Power formula: P = W/t
Power = work done ÷ time. AQA and OCR Gateway write P = W/t, and Edexcel writes P = E/t with E standing for work done. P is power in watts (W), W is work done in joules (J) and t is time in seconds (s). It is a recall equation for AQA, Edexcel and OCR Gateway, and those exam sheets print it. OCR Twenty First Century lists power with energy transferred instead.
Equation
P = W ÷ t
| Symbol | Quantity | Unit |
|---|---|---|
P | power | W |
W | work done | J |
t | time | s |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall | P = W/t |
| AQA Combined Science (8464) | Recall | P = W/t |
| Edexcel Physics (1PH0) | Recall | P = E/t |
| Edexcel Combined Science (1SC0) | Recall | P = E/t |
| OCR Gateway Physics A (J249) | Recall | P = W/t |
| OCR Twenty First Century Physics B (J259) | Not in this specification |
Calculator: P = W ÷ t
Power is how fast work gets done
Two people can carry the same box up the same stairs. They do the same work, because the force and the height are the same. The one who runs up has the greater power, because they do that work in less time.
One watt is one joule of work each second. A person climbing stairs briskly might manage a few hundred watts. A car engine can reach tens of thousands of watts, so its power is often quoted in kilowatts (kW), where 1 kW is 1000 W.
Watch the letters. In P = W/t, the W on top is work done in joules. The unit of power is also written W, for watts. Keep them apart by saying the words in your head.
Which boards list this form
- AQA (8463 and 8464): P = W/t, power = work done ÷ time.
- Edexcel (1PH0 and 1SC0): P = E/t, printed as power = work done ÷ time taken.
- OCR Gateway (J249): P = W/t.
- OCR Twenty First Century (J259): this work done form is not in its list. J259 prints power = energy transferred ÷ time instead.
Where it appears, the specification calls it a recall equation. That tells you how the board groups it, and the paper still hands it to you: from 2025 each board prints its whole list on the sheet. See the AQA list, or the OCR Twenty First Century list for the J259 version. The energy version has its own page, power from energy and time.
Rearranging it
- W = P × t
- t = W ÷ P
Many questions come in two steps. First find the work done with the work done equation, W = F s. Then divide by the time to get the power. The first worked example below does exactly this for a student running up the stairs.
Worked examples
P
- Work done first: W = F × s = 500 × 4 = 2000 J
- P = W ÷ t
- P = 2000 ÷ 5
- P = 400 W
400 W
W
- W = P × t
- W = 750 × 20
- W = 15 000 J
15 000 J
t
- Change to base units: 2 kW = 2000 W and 30 kJ = 30 000 J
- t = W ÷ P
- t = 30 000 ÷ 2000
- t = 15 s
15 s
Common mistakes
- Using a time in minutes. A motor that does 6000 J in 2 minutes has a power of 50 W, not 3000 W.
- Mixing kilowatts with joules. Turn 2 kW into 2000 W before you use it, or your time comes out 1000 times too large.
- Thinking a bigger force always means more power. Power depends on the work and on how long it takes, so a slow, strong push can have low power.
- Writing the answer in joules. Joules measure work; the unit for power is the watt, one joule per second.
Practise flipping P = W/t round to find t in the Equation Rearranger.
Questions people ask
What about horsepower?
Horsepower is an old unit you may see in car adverts. Physics measures power in watts, so change any other unit into watts before you use the equation.
Why does running upstairs feel harder than walking?
The work done is the same, but running does it in less time. Your muscles must supply a higher power, and that is what makes you out of breath.