Heat Engine Efficiency Calculator
A heat engine converts thermal energy from a hot reservoir into mechanical work while rejecting waste heat to a cold reservoir. The thermal efficiency is defined as eta = W / Qh = 1 - Qc / Qh, where Qh is the heat absorbed from the hot source, Qc is heat rejected to the cold sink, and W = Qh - Qc is the net work output. This calculator computes both the actual efficiency from heat values and the Carnot (maximum theoretical) efficiency from reservoir temperatures. Use it to analyze power plant performance, thermodynamics problems, and engine cycle analysis.
Heat engine efficiency formula
eta = W / Qh = 1 - Qc / Qh eta_Carnot = 1 - Tc / Th
eta is thermal efficiency (dimensionless, 0 to 1), W = Qh - Qc is net work output, Qh is heat absorbed (J), Qc is heat rejected (J). For Carnot efficiency, Tc and Th must be in Kelvin. The Carnot efficiency is the upper bound for any engine operating between those temperatures.
Real vs Carnot efficiency
- A steam power plant with Th = 800 K, Tc = 300 K has Carnot limit = 1 - 300/800 = 62.5%.
- Real steam plants achieve 35 to 45% due to heat losses, friction, and irreversibility.
- The ratio (actual efficiency / Carnot efficiency) is called the second-law efficiency or exergetic efficiency.
Frequently asked questions
What is thermal efficiency of a heat engine?
Thermal efficiency (eta) is the fraction of heat input that is converted to useful work: eta = W / Qh = 1 - Qc / Qh, where Qh is heat absorbed from the hot reservoir and Qc is heat rejected to the cold reservoir. Efficiency ranges from 0 to 1 (0% to 100%).
What is Carnot efficiency?
The Carnot efficiency is the theoretical maximum thermal efficiency for a heat engine operating between temperatures Tc and Th (in Kelvin): eta_Carnot = 1 - Tc / Th. No real engine can exceed this limit for given reservoir temperatures.
Can a heat engine ever be 100% efficient?
No. The second law of thermodynamics forbids 100% efficiency unless the cold reservoir is at absolute zero (0 K), which is physically impossible to achieve. Real engines have additional losses from friction, heat leaks, and irreversibilities.
What is the difference between efficiency and COP?
Heat engines are rated by efficiency (work output / heat input). Refrigerators and heat pumps are rated by COP (desired effect / work input). A heat engine with efficiency 0.35 converts 35% of heat to work; the remaining 65% is rejected.
What efficiencies do real heat engines achieve?
Steam turbine power plants: about 35 to 45% thermal efficiency. Combined-cycle gas turbines: up to 60%. Modern diesel engines: about 40 to 45%. These are well below the Carnot limit due to real-world irreversibilities.
Official sources
- OpenStax University Physics: 4.3 Heat Engines.
- ASHRAE: ASHRAE Handbook of Fundamentals (Thermodynamics).
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.