Carnot Efficiency Calculator

Formula

How this is calculated

Enter the hot reservoir temperature (T_hot) and the cold reservoir temperature (T_cold). A unit selector lets you supply values in kelvin or degrees Celsius; Celsius inputs are converted to kelvin by adding 273.15, because the Carnot relation is only valid on the absolute temperature scale.

The Carnot efficiency is η = 1 − T_cold / T_hot. This is the upper bound on the fraction of heat energy that any real heat engine can convert to useful work while operating between these two temperatures; no engine can exceed it. The donut chart splits incoming heat into the useful-work fraction (η) and the unavoidable wasted heat rejected to the cold reservoir (1 − η). Running the cycle in reverse gives refrigeration and heating, with coefficients of performance COP_fridge = T_cold / (T_hot − T_cold) and COP_heatpump = T_hot / (T_hot − T_cold).

The model assumes an idealized reversible cycle, so real machines always fall short due to friction, finite heat-transfer rates, and irreversibilities. Both temperatures must be above absolute zero, and T_hot must exceed T_cold; otherwise the result is undefined and the calculator asks for valid inputs. As T_cold approaches T_hot the efficiency tends to zero, and efficiency rises toward 1 only as T_cold approaches absolute zero.