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Work Done Calculator

Calculate the work done by a force with W = F · d · cosθ — enter force, distance and the angle between them, or solve for force or distance. Work is measured in joules.

 

Formula

$$ W = F\,d\cos\theta \qquad F = \frac{W}{d\cos\theta} \qquad d = \frac{W}{F\cos\theta} $$

Worked example

Pushing with 50 N over 10 m in the direction of motion (θ = 0°) does \( W = (50)(10)\cos0° = 500\ \text{J} \). If the force were at 60° to the motion, only \( \cos60°=0.5 \) counts, giving 250 J.

How it works

Work is energy transferred when a force moves an object. It equals the force times the distance moved times the cosine of the angle between them: W = F d cosθ. Only the component of force along the motion does work.

When force and motion are aligned (θ = 0), W = F d. A force perpendicular to motion (θ = 90°) does no work — which is why gravity does no work on a satellite in a circular orbit. Work is measured in joules (N·m).

Frequently asked questions

What is the formula for work done?

Work done is W = F d cosθ — force times distance times the cosine of the angle between the force and the direction of motion. With aligned force it simplifies to W = F d.

How do you calculate total work done?

Add the work done by each force, or use the net force along the displacement. By the work–energy theorem, the total work equals the change in kinetic energy.

Why does a force at 90° do no work?

Because cos90° = 0. A force perpendicular to the motion has no component along the displacement, so it transfers no energy — like the tension holding an object in circular motion.

What are the units of work?

The joule (J), equal to one newton-metre (N·m) — the same unit as energy.

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