For a basic energy calculation, efficiency is useful output divided by total input. Multiply that ratio by 100 to express it as a percentage: Efficiency (%) = (useful output ÷ total input) × 100. Compare like with like—such as joules with joules or watts with watts—and define which output is useful for the task.
What is the efficiency formula?
Use this formula for an introductory energy or work calculation:
Efficiency = useful output ÷ total input
To express the result as a percentage, multiply the ratio by 100. If the question asks only for the ratio, the decimal is also a valid answer. OpenStax defines efficiency in terms of useful energy or work output relative to total energy input; the University of Edinburgh’s physics glossary gives the percentage form.
OpenStax: Conservation of Energy · University of Edinburgh: Efficiency glossary
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How do you calculate percentage efficiency?
- Identify the total input to the system.
- Identify the output that performs the intended useful task.
- Divide useful output by total input, using comparable quantities and units.
- Multiply by 100 if the answer is required as a percentage.
For example, if a device receives 200 J of energy and delivers 150 J as useful output, then 150 J ÷ 200 J = 0.75. Multiply by 100 to get 75% efficiency. This is an arithmetic example, not a measured result for a particular device.
Rearranging the formula
- Useful output = efficiency as a decimal × total input.
- Total input = useful output ÷ efficiency as a decimal.
Use the decimal form in these rearranged equations: for example, 75% becomes 0.75.
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What counts as useful output?
Efficiency measures the share of input that reaches the output chosen as useful for the task. Set that definition before calculating. A petrol engine, for example, converts chemical energy in fuel partly into kinetic energy and partly into other forms, including exhaust heat. If the task is to propel a vehicle, the kinetic energy is the useful output being counted; not every energy transfer automatically belongs in the numerator.
Energy is conserved even when some of it does not perform the intended job. It may be transferred into heat, sound, or another form outside the useful output being measured. As OpenStax explains, “Even though energy is conserved in an energy conversion process, the output of useful energy or work will be less than the energy input.”
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How should you interpret the result?
In a basic energy-conversion problem, efficiency is ordinarily a fraction from zero to one, or 0% to 100% when expressed as a percentage. A result above 100% is not a typical energy-conversion efficiency: check whether the measure is actually a coefficient of performance, uses a different accounting convention, or has an incorrect boundary or calculation.
Efficiency is not the same as power. Power is the rate of energy transfer; efficiency is a ratio of useful output to input. Nor is efficiency the same as energy intensity. The U.S. Department of Energy describes energy intensity as energy used per unit of output or activity, while its energy-efficiency framing concerns providing a given service with less energy or producing more service from a given input.
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U.S. Department of Energy: Energy Intensity Indicators terminology and definitions
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.How to compare efficiencies fairly
A percentage is meaningful only in context. When comparing systems, use the same useful job, system boundary, input basis, and definition of output. This matters especially when a system produces more than one useful output: changing what is counted can change the reported efficiency.
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Combined heat and power (CHP)
A CHP system produces electricity and useful thermal output from fuel. The U.S. Environmental Protection Agency’s total-system method adds net useful electrical output and net useful thermal output, then divides by total fuel energy input. That method treats electricity and thermal energy as equal in value, which may not reflect their different practical value. EPA also describes effective electric efficiency, which adjusts for thermal output that would otherwise have been produced by conventional technology.
EPA reports that total-system efficiencies for CHP systems typically reach 60% to 80%. Its typical effective electric efficiency ranges are 50% to 70% for combustion-turbine CHP systems and 70% to 85% for reciprocating-engine CHP systems. These are EPA’s contextual typical ranges, not universal targets or a current product comparison; the page’s publication date is not stated. EPA cautions that assumptions implicit in each method are not appropriate in every case. Choose the measure that fits the comparison and state the assumptions.
U.S. EPA: Methods for Calculating CHP Efficiency
Illustrative textbook values
OpenStax lists these illustrative efficiencies: gasoline engine, 30%; diesel engine, 35%; coal power plant, 42%; and electric motor, 98%. They are examples in a textbook table, not performance guarantees for every engine, plant, or motor; the source search result does not state a publication year.
Does the same formula apply outside physics?
Not automatically. “Efficiency” can have specialized meanings in business, computing, and economics. For those contexts, define the relevant output, input, and system boundary first, then use the measure appropriate to that field. The energy formula above applies when the quantities being compared are useful energy or work output and total energy input.
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