Efficiency Calculator
Calculate efficiency as a percentage from energy input and energy output. Useful for motors, power supplies, and any process with losses.
Efficiency Calculator
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What the efficiency calculator does
No machine turns all the energy you put in into useful output; some always slips away. Efficiency is the fraction that does useful work, written as a percentage. This calculator finds it from the energy in and the energy out, and it can also work back to either energy if you know the efficiency.
Below is what efficiency really measures, the equation behind it, where the lost energy goes, and a worked example.
How to use it
- Choose what to find: efficiency, energy input, or energy output.
- Enter the other two. The energies carry their own units, and efficiency is a percentage.
- Press Calculate for the answer, or Reset to clear it.
What efficiency measures
Efficiency is the ratio of useful energy out to total energy in. Feed a machine 100 units of energy and get 80 useful units back, and it is 80 percent efficient: the other 20 units were spent but wasted, doing nothing you wanted. It is a plain measure of how much of your input actually reaches the goal.
Because the output is always part of the input, efficiency is always less than 100 percent for any real machine. You cannot get more useful energy out than you put in, which would be energy from nowhere, and you cannot even break even, because some loss is unavoidable. The figure tells you how good a machine is at its job, and it ranges widely: a car engine might manage only a quarter to a third, an electric motor often well over 90 percent.
The equation it solves
Efficiency is the useful energy output divided by the energy input, turned into a percentage:
efficiency = (energy output ÷ energy input) × 100%
Rearranged, the same relationship gives the other two quantities the calculator can find: the input needed for a wanted output, energy input = output ÷ (efficiency ÷ 100), and the output a given input will yield, energy output = (efficiency ÷ 100) × input.
Where the lost energy goes
The energy that does not show up as useful output is not destroyed, it is just turned into a form you cannot use for the job. Energy is always conserved, so every unit you put in goes somewhere. The lost part mostly becomes heat, generated by friction between moving parts, by air and fluid resistance, and by electrical resistance in wires. Some escapes as sound and vibration.
This is why machines run warm, why an engine needs cooling, and why a phone heats up under load. That warming is the wasted energy made visible. It also explains why perfect efficiency is impossible: friction and resistance can be reduced with good design and lubrication, but never abolished, so a little of the input always leaks away as heat. The art of engineering is to make that leak as small as the job allows.
Units and precision
Efficiency is a pure ratio, reported here as a percentage, so the units of energy you use do not affect it, as long as the input and output are in the same unit. The calculator lets you enter each energy in joules, kilojoules, kilowatt-hours, calories, and more, converting internally. Because it is a ratio, the same figure also applies if you compare power in to power out, or work in to work out, rather than energy. Results are shown with enough digits that you can read the precision you need.
A worked example
Suppose a machine takes in 1,000 joules of energy and delivers 750 joules of useful output.
The efficiency is (750 ÷ 1,000) × 100 = 75 percent. The remaining 250 joules, a quarter of the input, were lost, mostly as heat from friction. Knowing the efficiency, you could also work the other way: to get 750 joules of useful output from a 75 percent machine, you must supply 750 ÷ 0.75 = 1,000 joules in.
Questions people ask
How do you calculate efficiency?
Divide the useful energy output by the energy input and multiply by 100 to get a percentage. An output of 80 from an input of 100 is 80 percent efficient.
Can efficiency be more than 100 percent?
No. That would mean more useful energy out than in, which is impossible. Real machines are always below 100 percent because some energy is always lost.
Where does the lost energy go?
Mostly into heat, from friction, air resistance, and electrical resistance, with some as sound and vibration. The energy is conserved, just turned into a form you cannot use for the task.
Why can't a machine be 100 percent efficient?
Because friction and resistance can be reduced but never removed entirely, so a little input always leaks away as heat. Good design and lubrication shrink the loss but cannot abolish it.
References
A quick note on where the physics comes from. Efficiency as the ratio of useful output to input, and the fact that lost energy is conserved as heat rather than destroyed, are standard mechanics and thermodynamics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The joule and the other SI units follow the US National Institute of Standards and Technology.
- OpenStax, University Physics Volume 1, Section 7.4, Power (and machine efficiency). https://openstax.org/books/university-physics-volume-1/pages/7-4-power
- HyperPhysics, Georgia State University, Conservation of Energy. http://hyperphysics.phy-astr.gsu.edu/hbase/conser.html
- National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811
Bibek Lal Karna is a PhD student and graduate teaching assistant at the University of Mississippi, with deep interests in theoretical and gravitational physics. He is also the founder of NRCC and is strongly engaged in scientific teaching and communication. At Eon Tools, he reviews physics tools.