Carnot Efficiency Calculator

The maximum possible efficiency of a heat engine, η = 1 - T_cold/T_hot, with temperatures in kelvin.

The ratio T_cold/T_hot is only physically meaningful on an absolute scale; using °C or °F gives wrong results.

No real engine matches the Carnot limit because of friction, finite-time heat transfer, and other irreversibilities - it is an upper bound.

Raise the hot-reservoir temperature or lower the cold-reservoir temperature; widening the gap increases the ceiling.

Carnot is an idealized reversible cycle between two fixed temperatures and always sits above any real cycle running between the same extremes. Practical cycles add and reject heat over a range of temperatures and generate entropy, so their theoretical limits are lower and their actual efficiencies lower still. A steam Rankine plant might reach 33-45% where Carnot says 55%; a gasoline Otto engine typically runs 25-35%; a gas-turbine Brayton cycle around 35-40%, more in combined-cycle plants. Use the Carnot number as a ceiling to benchmark against, not as the efficiency a real machine will hit.

The Carnot COP is the ceiling, and real heat pumps fall below it. A typical residential air-source heat pump has a COP of about 3 to 4 in mild conditions, and ground-source (geothermal) units often reach 4 to 5, while the Carnot COP for the same temperatures can be much higher. COP drops as the gap between indoor and outdoor temperature widens, which is why heat pumps lose efficiency on very cold days. A COP of 3 still means 3 units of heat delivered per unit of electricity, because the device moves heat rather than generating it.