Efficiency Calculator

This efficiency calculator determines how efficiently a system converts input energy into useful output power and also supports calculations in the reverse direction.

Enter any two of the following values: Input Energy, Output Power or Efficiency, leave the corresponding field blank, and the tool will calculate the missing value. During calculation, units such as joules, kilowatt-hours and calories are automatically converted to each other so that unit is not a limitation.

What is efficiency?

Efficiency is a measure of how much energy inputted into a machine or process actually goes towards the intended work, and what proportion is wasted as useless energy.

In real systems some of the energy is always lost. A car engine heats up the air, a motor makes noise and gets hot, and an incandescent light bulb gives off light but also produces heat. Efficiency is a measure of how much of the input energy remains as useful power and how much is wasted.

Because efficiency compares two values of the same type of energy, it has no units itself; it is a pure number, usually expressed as a percentage.

Formula for efficiency:

Efficiency is denoted by the Greek letter eta (η) and is the ratio of useful output energy to input energy, expressed as a percentage.

Here, E-out is the useful energy output of a system and E-in is the energy input to the system. As these three quantities are related by the same relationship, the formula can be rearranged so that it calculates the energy instead of the efficiency.

Whether the energy is measured in joules, kilowatt hours or calories, the formula remains the same as long as the same unit is used for both input and output energy. The formula also holds true if power or work are used instead of energy. In all cases, the units will cancel each other out.

How to use this calculator:

Enter two known values and leave the third field blank. To calculate efficiency enter input energy and output energy. To calculate output enter input energy and efficiency. To calculate input enter output energy and efficiency.

Once two fields are filled in, the calculator will calculate the third value and display the efficiency as a result. A pie chart is also displayed at the same time to show the lost energy, loss rate, and remaining energy. This calculator has no mode of selection; leaving one field blank is enough to tell the calculator what to calculate.

Two optional switches allow for more detailed calculations. One adds a time period and shows input and output power. The other connects this stage in series with subsequent stages to show the overall efficiency of the whole system.

Formulation of efficiency

This table shows the same relationships in three ways, each of which corresponds to a possible missing quantity.

Example calculation

Suppose a machine takes in 1000 joules of energy and produces 469 joules of useful work.

The efficiency is the ratio of output energy to input energy.

Therefore the efficiency of this machine is 46.9%. The remaining 531 joules, or the 53.1% of the joules that were not converted into useful work, are lost as heat, sound, and friction.

The calculation in the opposite direction is just as simple. If the pump efficiency is 80% and a useful energy of 2000 joules is to be produced, then the input energy is the result of dividing the output power by the efficiency, so 2000 divided by 0.8, which equals 2500 joules. With this calculation tool you can simply read off the third value if you only enter two values.

Where does the lost energy go?

The difference between the input and output energy does not suddenly disappear. Energy is always conserved. It is simply converted into a form that is unavailable for current work.

Common causes are friction between moving parts which heats contact surfaces and electrical resistance which increases the temperature of wires and windings. Excess heat that is dissipated by noise, vibration, exhaust or cooling also represents losses. In incandescent light bulbs most of the input energy is converted to heat while only a small part becomes light, so they feel very hot.

Efficiency can be increased by better lubrication, lighter materials, tighter tolerances or suitable design to reduce these losses.

Typical efficiencies:

The technology makes a big difference to the efficiency. These rough values show the general level and how far real systems are from the ideal 100%.

Efficiency and performance

Power is the energy transferred per unit time and is measured in watts. One watt equals one joule per second. If the time taken to transfer the energy is known, then changing the energy into power will not change the efficiency result.

This is useful because many systems are rated in terms of power rather than energy. A motor that takes 1000 watts and produces 900 watts mechanical output has an efficiency of 90%, which is exactly the same as a system that consumes 1000 joules per second and outputs 900 joules. With this calculator you can switch on the power and enter a time period to see the corresponding input and output power.

Combination of several stages

Energy often goes through several stages before it is converted into useful work. In a power plant, fuels are burned, turbines are spun, generators are turned and then the electricity is transmitted on power lines. Each of these steps has its own efficiency.

The overall efficiency of a system is the product of the efficiencies of each stage, not their average.

Since each individual stage is less than 100%, the result of multiplying them together will always be lower than any one stage's efficiency. If all three stages are each 90% efficient, then the result is .9 times .9, times .9, which equals .729, or about 73%. A multi-stage switch in this calculator performs that calculation.

Why 100% efficiency cannot be achieved:

In real machines it is impossible to achieve 100% efficiency. Some of the energy will always be lost as heat to the surroundings and it is impossible to recover all that energy.

For heat engines this limit is even more strict. According to the second law of thermodynamics a heat engine can never convert all absorbed heat into work; it must always give some away to a lower temperature heat source. The theoretical maximum efficiency depends only on the temperatures involved, and even an ideal frictionless heat engine cannot achieve 100% efficiency. Since real heat engines have problems like friction and imperfections in components, actual efficiencies are even lower.

If it is claimed that the efficiency exceeds 100%, i.e. the output power exceeds the input power, then this either means that a measurement has been made incorrectly or an energy source has been overlooked and there is no ground-breaking discovery involved.

Areas of application for efficiency

Efficiency is a central concept in engineering and energy policy. Engineers use efficiency to compare combustion engines, electric motors, pumps, power plants, etc., and determine where the most wasted energy goes and which areas are cheapest to improve.

Efficiency also affects energy-saving labels for appliances and vehicles, the choice between incandescent and LED light bulbs, and reasons to insulate buildings. In all areas where energy is consumed or environmental impact created, efficiency measures and promotes conservation of more useful output from the same input.

Tips for accurate results:

Make sure the input and output are of the same type of quantity. Match energy with energy and electric power with electric power. The unit conversion can also be left to a calculator. Use useful power rather than total power as any energy that is not useful for its purpose must be considered lost.

Note that the result represents efficiency within a defined scope. The values obtained differ depending on whether, for example, the combustion of fuel in a power plant up to the supply of electricity to a house is calculated or only the electricity delivered to the house is considered, since there are losses during transmission between them.