Efficiency calculator for energy and power

Efficiency is the share of the energy put into a device that comes out as useful energy: efficiency = useful output ÷ total input × 100%. A motor that takes in 2,400 J and does 1,800 J of useful work is 1,800 ÷ 2,400 × 100 = 75% efficient, and the other 600 J is wasted, mostly as heat. This efficiency calculator is part of our Work, Energy and Power Calculator: it finds the efficiency, or the useful output or total input from the other two, and shows the wasted energy.

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Work, Energy and Power Calculator

Calculate work done, power and efficiency

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How to use the efficiency calculator

1. Open the Work, Energy and Power Calculator and choose Efficiency on the top row of Calculate.
2. Choose what to find: Efficiency, Useful output or Total input.
3. Type the two values you know. Energies can be in J, kJ or MJ (or eV and MeV), and efficiency is a percentage.
4. Read the answer and the working. Under it you get the wasted energy and, for efficiency, the same value as a decimal. The diagram shows the energy flowing in and splitting into useful and wasted parts.
5. The other topics in the calculator find the energies themselves: Work (W = Fd), Power (E = Pt) and P = Fv.

For power, type the useful and total power in watts into the same two boxes. Efficiency is a ratio, so it comes out the same whether both values are energies or both are powers; the wasted reading is then in watts, although the box still says J.

The efficiency formula

Rearranged, useful output = efficiency × total input ÷ 100, and total input = useful output × 100 ÷ efficiency. Leave out the × 100 and you get efficiency as a decimal between 0 and 1. Energy is conserved, so the wasted energy is simply total input − useful output, and no real device can be more than 100% efficient.

Sankey diagrams

A Sankey diagram shows where the energy goes, with each arrow's width drawn to scale. The calculator draws one for every answer. This one is for Example 1 below, a kettle:

Worked examples you can check in the calculator

Example 1: a kettle

A 2,000 W kettle runs for 150 s, and the water gains 270,000 J. How efficient is it? First find the energy supplied: choose Power, then Energy, and type P = 2000 and t = 150. E = Pt = 2000 × 150 = 300,000 J. Then choose Efficiency and type 270000 and 300000.

The calculator shows 30,000 J wasted and 0.9 as a decimal. The wasted energy heats the kettle itself and the air around it.

Example 2: useful output from an engine

An engine is 25% efficient and burns fuel that releases 80 kJ. How much useful work does it do? Choose Useful output, set the energy unit to kJ, and type 25 and 80. E_u = 25 × 80 ÷ 100 = 20 kJ, and 60 kJ is wasted.

Example 3: total input to lift a load

A motor that is 60% efficient lifts a 50 kg crate 3 m. The useful energy is the gravitational potential energy gained, mgh = 50 × 9.81 × 3 = 1,471.5 J. Choose Total input and type 1471.5 and 60:

So the motor needs 2,452.5 J of electrical energy, and 981 J of it is wasted.

Example 4: efficiency from power

A motor draws 500 W and delivers 350 W of mechanical power. Type 350 and 500 into Efficiency: η = 350 ÷ 500 × 100 = 70%. Each second 150 J is wasted, so the motor gives out 150 W of heat.

Example 5: comparing two lamps

Lamp A takes 40 W and gives out 4 W of light. Lamp B gives the same 4 W of light from 10 W. Typed into Efficiency, lamp A is 4 ÷ 40 × 100 = 10% efficient and lamp B is 4 ÷ 10 × 100 = 40%, so lamp B saves 30 W. For 1,000 hours of use, choose Power then Energy, type 30 W and 1,000 with the time unit set to hours: E = 30 × 3,600,000 s = 1.08 × 10⁸ J, which the calculator shows is 30 kWh of electricity saved.

How to improve efficiency

• Reduce friction in moving parts with lubrication, so less energy is wasted as heat.
• Insulate anything that is meant to stay hot, such as a kettle or an oven, to cut heat loss to the surroundings.
• Use thicker or lower-resistance wires to cut heating in cables.
• Streamline moving vehicles to reduce air resistance.

What the calculator doesn't do

• Heat engine and Carnot efficiency from temperatures. It works only from energies or powers.
• Fuel economy in miles per gallon or litres per 100 km. That is a different measure, not an efficiency.
• Several stages at once. For a power station with stages of 90% and 40%, multiply the decimals by hand: 0.9 × 0.4 = 0.36, or 36% overall.

Common mistakes

• Dividing the wrong way round. Useful output goes on top. An answer over 100% means the values are swapped.
• Mixing units. Both values must be in the same unit: both J, both kJ or both W.
• Mixing energy and power. Don't divide joules by watts. Turn power into energy with E = Pt first, or use powers for both.
• Forgetting the × 100. 0.75 and 75% are the same efficiency; say which you mean.
• Giving the wasted share. If 25% is wasted, the efficiency is 75%.

Read next

Physics · EnergyPotential energy calculator: mgh and ½kx² with stepsFree potential energy calculator: gravitational energy from mgh and elastic energy from ½kx², or rearrange for mass, height, gravity or extension.