Torque is the turning or twisting effect of a force around a pivot. It equals the force times the lever arm length times the sine of the angle between them. A larger force, a longer arm, or an angle closer to 90 degrees all increase the torque.

Why does the angle matter for torque?

Only the part of the force acting at right angles to the lever arm causes rotation. The sine of the angle captures this: at 90 degrees it is one, giving maximum torque, while a force pulling straight along the arm, at 0 degrees, produces no turning effect at all.

How do I convert newton metres to pound-feet?

Multiply newton metres by about 0.7376 to get pound-feet. So 15 newton metres is about 11.06 pound-feet. Newton metres are the SI unit, while pound-feet are still widely used for engine and fastener specifications, especially in the automotive world.

Torque Calculator

This calculator finds torque, the turning effect of a force, from the force applied, the length of the lever arm and the angle at which the force acts. Torque is what makes things rotate, and it is central to engineering and mechanics: it is why a longer spanner loosens a stubborn bolt more easily, how engines are rated, and what determines whether a structure twists or holds. Formally, torque is the force multiplied by the lever arm, the distance from the pivot to where the force is applied, multiplied by the sine of the angle between them. The angle matters because only the component of the force acting at right angles to the lever arm produces turning; a force pulling straight along the arm does nothing to rotate it. This tool captures all three factors. You enter the force in newtons, the lever arm length in metres, and the angle in degrees, with ninety degrees, a force applied straight across the arm, giving the maximum turning effect. The calculator returns the torque in newton metres, the SI unit, and also converts it to pound-feet, which is still common in the automotive world. It shows the perpendicular component of the force as well, so you can see how much of your effort is actually turning the object. The results update as you type, letting you explore how lengthening the lever arm or changing the angle changes the torque. Use it for mechanics and physics problems, for tightening to a specification, or to understand engine and tool ratings. The calculations use standard formulas and are rounded for display.

Force (N)

Lever arm (m)

Angle (degrees)

torque (newton metres)

In pound-feet11.06 lb-ft

Perpendicular force50 N

Max torque (90°)15 N·m

Torque = force x lever arm x sine of the angle. Maximum turning effect is at 90 degrees. Results rounded for display.

How it works

Torque is the applied force multiplied by the length of the lever arm and by the sine of the angle between the force and the arm. At ninety degrees the sine is one, giving the full turning effect; at zero degrees the sine is zero, so a force along the arm produces no torque. The perpendicular force is the force times the sine of the angle.

Worked example

Pushing with 50 newtons on a spanner 0.3 metres long, at a right angle, gives a torque of 50 times 0.3 times the sine of 90 degrees, which is 50 times 0.3 times 1, equals 15 newton metres. That converts to about 11.06 pound-feet. Doubling the spanner length to 0.6 metres would double the torque to 30 newton metres.

Related calculators

Force Calculator: linear force.
Horsepower Calculator: power from torque.
Kinetic Energy: energy of motion.
Velocity Calculator: velocity and speed.

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