The Physics of the Universe
HomeCalculators › Torque

Torque Calculator

Calculate the turning effect of a force with τ = F · r · sinθ — enter force, lever-arm length and the angle, or solve for force or radius. Torque is measured in newton-metres.

 

Formula

$$ \tau = F\,r\sin\theta \qquad F = \frac{\tau}{r\sin\theta} \qquad r = \frac{\tau}{F\sin\theta} $$

Worked example

Pushing with 40 N at the end of a 0.5 m wrench, perpendicular to it (θ = 90°), gives \( \tau = (40)(0.5)\sin90° = 20\ \text{N·m} \). At 30° the torque drops to \( 40 \times 0.5 \times 0.5 = 10\ \text{N·m} \).

How it works

Torque is the rotational equivalent of force — the twisting effect that makes something rotate about a pivot. It is τ = F r sinθ, where F is the force, r the distance from the pivot (lever arm) and θ the angle between them.

Torque is greatest when the force is applied perpendicular to the lever arm (θ = 90°, sinθ = 1) and at the greatest distance from the pivot — which is why a longer wrench loosens a bolt more easily. The unit is the newton-metre (N·m).

Frequently asked questions

How do you calculate torque?

Torque is τ = F r sinθ — force times the lever-arm length times the sine of the angle between them. When the force is perpendicular (θ = 90°), it simplifies to τ = F r.

What is the simple equation for torque?

For a force applied at right angles to the lever arm, τ = F × r — force times distance from the pivot. The full form τ = F r sinθ handles other angles.

What are the units of torque?

The newton-metre (N·m). Although dimensionally the same as the joule, torque is kept as N·m to distinguish it from energy.

Why does a longer wrench make it easier to turn a bolt?

Because torque increases with the lever-arm length r. A longer wrench means a larger r, so the same force produces more torque and turns the bolt more easily.

Related calculators