Efficiency Calculator

1. Enter any two of efficiency, useful output and total input.
2. Keep output and input in the same units (joules or watts).
3. Leave the one you want to find blank.
4. Read the result and the formula used.

Here is what each result means:

Efficiency measures how much of the energy or power you put into a machine comes out as useful work. It is the useful output divided by the total input, written as a percentage. A machine that takes in 1000 joules and delivers 750 joules of useful energy is 75 percent efficient, with the remaining 250 joules lost, usually as heat, sound or friction.

Because some energy is always lost in a real machine, efficiency is always less than 100 percent. The output and input must be measured in the same units, whether that is joules of energy or watts of power, so the percentage is a pure ratio. A higher efficiency means less waste and lower running costs, which is why engineers work hard to push it up.

Efficiency applies to almost any energy conversion: engines, motors, light bulbs, power plants and even the human body. A traditional light bulb might be only a few percent efficient at making light, wasting most of its energy as heat, while an electric motor can exceed 90 percent. Comparing efficiencies is the quickest way to see which device wastes the least.

It rearranges one relation to solve for whichever value you leave blank.

1. For efficiency, divide the output by the input and multiply by 100.
2. For output, multiply the input by the efficiency as a fraction.
3. For input, divide the output by the efficiency as a fraction.

Efficiency compares energy or power; see the power calculator and percentage calculator.

A machine turns 1000 joules of input into 750 joules of useful output.

Calculation: efficiency = 750 / 1000 x 100 = 75 percent. The wasted energy is 1000 minus 750, which is 250 joules lost as heat and friction.

One relation, rearranged for whatever you need to find.

All three come from efficiency equals output over input times 100, so any two of the values give the third. The output and input must share the same units for the ratio to make sense, since efficiency is a pure number expressed as a percentage.

Efficiency varies enormously from one device to another.

Electric motors are among the most efficient devices, wasting little energy, while heat engines are limited by physics to far lower values. Comparing these figures shows why switching from an incandescent bulb to an LED, or from a petrol engine to an electric motor, saves so much energy.

The first law of thermodynamics, conservation of energy, means you can never get more useful energy out of a machine than you put in, so real efficiency is always at or below 100 percent. Some energy always escapes as heat, sound, friction or electrical resistance, so 100 percent is the ceiling and no ordinary machine reaches it.

Heat engines, which turn heat into work, face a much stricter limit set by the second law of thermodynamics. The best possible efficiency of any heat engine working between a hot temperature and a cold temperature is the Carnot efficiency:

For example, a steam turbine with a hot side at 800 kelvin and a cold side at 300 kelvin has a Carnot limit of 1 minus 300 over 800, which is about 62 percent. No real turbine between those temperatures can beat that figure, and friction and losses pull the actual value lower still. This is the deep reason car engines and power stations are far from 100 percent efficient: it is physics, not poor engineering.

One apparent exception is worth knowing. A heat pump or refrigerator is rated by its coefficient of performance rather than an efficiency, and this value can be greater than 1, sometimes 3 or 4. That is not a violation of energy conservation, because the device moves existing heat rather than creating energy, so the coefficient of performance is a ratio of a different kind and is not capped at 100 percent.

The Energy Losses

Friction, heat, sound and electrical resistance all reduce the useful output and lower efficiency.

The Design

Better bearings, insulation and materials cut losses and raise efficiency.

The Type of Conversion

Some conversions, such as heat engines, are limited by physics to fairly low efficiencies.

Physics Homework

Solve for efficiency, output or input in an energy-transfer problem.

Engineering

Rate a motor, engine or power supply and compare designs.

Energy and Cost

See how much input energy a device wastes, and the savings from a more efficient one.

1. Different Units

Output and input must be in the same units. Mixing joules and watts gives a meaningless ratio.

2. Efficiency Over 100 Percent

A real machine cannot exceed 100 percent. A result above 100 means the output or input is wrong.

3. Confusing Output and Input

The useful output is always smaller than the total input. Swapping them inverts the answer.

4. Forgetting the Losses

The difference between input and output is the wasted energy, not part of the useful output.

5. Zero Input

Solving for efficiency cannot divide by an input of zero.

The relation is exact; only the displayed decimals are rounded.

Efficiency is the useful output of a machine divided by the total input, as a percentage. A machine that turns 1000 joules of input into 750 joules of useful output is 75 percent efficient.

Divide the useful output by the total input and multiply by 100. For 750 joules out of 1000 joules in, that is 750 divided by 1000 times 100, which is 75 percent.

No. A real machine always loses some energy, so its efficiency is always below 100 percent. A result above 100 means the output or input value is wrong.

Divide the output by the efficiency written as a fraction. Leave the input field blank and enter efficiency and output, and the calculator solves for it.

The wasted energy is the total input minus the useful output. For a 75 percent efficient machine taking in 1000 joules, 250 joules are wasted, usually as heat.

They must use the same units, such as joules for energy or watts for power. Because efficiency is a ratio, the units cancel and the result is a percentage.

Heat engines are limited by the laws of thermodynamics, which cap how much heat can become useful work. This is why car engines are often only 25 to 30 percent efficient.

For an ordinary machine the ceiling is 100 percent, set by conservation of energy. For a heat engine the limit is lower, given by the Carnot efficiency, 1 minus the cold temperature divided by the hot temperature, with both in kelvin.

A heat pump or refrigerator is rated by its coefficient of performance, which can be 3 or 4, not by efficiency. It moves existing heat rather than creating energy, so it does not break conservation of energy despite the high number.

Yes. Efficiency is the same ratio whether you use energy in joules or power in watts, as long as the output and input use the same unit.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Energy conversion efficiency (Wikipedia).
• Carnot efficiency and the second law (HyperPhysics, Georgia State University).
• Energy efficiency (US Department of Energy).
• Coefficient of performance (Wikipedia).
• Efficiency (Wikipedia).