By Zencalcy Editorial TeamLast reviewed About us
In physics, work is done only when a force moves an object along the direction of the force. Pushing a wall does no work no matter how hard you push; lifting a box does work equal to the force times the height. The cosine term accounts for forces applied at an angle to the motion.
Work done by a force at an angle to the motion.
W = F d cos θ
W is work in joules, F is force, d is displacement and θ is the angle between them. A force perpendicular to the motion (θ = 90°) does zero work, like the normal force on a sliding box.
| Symbol | Meaning |
|---|---|
| W | Work done, in joules. |
| F | Applied force, in newtons. |
| d | Displacement along the path, in metres. |
| θ | Angle between force and displacement. |
With the force aligned to the motion, W = 100 × 5 × cos 0° = 500 J. Pulling at 60° instead would do only 250 J of work over the same distance.
Continue with the Work Done by Friction Calculator, Efficiency Calculator, or the Elastic Potential Energy Calculator — or browse more work, energy and power tools and all physics calculators.
Yes. When the force opposes the motion, cos θ is negative and the force removes energy from the object — friction does negative work, which becomes heat.
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