♨️ Carnot Efficiency Calculator
Find the theoretical maximum efficiency of a heat engine from its hot and cold reservoir temperatures (η = 1 − T_c/T_h).
Efficiency η
0.5 (50.00%)
Carnot (maximum) efficiency: η = 1 − T_cold/T_hot, with temperatures in kelvin. Real engines fall below this limit. 🔒 Computed in your browser.
How the carnot efficiency calculator works
The Carnot efficiency is the highest any heat engine can achieve between two temperatures: η = 1 − T_cold/T_hot, with both temperatures in kelvin. Enter the two reservoir temperatures and the tool gives the efficiency (as a fraction and percentage); real engines always fall below this ideal limit.
Temperatures must be absolute (kelvin). No real engine reaches Carnot efficiency because of friction, irreversibility and finite heat transfer. It’s an upper bound.
Frequently asked questions
What is Carnot efficiency?
The maximum possible efficiency of a heat engine operating between two temperatures: η = 1 − T_cold/T_hot (in kelvin). It sets the ceiling no real engine can beat.
How do I calculate it?
Divide the cold-reservoir temperature by the hot-reservoir temperature (both in K) and subtract from 1. For T_h = 600 K and T_c = 300 K, η = 1 − 0.5 = 0.5 (50%).
Why must temperatures be in kelvin?
The formula uses absolute temperature ratios, which only make sense from absolute zero. Convert with K = °C + 273.15.
Can a real engine reach Carnot efficiency?
No, friction, heat loss and irreversibility always make real engines less efficient. Carnot is a theoretical maximum, useful as a benchmark.
How can I raise the efficiency?
Increase the hot temperature or decrease the cold temperature (a larger gap). That’s why power plants run boilers as hot as materials allow.
Worked example with Celsius inputs
A turbine runs between 400 °C and 30 °C. Convert to kelvin first: 673.15 K and 303.15 K. η = 1 − 303.15/673.15 ≈ 0.55, so at most about 55% of the heat input can become useful work.
What is the efficiency if the two temperatures are equal?
Zero. If T_cold = T_hot, then T_cold/T_hot = 1 and η = 0, with no temperature difference no heat engine can extract work. A larger gap between the reservoirs raises the ceiling.
Does Carnot efficiency depend on the working substance?
No. It depends only on the two absolute temperatures, not on whether the engine uses steam, air or any other fluid. That universality is a central result of the second law of thermodynamics.
What is the coefficient of performance of a fridge?
Running a Carnot cycle in reverse (a fridge or heat pump), the ideal coefficient of performance for cooling is T_cold/(T_hot − T_cold), a different measure from engine efficiency, describing heat moved per unit of work put in.
Why does raising the hot temperature help so much?
Because η = 1 − T_cold/T_hot, a higher T_hot lowers the ratio and lifts the ceiling. That is why power stations run their boilers as hot as the turbine materials safely allow, every extra degree buys a little more possible efficiency.