Carnot Efficiency Calculator
Work out the Carnot efficiency — the highest fraction of heat that any engine could ever turn into work while operating between a hot and a cold reservoir. Enter the two reservoir temperatures in degrees Celsius and the calculator converts them to kelvin and applies η = 1 − Tc/Th.
Enter Values
How to use this calculator
- Enter the hot reservoir temperature Th in °C (for example, the combustion or steam temperature).
- Enter the cold reservoir temperature Tc in °C (for example, cooling water or ambient air). It must be colder than the hot side.
- Read the Carnot efficiency as both a fraction and a percentage, plus both temperatures shown in kelvin.
How it works
The Carnot efficiency uses absolute (kelvin) temperatures, so each Celsius input is converted with K = °C + 273.15. The maximum possible efficiency is η = 1 − Tc/Th. Because it depends only on the ratio of the two absolute temperatures, a bigger temperature gap gives a higher ceiling. This is a limit, not a prediction: no real engine reaches it because friction, turbulence and heat losses are all irreversible.
Worked example
Worked example. With a hot side of 300 °C (573.15 K) and a cold side of 30 °C (303.15 K), η = 1 − 303.15/573.15 = 0.4711, or 47.11 %. So even a perfect engine between those temperatures could convert at most about 47 % of the heat into work.
Common mistakes
- Using Celsius directly in η = 1 − Tc/Th. The formula only works with absolute temperatures — always convert to kelvin first.
- Swapping the hot and cold values. Tc must be the colder reservoir; if Tc ≥ Th the formula is meaningless.
- Treating the result as a real-world efficiency. It is a theoretical ceiling; actual engines run far below it.
Frequently asked questions
Why does Carnot efficiency need kelvin?
The ratio Tc/Th is only physically meaningful on an absolute scale where zero is absolute zero. Using Celsius (which puts zero at the freezing point of water) would give the wrong ratio and can even produce nonsense like negative or infinite efficiency.
Can a real engine reach the Carnot efficiency?
No. Carnot efficiency assumes a perfectly reversible cycle with no friction or heat loss. Real engines have irreversibilities everywhere, so their efficiency is always lower — often less than half of the Carnot value.
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Tip: Enter any known values to calculate the remaining results.
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