Efficiency formula
Efficiency = useful output energy transfer ÷ total input energy transfer. Both energies are in joules (J), so the units cancel and efficiency has no unit. You can give it as a decimal, or multiply by 100 for a percentage. AQA also allows useful power output ÷ total power input. Every board lists the energy version, and the exam paper prints it on the equation sheet.
Equation
efficiency = (useful energy ÷ total energy) × 100%
| Symbol | Quantity | Unit |
|---|---|---|
efficiency | efficiency | % |
useful | useful energy | J |
total | total energy | J |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall | useful output energy transfer ÷ total input energy transfer |
| AQA Combined Science (8464) | Recall | useful output energy transfer ÷ total input energy transfer |
| Edexcel Physics (1PH0) | Recall | useful energy transferred by the device ÷ total energy supplied to the device |
| Edexcel Combined Science (1SC0) | Recall | useful energy transferred by the device ÷ total energy supplied to the device |
| OCR Gateway Physics A (J249) | Recall | useful output energy transfer ÷ input energy transfer |
| OCR Twenty First Century Physics B (J259) | Recall | useful energy transferred ÷ total energy transferred |
Calculator: efficiency = (useful energy ÷ total energy) × 100%
Equation
efficiency = (useful power ÷ total power) × 100%
| Symbol | Quantity | Unit |
|---|---|---|
efficiency | efficiency | % |
useful | useful power | W |
total | total power | W |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall | useful power output ÷ total power input |
| AQA Combined Science (8464) | Recall | useful power output ÷ total power input |
| Edexcel Physics (1PH0) | Not in this specification | |
| Edexcel Combined Science (1SC0) | Not in this specification | |
| OCR Gateway Physics A (J249) | Not in this specification | |
| OCR Twenty First Century Physics B (J259) | Not in this specification |
Calculator: efficiency = (useful power ÷ total power) × 100%
What efficiency measures
No machine turns all its input energy into the thing you want. A car engine wants to move the car, but much of the energy from the fuel ends up heating the engine and the air. Efficiency tells you what fraction of the input does the useful job.
The rest is wasted energy. It usually spreads out into the surroundings as heat, so it is hard to use again. An efficiency of 0.25 means a quarter of the input is useful and three quarters is wasted.
How each board writes it
None of the three boards gives efficiency a letter of its own. They all write it in words.
- AQA (8463 and 8464): two versions. One uses useful output energy transfer and total input energy transfer. The other uses useful power output and total power input.
- Edexcel (1PH0 and 1SC0): useful energy transferred by the device ÷ total energy supplied to the device.
- OCR Gateway (J249): useful output energy transfer ÷ input energy transfer.
- OCR Twenty First Century (J259): useful energy transferred ÷ total energy transferred.
All of these are recall equations in their specifications. That is the board's own grouping, and for exams from 2025 onwards the words are printed on the sheet you are handed in the exam. Only AQA prints the power version, which you can see on the AQA equation list. The full comparison is on the physics equation sheet page.
Energy or power?
Use energies when the question gives joules. Use powers when it gives watts. Both give the same efficiency, because power is just energy per second, as the power equation shows.
Wasted energy often heats something up. You can work out how much heating that causes with the specific heat capacity equation.
Worked examples
efficiency
- Change the input to joules: 2.5 kJ = 2500 J
- efficiency = useful output ÷ total input
- efficiency = 1800 ÷ 2500
- efficiency = 0.72
- As a percentage: 0.72 × 100 = 72%
0.72
P
- Change the input power to watts: 5 kW = 5000 W
- useful power output = efficiency × total power input
- useful power output = 0.6 × 5000
- useful power output = 3000 W
3000 W
efficiency
- efficiency = useful output ÷ total input
- efficiency = 30 ÷ 120
- efficiency = 0.25
- As a percentage: 25%
0.25
Common mistakes
- Putting the total on top. An efficiency above 1, or above 100%, tells you the fraction is upside down.
- Using the wasted energy as the useful energy. Read the question to see which output it wants, such as light from a lamp.
- Dividing kilojoules by joules. Both energies need the same unit before you divide, or the answer is off by 1000.
- Writing 72 when the question asks for a decimal. Check whether it wants 0.72 or 72%, and give that form.
Swap between efficiency, useful output and total input in the Equation Rearranger.
Questions people ask
Can anything be 100% efficient?
Not in practice. Some energy is always lost, often as heat from friction or electrical resistance. An electric heater comes close, because its heating is the useful output.
Why does efficiency have no unit?
You divide joules by joules, or watts by watts. The units cancel and leave a plain number.
How can I make a machine more efficient?
Cut the waste. Oil moving parts to reduce friction, insulate hot parts, and use thicker wires so less energy heats the cables.