Hong Life CalculatorsUnderstanding the efficiency calculator — concept and principle
This calculator finds the efficiency of a machine or process from its input and useful output, or works backwards from a known efficiency to the output you get or the input you need. It applies to motors, boilers, power supplies, engines, lamps and any other energy conversion.
How it is calculated
η = useful output ÷ input × 100%
Losses = input − output; losses (% of input) = 100% − η
Output = input × η; input needed = output ÷ η
- Input and output must be in the same unit, either energy (J, kWh) or power (W, kW).
- "Input needed per unit of output" is 1 ÷ η.
The principle
Energy is conserved, so whatever goes in must come out somewhere. The part that comes out in the form you want is the useful output. The rest becomes heat, sound, vibration or friction and is counted as loss. Because nothing can come out that did not go in, the efficiency of a conversion can never exceed 100%. When several stages run in series, each stage passes on only its fraction, so the overall efficiency is the product of the stage efficiencies: a 90% motor driving a 70% pump gives 63%.
Worked example
Default inputs: find efficiency, input 1,000, useful output 850.
- η = 850 ÷ 1,000 = 0.85 = 85%.
- Losses = 1,000 − 850 = 150, which is 15% of the input.
- Input needed per unit of output = 1 ÷ 0.85 = 1.176.
How to read the result
The higher the efficiency, the less input you pay for each unit of useful output. Typical values vary widely: large electric motors and transformers often reach well above 90%, while a car's petrol engine turns only a minority of its fuel energy into work. The "input per unit of output" figure is useful for running costs: at 1.176, every kWh delivered costs 1.176 kWh bought. A small gain in efficiency at high values cuts losses sharply, from 15% to 10% when η goes from 85% to 90%.
Common mistakes
- Mixing units, such as electrical input in kW and output in hp.
- Adding stage efficiencies instead of multiplying them.
- Quoting a heat pump's coefficient of performance as an efficiency over 100%. It moves heat rather than converting it, so it is a different ratio.
- Using a nameplate efficiency at part load, where it is often lower.
Frequently asked questions
Can efficiency be over 100%?
Not for an energy conversion. A result over 100% means a measurement error or a missing input.
What is the efficiency of a human body?
For mechanical work such as cycling it is roughly 20–25%; most food energy becomes heat.
How do I find overall efficiency of a system?
Multiply the efficiencies of each stage written as decimals.
Sources: OpenStax, College Physics 2e (2022), section 7.6 "Conservation of Energy"