Otto Cycle Efficiency Calculator
Calculate the ideal thermal efficiency of a gasoline engine from compression ratio using the Otto cycle formula.
See how design choices affect fuel efficiency.
What is the Otto Cycle?
The Otto cycle is the theoretical thermodynamic model of a gasoline (spark-ignition) engine. It assumes ideal conditions — no friction, perfect combustion, no heat loss — giving the maximum possible efficiency for a given engine design.
Formula: η = 1 - (1 / r)^(γ - 1)
Where:
- η = thermal efficiency (as a decimal; multiply by 100 for %)
- r = compression ratio (volume of cylinder at BDC / volume at TDC)
- γ = heat capacity ratio of the working gas (1.40 for air or diatomic gases)
The four strokes of the Otto cycle:
- Isentropic compression — piston compresses the air-fuel mixture
- Constant-volume heat addition — spark ignites fuel, pressure rises sharply
- Isentropic expansion — hot gas pushes piston down (power stroke)
- Constant-volume heat rejection — exhaust valve opens, pressure drops
Compression ratio guidelines:
- Regular gasoline engines: r = 8–10 (efficiency 56–60%)
- High-performance engines: r = 11–13 (efficiency 62–65%)
- Too high → knock/detonation with standard fuel
- Diesel engines: r = 14–22 (use the Diesel cycle formula instead)
Real vs ideal efficiency: Real engines achieve only 55–65% of the theoretical Otto cycle efficiency. Losses come from friction, heat transfer through cylinder walls, incomplete combustion, and valve timing compromises.
Practical impact: Every 1-unit increase in compression ratio raises efficiency by about 2–4 percentage points. This is why high-octane fuel matters — it allows higher compression ratios without engine knock.