How to Calculate Torque

The tendency of a force to turn something about a pivot is its moment, or torque.

$F$ is the force, $r$ the distance from the pivot to where it is applied, and $\theta$ the angle between the arm and the force. The same force turns better the further out it acts and the closer it is to a right angle. This is why a door handle sits as far from the hinges as it can.

Balancing a lever

A lever balances when the moments on either side of the pivot are equal. If the other side reaches further out, a smaller force will hold it. That is how a lever lifts something heavy.

Example

A 50 N force is applied at right angles, 0.4 m from the pivot. The torque is $50 \times 0.4 \times \sin 90° = 20$ N·m. To balance it 1.2 m out on the other side takes only $20 \div 1.2 = 16.7$ N: three times the distance, a third of the force.

The angle matters

That same 50 N applied at 30 degrees to the arm picks up a factor of $\sin 30° = 0.5$ and produces only 10 N·m. Applied straight along the arm, at 0 degrees, $\sin 0° = 0$ and it does not turn the object at all. The direction of a push counts as much as its size.

Notes

Force and torque are different quantities. Force is measured in newtons, torque in newton metres, which carries the distance in it.