Work done formula: W = Fs
Work done = force × distance moved along the line of the force. AQA and OCR write W = F s, and Edexcel writes E = F d. W (or E) is the work done in joules (J), F is the force in newtons (N) and s (or d) is the distance in metres (m). All three boards list it for recall, and their exam sheets print it.
Equation
W = F s
| Symbol | Quantity | Unit |
|---|---|---|
W | work done | J |
F | force | N |
s | distance | m |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall | W = F s |
| AQA Combined Science (8464) | Recall | W = F s |
| Edexcel Physics (1PH0) | Recall | E = F d |
| Edexcel Combined Science (1SC0) | Recall | E = F d |
| OCR Gateway Physics A (J249) | Recall | W = F s |
| OCR Twenty First Century Physics B (J259) | Recall | W = F s |
Calculator: W = F s
What work means in physics
In everyday speech, work is anything that takes effort. In physics it has a narrow meaning. Work is done when a force moves something through a distance. The work done is the energy transferred by that force.
Holding a heavy bag still for a minute feels tiring, but the bag does not move, so the work done on the bag is zero. Carry it up the stairs and you do work on it, because you push upwards and it moves upwards.
Only the distance along the line of the force counts. If you push a sledge along flat snow, the distance it slides forwards is the one that matters. Its weight acts downwards and it does not move downwards, so gravity does no work on it.
Printed forms by board
- AQA (8463 and 8464): W = F s, work done = force × distance along the line of action of the force.
- Edexcel (1PH0 and 1SC0): E = F d, work done = force × distance moved in the direction of the force.
- OCR Gateway (J249) and OCR Twenty First Century (J259): W = F s.
Edexcel uses E because work done is an amount of energy. It is the same relationship with different letters. Every specification here files it under recall. Exam papers from 2025 on include every equation, recall or given, on the board's sheet. The Edexcel page sets out that board's letters in full.
Rearranging, and where it leads
- F = W ÷ s
- s = W ÷ F
Braking questions use the second form. The brakes must do enough work to remove all of the car's kinetic energy. Divide that energy by the braking force and you get the stopping distance.
Lifting is a special case. The force you need is the weight, and the distance is the height, so the work done equals the gravitational potential energy gained. How quickly the work gets done is the job of the power and work equation. The force equation helps when you must find F first.
Worked examples
W
- Change the distance to metres: 250 cm = 2.5 m
- W = F × s
- W = 40 × 2.5
- W = 100 J
100 J
F
- Change the work done to joules: 18 kJ = 18 000 J
- F = W ÷ s
- F = 18 000 ÷ 6
- F = 3000 N
3000 N
s
- s = W ÷ F
- s = 150 000 ÷ 5000
- s = 30 m
30 m
Common mistakes
- Mixing up W for work done with W for weight. Read the question to see which one it means, and write the word next to the symbol.
- Using a distance that is not along the force. For a crate lifted onto a shelf, use the height gained, not the length of the ramp you walked up.
- Keeping the distance in centimetres. A 30 N push over 80 cm is 24 J, but using 80 gives 2400 J.
- Thinking effort always means work. A wall you lean on does not move, so no work is done on it however hard you push.
Solve W = F s for any of its three letters in the Equation Rearranger.
Questions people ask
Is work done the same as energy transferred?
Yes. When a force does 500 J of work, it moves 500 J of energy from one store to another. That is why both are measured in joules.
What is one joule?
One joule is the work done when a force of 1 N moves something 1 m along the line of the force. Lifting an apple about 1 m takes roughly 1 J.