Efficiency Calculator

The formula

Efficiency (η, the Greek letter eta) is the ratio of useful output to total input, expressed as a percentage:

η = (useful output ÷ total input) × 100%

Where:

• η = efficiency, a percentage between 0% and 100%.
• useful output = the energy or work that does the job you want.
• total input = the energy or work supplied to the system.

Both the output and the input must be in the same unit, joules with joules, watts with watts, calories with calories. Because they share a unit, the ratio is dimensionless and the units cancel, leaving a clean percentage. The energy lost (to friction, heat, sound, or drag) is simply:

energy lost = total input − useful output

Worked example

A car engine burns fuel that releases 1000 joules of chemical energy, but only 250 J end up as useful motion at the wheels. The efficiency is:

η = (250 J ÷ 1000 J) × 100% = 25%

The energy lost is 1000 − 250 = 750 J, mostly as heat through the radiator and exhaust. A 25% result is typical for a petrol engine, most of the fuel’s energy never reaches the road.

Quick reference

Common pitfalls

• Mixing units. Output and input must use the same unit. Comparing 250 J of work against 1000 calories of fuel without converting first gives a meaningless answer.
• Output above input. Efficiency can never exceed 100%, that would create energy from nothing. If your output looks larger than your input, you have mislabelled one of the values.
• Power vs. energy. You can use power (watts) instead of energy (joules) as long as both values are powers measured over the same period; the ratio still holds.
• Forgetting the losses. The energy lost (input − output) is real heat, friction, or sound. A higher efficiency means less of your input is being wasted, not that the machine produces more.