How to calculate efficiency
Efficiency tells you what fraction of the energy put into a device ends up doing something useful. Your equation sheet gives it for energy and for power:
efficiency = useful output energy transfer ÷ total input energy transfer
efficiency = useful power output ÷ total power input
Efficiency has no unit. You can give it as a decimal, such as 0.80, or as a percentage by multiplying by 100, such as 80%. Both are accepted, but give the one the question asks for.
The useful output can never be bigger than the total input, so efficiency is always less than 1 (100%). If you get an answer above 1, the two values are the wrong way round.
The energy that isn't useful is wasted, usually as thermal energy heating the surroundings. Wasted energy = total input − useful output. A motor with an input of 500 J and a useful output of 400 J wastes 100 J and is 80% efficient.
Devices can be made more efficient by reducing waste: lubricating moving parts cuts friction, and insulation reduces unwanted heating of the surroundings.
Common mistakes that cost marks
- Putting the values the wrong way round. Useful output goes on top. An efficiency above 1 (100%) means they are swapped.
- Using a percentage in a calculation. To find useful output, convert 25% to 0.25 first.
- Mixing energy and power. Use joules for both or watts for both, never one of each.
- Adding a unit. Efficiency has no unit; write it as a decimal or a percentage.
- Giving a decimal when a percentage is asked for (or the reverse). Read the question and multiply or divide by 100 as needed.
Practice questions
Try each one on paper first, then reveal the worked answer.
Q1A motor has a total input energy of 500 J. Its useful output energy is 400 J. Calculate its efficiency as a percentage.[2 marks]
- efficiency = useful output ÷ total input
- efficiency = 400 ÷ 500 = 0.80
- 0.80 × 100
- efficiency = 80%
Q2A light bulb is 25% efficient. It is supplied with 2000 J of energy. Calculate the useful energy output.[3 marks]
- Convert: 25% ÷ 100 = 0.25
- Rearrange: useful output = efficiency × total input
- useful output = 0.25 × 2000
- useful output = 500 J
Q3An electric motor is 90% efficient and produces 1350 J of useful energy. Calculate the total energy supplied to it.[3 marks]
- Convert: 90% ÷ 100 = 0.90
- Rearrange: total input = useful output ÷ efficiency
- total input = 1350 ÷ 0.90
- total input = 1500 J
Frequently asked questions
What is the efficiency equation?
Efficiency = useful output energy transfer ÷ total input energy transfer. You can also use useful power output ÷ total power input.
Does efficiency have a unit?
No. Efficiency is a ratio, so give it as a decimal (such as 0.75) or as a percentage (75%).
Can efficiency be more than 100%?
No. A device can’t output more useful energy than is put into it. If your answer is above 100%, you have probably swapped the useful output and total input.
How do you work out wasted energy?
Wasted energy = total input energy − useful output energy. Most wasted energy heats the surroundings.