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Otto Cycle Efficiency Calculator

Find an engine's Otto cycle efficiency.

How it is calculated

The tool evaluates η = 1 − 1 / r^(γ−1) and shows the result as a percentage. r is the compression ratio (the cylinder volume at the start of compression divided by the volume at the end, a plain number) and γ is the heat capacity ratio Cp/Cv of the working gas, also a plain number. Both inputs must be greater than 1, otherwise the tool gives no result.

This is the ideal air-standard efficiency: no friction, no heat loss through the cylinder walls, instant combustion and a constant γ. Real engines come out well below the figure. The result depends only on r and γ, not on temperature or fuel quantity.

Worked example

Compression ratio r = 10 with γ = 1.4. The exponent is γ − 1 = 0.4. Then 10^0.4 ≈ 2.5119, and 1 / 2.5119 ≈ 0.3981. So η = 1 − 0.3981 = 0.6019. The tool reports 60.19%. Raising r to 12 with the same γ gives 62.99%, a gain of under three points for two extra units of compression.

Try this example →

Common mistakes

  • Entering a percentage or fraction for the compression ratio. Type 10 for a 10:1 engine, not 0.1 or 10%.
  • Using γ = 1 or leaving out the 1.4 for air. At γ ≤ 1 the formula has no meaning and the tool returns nothing; for air at ordinary temperatures 1.4 is the usual value.
  • Confusing the compression ratio with the pressure ratio of a turbocharger or the expansion ratio of an Atkinson-type engine. This formula uses the volume ratio.
  • Expecting the answer to match fuel economy or measured engine efficiency. It is a theoretical ceiling for the ideal cycle.
  • Assuming the gain is linear. Each extra step of compression raises efficiency by less than the previous one.

About this calculator

This calculator finds the theoretical thermal efficiency of an Otto cycle engine — the idealized four-stroke cycle (intake, compression, combustion, expansion, exhaust) that models a gasoline spark-ignition engine — using η = 1 − 1/r^(γ−1), where r is the compression ratio and γ is the heat capacity ratio of the working gas (about 1.4 for air). The formula shows that efficiency rises with compression ratio but with diminishing returns, which is why real engines balance higher compression against knock resistance and fuel octane requirements rather than pushing r indefinitely.

Automotive and mechanical engineers use this to evaluate the theoretical efficiency ceiling when optimizing engine compression ratios during design; thermodynamics students use it as a standard worked cycle alongside the Diesel and Brayton cycles; and engine designers reference it when weighing compression ratio changes against fuel requirements and emissions. Enter the compression ratio and gas heat capacity ratio to get the theoretical Otto cycle efficiency.

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