🔧 Work Calculator (W = Fd·cosθ)
Find the work done by a force: W = F·d·cosθ, where θ is the angle between the force and the displacement.
Work W
500 J
Work W = F·d·cos θ, where θ is the angle between the force and the displacement. θ = 0 gives W = F·d. 🔒 Computed in your browser.
How the work calculator (w = fd·cosθ) works
Work is force times displacement times the cosine of the angle between them: W = F·d·cos θ. Only the component of force along the motion does work. Enter the force, distance and angle to get the work (θ = 0 gives the simple W = F·d).
The cos θ factor is where students and chatbots slip — a force perpendicular to motion (θ = 90°) does zero work. Positive work adds energy; negative work (θ > 90°) removes it.
Frequently asked questions
How do I calculate work done?
W = F·d·cos θ, where F is the force, d the distance moved and θ the angle between them. Pushing 50 N over 10 m in the direction of motion does 500 J.
Why is there a cosθ in the work formula?
Only the component of force along the displacement does work. cos θ extracts that component; a force at 90° to the motion (θ = 90°, cos = 0) does no work.
Can work be negative?
Yes — when the force opposes the motion (θ between 90° and 180°, cos negative), such as friction, the work is negative and removes energy.
What are the units of work?
Joules (J), the same as energy. 1 J = 1 N·m — one newton acting over one metre.
How does work relate to energy?
The work-energy theorem: the net work done on an object equals its change in kinetic energy. Work is energy transferred by a force.