The Carnot Efficiency Calculator finds the theoretical ceiling on how efficient any heat engine can be, based only on its hot and cold reservoir temperatures. It's the benchmark engineers compare real engines against — a turbine, a car engine, or a power plant can never beat it, only approach it.
How the Carnot Efficiency Calculator works
The calculator applies η = 1 − Tc/Th, the formula French engineer Sadi Carnot derived in 1824 for an idealized, fully reversible heat engine. Th and Tc are absolute temperatures in Kelvin — the hot source the engine draws heat from, and the cold sink it rejects heat to. The result, η, is the maximum fraction of that heat which any engine — real or ideal — can convert into useful work while operating between those two temperatures.
This is a consequence of the second law of thermodynamics, not an engineering limitation: even a perfectly frictionless, lossless engine still cannot convert all its heat input into work, because some heat must flow to the cold reservoir to complete the cycle. When a heat input (Qin) is supplied, the calculator multiplies it by η to show the maximum possible work output, and the remainder as rejected heat.
Inputs and what they mean
Th (hot reservoir) and Tc (cold reservoir) must both be entered in Kelvin — using Celsius or Fahrenheit will give a meaningless ratio, since those scales don't start at absolute zero. Typical ranges: a car engine might run Th around 800-1,200 K against an ambient Tc near 300 K; a coal power plant boiler might reach 800-900 K against a condenser near 300-320 K. The gap between Th and Tc, not either temperature alone, is what drives efficiency — a small ΔT caps the ceiling low even if both temperatures are high.
Qin (heat input, in joules) is optional — it's only needed to compute a work output on the Work Output tab. Leave it at the default or enter your own value; it does not affect the efficiency percentage itself.
Limits and edge cases
This calculator computes the Carnot (ideal, reversible) efficiency — it is always an upper bound, never an achievable target. Real engines lose additional efficiency to friction, turbulence, incomplete combustion, and heat leakage, so their actual thermal efficiency (W/Qin measured directly) sits well below the Carnot number shown here. If Th is not greater than Tc, the formula is non-physical and the calculator will flag the input rather than show a negative or meaningless efficiency. As Tc approaches absolute zero (0 K) the Carnot efficiency approaches 100% — but 0 K is unreachable in practice, per the third law of thermodynamics, so 100% efficiency is never attainable.