Work Calculator
Find the mechanical work done by a force acting over a distance at any angle.
N
m
°
- 1
Angle in radians
0° × π ÷ 180 = 0 - 2
cos θ
cos(0 rad) = 1 - 3
Work done
50 × 10 × 1 = 500W = F × d × cos θ — the component of force along the displacement times distance.
Formula
How this is calculated
This calculator finds the mechanical work done by a constant force using W = F × d × cos(θ). Force F is entered in newtons (N), displacement d in metres (m), and θ is the angle in degrees between the force vector and the direction of motion. Internally the angle is converted to radians before taking its cosine, and the result comes out in joules (J).
The key idea is that only the part of the force pointing along the motion does work. The cos(θ) factor projects the force onto the direction of travel: at θ = 0° the force is fully aligned and work is maximised (cos 0° = 1); at θ = 90° the force is perpendicular and no work is done (cos 90° = 0); beyond 90° cos(θ) turns negative, so the force opposes the motion and work is negative — energy is removed, as friction does. The joule result is also shown in kilojoules and kilocalories (1 kcal = 4184 J) for convenience.
This assumes a constant force over a straight-line displacement and ignores friction, air resistance, and any variation in the force along the path. For varying forces or curved paths the true work is an integral of force over distance rather than this single product.
Examples
| Input | Result |
|---|---|
| F = 50 N, d = 10 m, θ = 0° | W = 500 J |
About this calculator
In physics, work is done when a force moves an object through a distance. It is calculated as W = F × d × cos(θ), where F is the force in newtons, d is the displacement in metres and θ is the angle between the force and the direction of motion. The result is in joules (J).
The cosine term means only the component of force along the direction of motion does work. When the force is fully aligned with the movement (θ = 0°), cos(θ) = 1 and work is maximised. When the force is perpendicular to the motion (θ = 90°), no work is done at all — which is why carrying a load horizontally at constant height does zero mechanical work.
Frequently asked questions
Work equals force times distance times the cosine of the angle between them: W = F·d·cos(θ), measured in joules.
Only the part of the force that points along the direction of motion does work. The cos(θ) factor extracts that component, so a perpendicular force (θ = 90°) does no work.
Yes. If the angle exceeds 90°, cos(θ) is negative, meaning the force opposes the motion and removes energy — for example, friction doing negative work.
Also known as
TG we-Calculate Editorial Team. (2026). Work Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/work-calculator
TG we-Calculate Editorial Team. "Work Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/work-calculator.
TG we-Calculate Editorial Team, "Work Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/work-calculator
@misc{wecalculate_work_calculator, title = {Work Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/work-calculator}}, year = {2026}, note = {TG we-Calculate} }
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