Carnot Efficiency Calculator

This Carnot efficiency calculator gives the theoretical upper limit on how much of the heat flowing from a hot reservoir to a cold one can be turned into work. Enter the hot and cold temperatures in °C, °F or kelvin and it returns the Carnot efficiency, the ideal coefficient of performance (COP) for a refrigerator and a heat pump working between the same temperatures, and — if you give a heat input — the maximum work output and the heat that must be rejected.

Students use it for thermodynamics homework on the second law; engineers and energy enthusiasts use it to sanity-check claims about power plants, engines, solar-thermal systems or heat pumps. No real machine reaches the Carnot limit, so comparing an actual efficiency or COP with the ideal value shows how much room for improvement there is.

The formula only works with absolute temperatures, so the calculator converts everything to kelvin first. The hot reservoir must be hotter than the cold one; if the temperatures are equal, no work can be extracted and the ideal COP becomes unbounded.

A Carnot engine is a reversible cycle of two isothermal and two adiabatic steps. Because it generates no entropy, Qc/Qh = Tc/Th, so the fraction of heat converted to work is η = 1 − Tc/Th. Any real engine operating between the same two temperatures is less efficient, which is one statement of the second law of thermodynamics.

Running the cycle backwards gives an ideal refrigerator, whose coefficient of performance is the heat removed per unit work, Tc/(Th − Tc), or an ideal heat pump, which delivers Th/(Th − Tc) units of heat per unit work. Temperatures must be absolute (kelvin); the calculator converts °C with K = °C + 273.15 and °F with K = (°F − 32) × 5/9 + 273.15.