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Torque Calculator

Calculate the torque produced by a force applied at a distance from a pivot, at any angle, in metric (N, m) or imperial (lbf, ft) units.

Torque
15 N·m
Max possible torque at this force and lever arm (at 90°)
15 N·m

How it works

Torque (moment of force) is τ = F × r × sin(θ), where F is the applied force, r is the lever-arm distance from the pivot to where the force acts, and θ is the angle between the force vector and the lever arm. Only the component of force perpendicular to the lever arm produces rotation, which is exactly what the sine term captures — a force applied straight along the lever arm (0° or 180°) produces zero torque, while a perpendicular force (90°) produces the maximum torque possible for that force and lever-arm length.

Force and length are converted to newtons and meters (the units this formula is conventionally published in) before the calculation runs, then the result is converted back to whichever unit system is active, so the Metric/Imperial toggle only changes display units, never the underlying physics.

FAQ

Why does the same force produce less torque at a smaller angle?

Because only the part of the force that acts perpendicular to the lever arm contributes to rotation — a force applied at a shallow angle is mostly pulling or pushing along the arm itself, which doesn't turn it. That's why loosening a bolt with a wrench works best when you pull perpendicular to the wrench handle, not along its length.

What's the difference between torque and work or energy?

Torque and work/energy share the same units dimensionally (force × distance), but they measure different things: torque is a rotational tendency at an instant, while work is force applied over an actual distance traveled. That's also why torque is conventionally written as newton-meters rather than joules, even though the units are equivalent, to avoid implying energy was transferred.

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