Torque is the turning effect of a force, and the formula for torque is one of the most useful relationships in mechanics. This guide shows how to calculate torque from a force and a lever arm, and how to find it from power and speed when a shaft is turning.

The formula for torque

The formula for torque multiplies the force by the perpendicular distance from the pivot to the line of the force:

T = F × r

F is the force, r is the lever arm, and T is the torque, measured in newton metres. The further the force acts from the centre, the more torque it makes, which is why a long wrench loosens a bolt a short one cannot. The torque calculator applies this directly and converts between newton metres and pound feet.

Why the perpendicular distance matters

Only the part of the force at right angles to the lever arm produces torque. Push straight along the arm toward the pivot and you make no torque at all. When the force acts at an angle, the full formula adds the angle: T = F × r × sinθ.

How to calculate torque: example

A force of 200 N on a wrench 0.3 m long gives T = 200 × 0.3 = 60 N·m. That is the twist applied to the bolt. To find the tightening torque a fastener needs, the bolt torque calculator uses the bolt size and clamp load.

Finding torque from power

Rotating machinery is rated by power, but what turns a load is torque. The power torque relationship links them through rotational speed:

T (N·m) = 9550 × P (kW) ÷ N (rpm)

So a 10 kW motor at 1500 rpm produces about 63.7 N·m. This is why gearboxes exist: gearing down trades speed for a large increase in torque. The horsepower calculator finds the power you need first.

Gearing then multiplies the torque, and the gear ratio calculator shows by how much.

The dimensional formula for torque

The torque dimensional formula is [M L² T⁻²], the same dimensions as energy. Torque is quoted in newton metres rather than joules to keep the twisting effect distinct from work done.

Common mistakes

• Using the wrong distance. The formula for torque needs the perpendicular lever arm, not the straight-line distance to the force.
• Confusing torque and energy. They share dimensions, but torque is a twist in N·m, not joules of work.
• Ignoring speed. To find torque from power you must include rpm; power alone is not enough.

Quick reference

Torque from force: T = F × r. Torque at an angle: T = F × r × sinθ. Torque from power: T = 9550 × kW ÷ rpm. Put your own numbers into an online calculator on CalculateGuide.