does the angle really change the torque that much?
Yes. Torque scales with sin(θ), so a force along the lever (0°) produces no rotation at all, 30° gives half the maximum, and only a perpendicular push (90°) delivers the full F × r. Keep the force square to the arm for the most effect.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/torque/curl
curl "https://calculator.free/api/v1/torque/?solve=torque&force=100&length=0.5"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/torque/?" + new URLSearchParams({
"solve": "torque",
"force": "100",
"length": "0.5"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.