Work Calculator — work done by a force (W = Fd cos θ)

How it works

Work measures the energy transferred when a force moves an object. For a constant force, it is the component of that force along the displacement, times the distance moved (OpenStax University Physics):

W = F × d × cos θ

Here θ is the angle between the force and the direction of motion. Force is in newtons and distance in metres, so work comes out in joules (J) — one joule is one newton-metre.

The cosine factor is the key idea: only the part of the force pointing along the motion does work. When you push directly in the direction of travel (θ = 0°, cos θ = 1) you get the full F × d. When the force is perpendicular to the motion (θ = 90°, cos θ = 0) it does no work — which is why carrying a heavy box across level ground, or the tension in a string swinging a ball in a circle, does zero work on the object. A force that opposes the motion (θ = 180°) does negative work, removing energy — as friction does.

Worked example

A 20 N force pushing an object 5 m in the same direction (θ = 0°):

W = 20 × 5 × cos 0° = 20 × 5 × 1 = 100 J

Tilt the force to 60° above the motion and only half counts: 20 × 5 × cos 60° = 50 J.

Frequently asked questions

What is work in physics?

Work is the energy transferred to or from an object by a force acting over a distance. It equals the force component along the motion times the distance moved, measured in joules.

What is the formula for work?

W = F × d × cos θ, where F is the force, d is the distance, and θ is the angle between the force and the direction of motion. With newtons and metres, work is in joules.

Why does the angle matter?

Only the part of the force along the direction of motion does work. The cosine of the angle picks out that component: cos 0° = 1 (full effect), cos 90° = 0 (no work), cos 180° = −1 (negative work).

Can work be negative?

Yes. When a force opposes the motion — like friction or a braking force — the angle is more than 90°, the cosine is negative, and the work is negative, meaning energy is taken away from the object.

How is work related to energy?

Work is a transfer of energy. The work-energy theorem says the net work done on an object equals its change in kinetic energy, so doing 100 J of net work on an object increases its kinetic energy by 100 J.

What are the units of work?

Joules (J). One joule is the work done by a force of one newton acting through one metre, so a joule is a newton-metre. Larger amounts are often given in kilojoules (1 kJ = 1,000 J).