By Zencalcy Editorial TeamLast reviewed About us
Torque measures how effectively a force twists an object about a pivot. It depends on the force, the distance from the pivot and the angle between them: only the component of force perpendicular to the lever arm contributes. A force pointing straight at the pivot produces no torque at all.
Turning effect of a force about a pivot.
τ = F r sin θ
τ is torque, F the applied force, r the distance from pivot to the point of application, and θ the angle between the force and the lever arm. At θ = 0° or 180° the torque is zero.
| Symbol | Meaning |
|---|---|
| τ | Torque about the pivot, in newton-metres. |
| F | Applied force, in newtons. |
| r | Lever-arm distance from the pivot, in metres. |
| θ | Angle between the force and the lever arm. |
A 50 N push perpendicular to a 0.3 m wrench gives τ = 50 × 0.3 × sin 90° = 15 N·m, about 11.1 lb·ft. Angling the push to 45° reduces it to 10.6 N·m.
Continue with the Beam Reaction Calculator, Center of Mass Calculator, or the Hooke's Law Calculator — or browse more statics tools and all physics calculators.
Only the perpendicular component of the force creates rotation. Pushing along the wrench toward the bolt does nothing; pushing at right angles does the most.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
Reference material used to build and check this calculator:
Last reviewed: September 2026. See how we build and check every tool on the about page.
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Content updated: September 2026