What is the Otto cycle?

The Otto cycle is the ideal thermodynamic cycle for a spark-ignition (gasoline) engine. It consists of two isentropic (adiabatic reversible) processes and two constant-volume (isochoric) heat exchange processes. Real engines approximate this cycle.

What is the thermal efficiency formula?

Ideal Otto cycle thermal efficiency is η = 1 − (1 / r^(γ−1)), where r is the compression ratio and γ (gamma) is the heat capacity ratio Cp/Cv. For air, γ = 1.4.

What is a typical compression ratio for gasoline engines?

Most gasoline engines use a compression ratio between 8:1 and 12:1. Higher ratios increase efficiency but require higher-octane fuel to prevent knock (auto-ignition). Diesel engines run 14:1 to 23:1 and follow the Diesel cycle instead.

Why does efficiency increase with compression ratio?

A higher compression ratio means the gas is compressed more before combustion. This raises peak temperatures and pressures, so more of the heat energy added is converted to work rather than rejected to the exhaust.

What is γ (gamma) and what value should I use?

γ is the ratio of specific heats Cp/Cv for the working fluid. For air or diatomic gases at moderate temperatures, γ ≈ 1.4. At higher temperatures the value drops slightly (toward 1.3) because vibrational modes become active. Use 1.4 for standard air-standard analysis.

Otto Cycle Efficiency

Enter compression ratio and heat capacity ratio to calculate the ideal Otto cycle thermal efficiency and cycle performance metrics.

Cycle Parameters

Compression Ratio (r)

Typical gasoline engines: 8 – 12

Heat Capacity Ratio γ (Cp/Cv)

Air (diatomic ideal gas): 1.4

Heat Input q_in (kJ/kg) (optional)

Used to compute net work output

Common Compression Ratios

Engine type	r
Regular gasoline	8:1
High-performance gasoline	10:1
Premium/turbo gasoline	12:1
Atkinson cycle (hybrid)	14:1

Click a row to load its ratio.

Ideal Thermal Efficiency

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Enter values and press Calculate

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Efficiency η

—

decimal

Net Work w_net

—

kJ/kg

Heat Rejected q_out

—

kJ/kg

Formula

η = 1 − (1 / r^(γ−1))

r = compression ratio

γ = heat capacity ratio C_p/C_v

η = thermal efficiency

w_net = η × q_in

Summary

Enter compression ratio and heat capacity ratio to calculate the ideal Otto cycle thermal efficiency and cycle performance metrics.

How it works

Enter the compression ratio (r) — the ratio of maximum to minimum cylinder volume, typically 8–12 for gasoline engines.
Enter the heat capacity ratio (γ) — the ratio of specific heats Cp/Cv; defaults to 1.4 for air (diatomic ideal gas).
The calculator applies η = 1 − (1 / r^(γ−1)) to compute ideal thermal efficiency.
Net work and heat input are shown per unit mass using standard cycle state points.
Results update instantly as you adjust either input.

Use cases

Estimate the theoretical efficiency ceiling of a gasoline engine at a given compression ratio.
Compare how different compression ratios affect Otto cycle performance.
Solve thermodynamics homework problems on air-standard Otto cycles.
Understand why higher compression ratios improve efficiency but raise knock risk.
Evaluate efficiency differences between air (γ = 1.4) and other working fluids.
Cross-check textbook Otto cycle examples against known results.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu