Efficiency Calculator and Formula

The efficiency formula is efficiency = useful output energy transfer ÷ total input energy transfer; multiply by 100 to give a percentage. With power, efficiency = useful power output ÷ total power input.

Efficiency formula

By energy
η = EusefulEtotal · 100%
η = EusefulEtotal · 100%Euseful = η·Etotal100%Etotal = Euseful·100%η
By power
η = PusefulPtotal · 100%
η = PusefulPtotal · 100%Puseful = η·Ptotal100%Ptotal = Puseful·100%η
η
efficiency, %
Euseful
useful output energy, J
Etotal
total input energy, J
Puseful
useful output power, W
Ptotal
total input power, W

Convert every value to SI units (m, s, kg, A, V, Ω) before substituting into the formula. The calculator does this for you and shows the conversion as a step.

75 %%
ηefficiency
75 %
efficiency: 75 %
Sankey diagram: of the total input energy, 400 J, the useful output is 300 J and the rest is wasted, mostly by heating the surroundings. Efficiency: 75 %.

Step-by-step solution

  1. Formulaη = EusefulEtotal · 100%
  2. Substituteη = 300 J400 J · 100%
  3. Answerη = 75 %

Efficiency examples

  1. Example 1

    An electric motor is supplied with 100 J of energy and transfers 75 J usefully to lift a load. Calculate the efficiency of the motor.

    Given:Euseful = 75 JEtotal = 100 J
    1. Formulaη = EusefulEtotal · 100%
    2. Substituteη = 75 J100 J · 100%
    3. Answerη = 75 %
  2. Example 2

    A car engine has an efficiency of 30 %. Calculate the useful energy output when the fuel supplies 2000 J of energy.

    Given:η = 30 %Etotal = 2000 J
    1. FormulaEuseful = η·Etotal100%
    2. SubstituteEuseful = 30 % · 2000 J100%
    3. AnswerEuseful = 600 J
  3. Example 3

    An electric drill has a total input power of 1.2 kW and a useful output power of 900 W. Calculate the efficiency of the drill.

    Given:Puseful = 900 WPtotal = 1.2 kW
    1. Formulaη = PusefulPtotal · 100%
    2. In SI unitsPtotal = 1.2 kW = 1200 W
    3. Substituteη = 900 W1200 W · 100%
    4. Answerη = 75 %

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What does efficiency mean?

Efficiency measures how much of the energy put into a device ends up where you want it. At GCSE it is efficiency = useful output energy transfer ÷ total input energy transfer, or, using power, efficiency = useful power output ÷ total power input. The result is a decimal between 0 and 1; multiply by 100 to give a percentage. The Greek letter η (eta) is often used as the symbol.

No real device is 100% efficient. The energy that is not transferred usefully is wasted: it is dissipated, usually by heating the device and its surroundings, sometimes as sound. Energy is still conserved, since useful energy plus wasted energy always equals the total input, so an efficiency above 100% means there is a mistake in the values.

A real-life picture: a filament lamp transfers only a small fraction of its input energy as light and the rest heats the room, while an LED lamp gives the same light with far less wasted energy. Lubricating moving parts to reduce friction and adding thermal insulation are common ways to improve efficiency. A Sankey diagram shows the split, with the widths of the arrows drawn to scale.

Common mistakes

  • Dividing the wrong way round: it is useful ÷ total, never total ÷ useful. If you get more than 100%, you have probably swapped them.
  • Mixing units: both energies must be in J, or both powers in W. For example, 1.2 kW is 1200 W.
  • Confusing a decimal with a percentage: 0.75 and 75% are the same efficiency, but 0.75% is not.
  • Putting the wasted energy on top of the fraction instead of the useful energy.
  • Mixing energy and power in one calculation. Use energy with energy, or power with power.

Frequently asked questions

Efficiency = useful output energy transfer ÷ total input energy transfer. Multiply by 100 to give it as a percentage.

Divide the useful power output by the total power input. Both powers must be in the same unit, such as watts.

No. Energy cannot be created, so a device can never give out more useful energy than it takes in. A result over 100% means the useful and total values have been swapped or mistyped.

It is dissipated to the surroundings, usually by heating them and sometimes as sound. It is not destroyed, but it spreads out and becomes less useful.

No. It is a ratio of two energies or two powers, so the units cancel. It is written as a decimal, such as 0.6, or as a percentage, such as 60%.