Carnot Efficiency Calculator
Enter the cold and hot reservoir temperatures in kelvin to get the maximum possible efficiency of a heat engine — the hard limit no real machine can beat.
Fraction and percentage
Enter the two temperatures and the Carnot efficiency calculator returns the efficiency both as a fraction (0–1) and as a percentage.
Use kelvin
Temperatures must be absolute — add 273.15 to a Celsius value before you enter it, and keep the hot temperature above the cold one.
What is the Carnot efficiency?
The ceiling on every heat engine
The Carnot efficiency calculator gives the theoretical maximum fraction of heat that a heat engine can turn into useful work while running between a hot reservoir and a cold reservoir. Named after Sadi Carnot, it depends only on the two absolute temperatures — not on the working fluid, the design, or the fuel. It is an upper limit set by the second law of thermodynamics: a perfectly reversible engine would reach it, and every real engine falls short. Knowing it tells you the best you could ever hope for before friction, heat leaks, and finite-speed losses take their cut.
Enter the cold and hot temperatures in kelvin to get the maximum efficiency as a fraction and as a percentage instantly.
The Carnot efficiency is one minus the ratio of the cold reservoir temperature to the hot reservoir temperature, with both temperatures measured on the absolute (kelvin) scale.
η = 1 − T_cold / T_hotA worked example makes the steps clear. Suppose an engine draws heat from a 500 K source and rejects it to surroundings at 300 K. First take the ratio of the temperatures: 300 / 500 = 0.6. Then subtract it from one: 1 − 0.6 = 0.4. The Carnot efficiency is 0.4, or 40% once multiplied by 100. The wider the gap between the hot and cold temperatures, the closer the ratio gets to zero and the higher the efficiency climbs — which is why power plants run their boilers as hot as the materials allow and dump waste heat as cold as they can.
The formula is exact, but it describes an ideal that no hardware reaches.
A theoretical maximum in absolute temperature
The Carnot efficiency is the theoretical maximum, not a prediction of what a real engine delivers — friction, turbulence, heat leaks, and finite-speed heat transfer all push actual efficiency well below it. Temperatures must be absolute: enter them in kelvin (add 273.15 to a Celsius value), keep the hot temperature above the cold one, and keep the cold temperature at or above zero, so the efficiency stays inside its valid 0–1 range.