Carnot Efficiency Calculator
Maximum theoretical efficiency of a heat engine between two temperatures, plus the Carnot COP for a refrigerator or heat pump working between the same reservoirs.
How it works
η = 1 − T_cold ÷ T_hot (kelvin) · COP_ref = T_c ÷ (T_h − T_c) · COP_hp = T_h ÷ (T_h − T_c)
The second law caps every heat engine at the Carnot efficiency, which depends only on the absolute temperatures of the reservoirs — widen the gap and the ceiling rises. Real engines fall well short: a car engine at 500 °C exhaust and 25 °C ambient has a Carnot limit of 61% but achieves about 30%. The same relation gives the maximum coefficient of performance for fridges and heat pumps.
Worked example
T_h = 500 °C (773 K), T_c = 25 °C (298 K): η = 1 − 298/773 = 61.4%.
Frequently asked questions
Why must I use kelvin?
The ratio only works on an absolute scale; using °C would give nonsense like negative efficiencies.
Can a heat pump COP be above 1?
Yes — a heat pump moves heat rather than creating it, so a COP of 3–5 is normal and the Carnot value is the ceiling.
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This calculator is for educational purposes. Double-check important results before acting on them.