🔧 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.
Worked example: dragging a crate
Pulling a crate 8 m with a 50 N rope held at 30° to the ground does W = F·d·cos θ = 50 × 8 × cos 30° ≈ 346 J, less than the 400 J from pulling horizontally, because only the horizontal component moves the crate.
Does holding a heavy object do work?
No, if the object does not move (d = 0), no work is done in the physics sense, however tiring it feels. Work requires a force acting through a displacement.
What is the difference between work and power?
Work is the total energy transferred by a force (in joules); power is how fast that work is done (in watts, or joules per second). Doing the same work in less time requires more power.
Does gravity do work on an object?
Yes, when the object moves vertically: gravity does positive work as it falls and negative work as it rises, equal in size to mgh. Moving horizontally, gravity is perpendicular to the motion and does no work.