Carnot Cycle Efficiency Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
Carnot efficiency is calculated with η = 1 − (Tcold ÷ Thot), in kelvins. Between a cold source at 300 K and a hot source at 600 K, the maximum theoretical efficiency reaches 50%.
Explanation
The Carnot cycle, formulated by physicist Sadi Carnot in 1824, describes the absolute maximum theoretical efficiency that any heat engine (motor, power plant) can reach when operating between a hot source and a cold source of given temperatures. It's a fundamental limit of thermodynamics, not a technological constraint that a better design could work around: no real machine, however well designed, can exceed this theoretical efficiency between the same two temperatures, a direct consequence of the second law of thermodynamics. Perhaps the most counterintuitive result of this formula is that 100% efficiency is only achievable in a limiting case impossible in practice: either a cold source at absolute zero (0 K, a physically unreachable temperature), or an infinitely hot source. In practice, real heat engines (combustion engines, thermal power plants) always achieve efficiency noticeably below this theoretical Carnot ceiling, because of real losses (friction, imperfect heat transfers, various irreversibilities) that the ideal Carnot cycle doesn't account for. This theoretical efficiency nonetheless remains a valuable benchmark in engineering: it sets the absolute upper limit that any optimization can approach, without ever perfectly reaching it, and lets you judge how close or far a real machine is from this theoretical ideal, a gap directly quantifiable with our energy efficiency calculator. The gas used in the cycle also follows our ideal gas law calculator at each stage of the cycle.
Example: cold source at 300 K, hot source at 600 K
Inputs
Cold temperature: 300 K. Hot temperature: 600 K.
Calculation
η = 1 − (300 ÷ 600) = 1 − 0.5 = 0.5, or 50%.
Result
The maximum theoretical efficiency between these two sources is 50%.
Frequently asked questions
Why use kelvins rather than degrees Celsius in this formula?
Because kelvin is an absolute temperature scale, where 0 K corresponds to absolute zero (the total absence of thermal energy): it's this absolute reference that gives physical meaning to the ratio of the two temperatures in the formula. Using degrees Celsius, a relative scale with an arbitrary zero, would give an incorrect result, since the ratio of two Celsius temperatures has no coherent physical meaning.
Why do real heat engines have lower efficiency than Carnot?
Because the Carnot cycle is an ideal theoretical model, entirely reversible and with no parasitic energy loss. Real machines inevitably experience mechanical friction, imperfect heat transfers between the system's different parts, and other irreversible phenomena that dissipate part of the available energy, reducing actual efficiency well below this absolute theoretical limit.
Why does a power plant seek very high operating temperatures?
Because the larger the gap between the hot temperature and the cold temperature (relative to the hot temperature), the higher the theoretical Carnot efficiency: raising the hot source's temperature (within the limits of what the plant's materials can withstand) therefore brings the maximum achievable efficiency closer to 100%, which explains the constant search for materials able to withstand ever higher temperatures in thermal power plant design.