Carnot Efficiency Calculator
Calculate the maximum theoretical efficiency of a heat engine (Carnot efficiency) and the maximum COP for heat pumps and refrigerators.
The Carnot cycle sets the theoretical maximum efficiency for any heat engine operating between two temperatures:
η_Carnot = 1 − T_cold/T_hot
For refrigerators and heat pumps: COP_refrigerator = T_cold / (T_hot − T_cold) COP_heat_pump = T_hot / (T_hot − T_cold)
Where temperatures must be in Kelvin.
What does Carnot efficiency mean?
No real heat engine can exceed Carnot efficiency. This is a consequence of the Second Law of Thermodynamics. Even a perfect engine (no friction, no heat losses) is limited by the temperature difference between the hot and cold reservoirs.
Real engine efficiencies vs. Carnot:
- Modern coal power plant: actual 33–40%, Carnot limit ≈ 60%
- Combined cycle gas turbine: actual 55–60%, Carnot limit ≈ 65%
- Steam locomotive: actual 5–10%, Carnot limit ≈ 40%
- Car engine (gasoline): actual 20–35%, Carnot limit ≈ 55%
COP of heat pumps: A heat pump with COP = 4 means it delivers 4 kW of heat for every 1 kW of electricity — it “moves” heat rather than generating it. Air-source heat pumps in mild climates typically achieve COP = 3–5.
The Carnot COP represents the maximum achievable. Real heat pumps achieve 40–60% of Carnot COP.