Work
Calculate work, force, or displacement with W = Fd and step-by-step joule working.
Key formula
W = Fd
How do you calculate work?
When force and displacement point the same way, W = F × d. Multiply force in newtons by distance in metres; the result is joules. Rearrange to F = W/d or d = W/F. If the force acts at an angle θ to the displacement, use W = Fd cos θ.
About this tool
Work is energy transferred when a force moves an object along the direction of that force. This page keeps W = Fd visible so you can solve for work, force, or displacement without mixing joules, newtons, and metres.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: 50 N over 3.0 m
F = 50 N, d = 3.0 m, same direction. W = (50)(3.0) = 150 J.
Example 2: find force from 120 J and 2.5 m
W = 120 J, d = 2.5 m. F = W/d = 120 / 2.5 = 48 N in the direction of motion.
Example 3: force at 60° to displacement
F = 20 N, d = 4.0 m, θ = 60° between F and d. W = Fd cos θ = (20)(4.0) cos 60° = 80 × 0.5 = 40 J.
Frequently asked questions
What is the work formula?
W = Fd when force and displacement are parallel. W = Fd cos θ when they meet at angle θ. Work is in joules when F is in newtons and d is in metres.
Can work be negative?
Yes. If the force component opposes the displacement (θ > 90°), cos θ is negative and work is negative. That means energy is removed from the object, as when friction slows a box.
What is the difference between work and power?
Work W is energy transferred (joules). Power P is the rate of doing work: P = W/t (watts). Use the power calculator when time is part of the question.
How does work relate to kinetic energy?
The work–energy theorem says net work on an object equals its change in kinetic energy: W_net = ΔKE. Lifting also ties to potential energy: W against gravity ≈ mgh.
Why is work zero for carrying a bag horizontally?
The upward support force is perpendicular to horizontal displacement, so cos 90° = 0. No work is done by that force on the bag, even though you feel tired (that is muscle chemistry, not W = Fd on the bag).