Last updated: 2026-06-15

Carnot Efficiency

Every heat engine — a car engine, a steam turbine, a jet — takes in heat at a high temperature, turns some of it into work, and dumps the rest at a lower temperature. The Carnot efficiency is the hard ceiling on how much of that heat any engine could ever convert to work, set purely by the two temperatures it runs between. No clever design can beat it. This calculator finds that ceiling, and the work and waste heat that follow from a given heat input.

Where the formula comes from

Sadi Carnot imagined a perfectly reversible engine — no friction, no turbulence, no rushed heat transfer. For such an ideal cycle the heat exchanged with each reservoir is proportional to its absolute temperature, so the fraction of heat not converted to work is exactly $T_c/T_h$. The efficiency, the fraction that is converted, is therefore $\eta = 1 - T_c/T_h$. Because real engines are irreversible, they always do worse.

Formula

Both temperatures must be absolute (kelvin), because the formula uses their ratio.

Worked example

An engine running between $T_h = 600\ \text{K}$ and $T_c = 300\ \text{K}$, taking in $Q_h = 1000\ \text{J}$ per cycle:

So even a flawless engine between these temperatures could turn only half the heat into work; the other half must be rejected to the cold side.

Why you can never reach 100%

Efficiency would hit 100% only if $T_c/T_h = 0$ — a cold reservoir at absolute zero, or a hot one at infinite temperature. Both are out of reach, which is the second law of thermodynamics stated as a number: some heat must always be thrown away. The practical lesson is that the way to a more efficient engine is to widen the temperature gap, usually by running the hot side as hot as the materials allow.

Limitations

The Carnot value is an idealised upper bound, not a prediction of any real engine's output. Actual engines lose efficiency to friction, finite-speed heat transfer, leaks and exhaust losses, so they reach only a fraction of the Carnot limit. The formula also assumes two fixed-temperature reservoirs and a reversible cycle; engines with changing temperatures (like the real Otto or Brayton cycles) have their own, lower efficiency expressions.