Torque Calculator
Find torque, force, or lever arm distance.
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Formulas
τ = F × d × sin(θ)Maximum torque when force is perpendicular (θ = 90°)
Torque
Rotational equivalent of force. A 50N force on a 30cm wrench produces 15 N·m. Car engines: 100-500 N·m. Bicycle pedal: ~15-50 N·m.
How Torque Is Calculated
Torque is the rotational equivalent of force — it measures how much a force tends to rotate an object about a pivot. It depends on the force, the distance from the pivot, and the angle at which the force is applied:
τ = F × d × sin(θ)τ is torque in newton-metres, F is force in newtons, d is the distance from the pivot (lever arm), and θ is the angle between the force and the lever arm.
Torque is maximised when the force is applied perpendicular to the lever arm (θ = 90°, sin = 1). A force applied straight along the arm produces no torque at all.
Worked Examples
A 50 N force on a 0.3 m wrench, applied at 90°:
τ = 50 × 0.3 × sin(90°) = 15 N·m
The same force at 60°:
τ = 50 × 0.3 × sin(60°) = 13 N·m
The off-angle force delivers less rotational effect, which is why you push a wrench at a right angle for maximum leverage.
Ways to Increase Torque
| Method | Effect |
|---|---|
| Longer lever arm | Proportional increase |
| Greater force | Proportional increase |
| Apply at 90° | Maximises the sin term |
Doubling the lever arm doubles the torque for the same force — the principle behind breaker bars and long-handled tools.
Frequently Asked Questions
What is the difference between torque and force?
Force is a straight-line push or pull; torque is the rotational effect of a force about a pivot. Torque is force multiplied by the perpendicular distance to the pivot.
Why does angle matter?
Only the component of force perpendicular to the lever arm produces rotation. The sin(θ) term extracts that perpendicular component.
What units are used for torque?
Newton-metres (N·m) in SI, or pound-feet (lb·ft) in imperial. They measure rotational force, not energy, even though joules share the same base units.