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Carnot Efficiency Calculator

Find the theoretical maximum efficiency between two temperatures.

Result

61.44%
0.63

How it is calculated

The Carnot efficiency is the theoretical upper limit for any heat engine working between a hot and a cold reservoir: η = 1 − Tc ÷ Th. The temperatures must be absolute, so the tool takes your hot and cold values in °C and adds 273.15 to get kelvin. The hot temperature must be above the cold one and both must be above absolute zero. The efficiency is shown as a percentage. The tool also gives the Carnot cooling coefficient of performance, Tc ÷ (Th − Tc), which applies to an ideal refrigerator between the same temperatures. Real engines are always below the Carnot value because of friction, heat losses and irreversibility.

Worked example

A heat source at 500 °C and surroundings at 25 °C. Convert to kelvin: Th = 773.15 K, Tc = 298.15 K. Ratio: 298.15 ÷ 773.15 = 0.3856. Efficiency: 1 − 0.3856 = 0.6144, shown as 61.44%. No engine can convert more than about 61% of the heat into work between these two temperatures. The cooling coefficient of performance is 298.15 ÷ 475 = 0.63.

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Common mistakes

  • Using °C in the ratio instead of kelvin. (1 − 25 ÷ 500) gives 95%, a wildly wrong answer, because the ratio must be taken of absolute temperatures.
  • Entering the temperatures in °F or K. The fields expect °C; K values would be offset by 273.
  • Swapping hot and cold. If the hot value is not above the cold value, no result is shown.
  • Expecting a real engine to reach this figure. It is an upper bound for an ideal reversible engine; real engines reach a fraction of it.
  • Using the cooling coefficient for a heat engine. That value belongs to refrigerators, and can be above 1 when the temperature difference is small.

Sources

About this calculator

This calculator finds the theoretical Carnot efficiency of a heat engine: η = 1 − Tc/Th, where Tc and Th are the absolute (Kelvin) temperatures of the cold and hot reservoirs. This is the maximum efficiency any heat engine can achieve between those two temperatures, as set by the second law of thermodynamics — no real engine can exceed it.

Mechanical and thermal engineers use it as a benchmark when designing power plants, engines, or refrigeration cycles, comparing a real machine's actual efficiency against this theoretical ceiling to see how much room for improvement remains. Physics students use it to build intuition for the second law.

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Comments (1)

  • Editorial team

    The cooling figure shown is for an ideal refrigerator. For an ideal heat pump between the same two temperatures, the heating coefficient is that value plus one: with the 500 and 25 degree case it would be about 1.63 rather than 0.63. Real machines fall well short of both numbers, so use them as ceilings when judging a datasheet. Are you checking a power cycle, a fridge or a heat pump? Tell us which output you would want next.

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