Efficiency
Efficiency measures how much of the energy supplied to a device does the job you wanted. One formula, one impossible answer to watch for, and one diagram.
1. The formula
Efficiency = (useful energy output ÷ total energy input) × 100%
It works identically with power:
Efficiency = (useful power output ÷ total power input) × 100%
Efficiency has NO units — it is a ratio, given as a percentage or a decimal.
Example: a motor takes in 500 J and does 300 J of useful work.
- Efficiency = (300 ÷ 500) × 100 = 60%
Example: a lamp rated 60 W emits 12 W of light.
- Efficiency = (12 ÷ 60) × 100 = 20%
Divide the USEFUL output by the TOTAL input — not the other way round, and not output by wasted energy. Inverting the fraction is the most common error, and it gives an answer over 100%.
2. Efficiency can never exceed 100%
A device can NEVER be more than 100% efficient, because it cannot output more energy than it takes in — that would break the conservation of energy.
The output must always be LESS than the input. If your calculation gives more than 100%, you have swapped input and output. Tutors flagged this as a self-check worth doing on every answer.
In practice, no real device reaches 100% — some energy is always wasted, usually as thermal energy from friction or electrical resistance, and sometimes as sound.
3. Useful and wasted energy
Total input = useful output + wasted output
That relationship lets you find any one of the three from the other two.
Example: a device takes 800 J and wastes 300 J.
- Useful output = 800 − 300 = 500 J
- Efficiency = (500 ÷ 800) × 100 = 62.5%
Deciding what counts as “useful” depends on the device’s purpose:
| Device | Useful output | Wasted output |
|---|---|---|
| Lamp | light | thermal |
| Motor | kinetic | thermal, sound |
| Loudspeaker | sound | thermal |
| Electric heater | thermal | — (almost 100% efficient) |
| Kettle | thermal (in the water) | thermal to surroundings and casing |
An electric heater is nearly 100% efficient, because thermal energy is exactly what you want from it. Nothing is wasted — the “waste” for other devices is this device’s purpose. This is a favourite exam point.
Never say energy is “lost” or “destroyed”. Say it is wasted or dissipated — it has spread out to the surroundings, usually as thermal energy, but the total is conserved.
4. Sankey diagrams
A Sankey diagram shows energy flow as arrows whose width is proportional to the energy.
- Input enters from the left
- Useful output continues to the right
- Wasted energy branches off, usually downwards
- Total width in = total width out — conservation, drawn
Reading efficiency from one: compare the width of the useful output arrow with the width of the input arrow.
Draw arrows to scale and label each with its energy and type. An unlabelled or out-of-scale diagram loses marks even when the physics is right.
5. Improving efficiency
Reduce the wasted energy:
| Method | Reduces |
|---|---|
| Lubrication | friction → less thermal energy |
| Streamlining | air resistance |
| Insulation | thermal energy transfer |
| Thicker / lower-resistance wires | electrical heating |
| LED instead of filament lamps | thermal waste |
Efficiency questions often ask for a method AND its effect. “Lubricate the moving parts, which reduces friction, so less energy is wasted as thermal energy” is the full answer.
6. Mistakes that cost marks
Inverting the fraction — input over output.
Giving an efficiency over 100%.
Using wasted energy instead of useful energy in the numerator.
Forgetting to multiply by 100 for a percentage.
Giving units for efficiency.
Saying energy is lost or destroyed.
Misidentifying which output is “useful” for the device.
Sankey arrows not to scale, or unlabelled.
Frequently asked questions
What is the formula for efficiency? (useful energy output ÷ total energy input) × 100%.
Can I use power instead of energy? Yes — the formula is identical with power.
What are the units of efficiency? None — it is a percentage or a ratio.
Can efficiency be more than 100%? No — that would break the conservation of energy.
What should I do if I get more than 100%? You have swapped the input and output.
Where does the wasted energy go? It is dissipated to the surroundings, usually as thermal energy.
Is energy destroyed when it is wasted? No — it is conserved, just spread out and no longer useful.
Why is an electric heater almost 100% efficient? Because thermal energy is the useful output — it is exactly what you want.
What does a Sankey diagram show? Energy transfers, with arrow width proportional to energy.
How do I improve efficiency? Reduce waste — lubricate, insulate, streamline, use lower-resistance wires.
Quick revision checklist
- I know the efficiency formula for energy and power
- I divide useful output by total input
- I multiply by 100 for a percentage
- I know efficiency has no units
- I know it can never exceed 100%, and why
- I check my answer against that limit
- I know input = useful + wasted
- I can identify the useful output for each device
- I know why a heater is nearly 100% efficient
- I say energy is wasted or dissipated, not lost
- I can draw and read a Sankey diagram
- I can suggest improvements with their effect
These notes cover efficiency in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons. This was one of the less-covered subtopics in that set, so the page follows the syllabus closely rather than being padded. Always check the current syllabus and formula list for your own exam series.
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