Efficiency
Ratio of useful output to input power.
Formula
Variables
Example
A motor giving 800 W out for 1000 W in is 80% efficient.
How it works
Efficiency compares how much of the power put into a device is converted into useful output power. The ratio is then multiplied by 100% so it is expressed as a percentage, making it easy to see how much of the input is actually being used well. Because some energy is always lost as heat, sound, friction, or other waste, efficiency is usually less than 100%.
When to use it
Use this formula when analysing machines or electrical devices to see how effectively they convert input power into useful output power. It is common in engineering, motors, generators, heaters, and any situation where you want to compare useful performance with power supplied.
Worked example, step by step
A pump uses 500 W of electrical power and delivers 350 W of useful hydraulic power. η = (P_out / P_in) × 100% η = (350 / 500) × 100% η = 0.7 × 100% η = 70% So the pump is 70% efficient.
Common mistakes to avoid
- Using energy values without matching the time period, when the formula needs power values
- Putting input power in the numerator instead of output power
- Forgetting to multiply by 100% if the answer is meant to be a percentage
Did You Know?
No real machine is 100% efficient — the second law of thermodynamics forbids it.
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