Heat Engine Efficiency Calculator

Efficiency η is the ratio of useful work output to heat absorbed from the hot reservoir: η = W_out / Q_hot. Using energy conservation, you can also write η = 1 − Q_cold/Q_hot, where Q_cold is heat rejected to the cold reservoir. Express η as a decimal or percentage. An engine that absorbs 1000 J and produces 300 J of work has η = 0.30, or 30%. Real engines lose the rest as heat to surroundings. No engine working between two reservoirs can beat the Carnot limit, which depends only on the temperatures.

Carnot efficiency sets the ceiling for any heat engine working between two temperatures: η = 1 − T_cold/T_hot, with both temperatures in kelvin. So an engine running between 800 K and 300 K has a maximum efficiency of 1 − 300/800 = 0.625, or 62.5%. The calculator does the kelvin conversion if you input Celsius, but you must enter both as absolute temperatures or the ratio falls apart. Carnot's result tells you the best you could possibly do with reversible processes — real engines always come in lower because of friction, finite-time heat transfer, and other irreversibilities.

Once you know the efficiency η and the heat input Q_hot, the work output follows directly: W = η × Q_hot. So a 35% efficient engine fed 5000 J extracts W = 0.35 × 5000 = 1750 J of useful work. The other 3250 J leaves as waste heat. This is how power plant designers estimate net output: they know the fuel's heat content and the cycle efficiency, then multiply. Reverse-solving works too — known work and efficiency tell you how much heat you must supply, useful for sizing boilers and combustion chambers.

Carnot's formula η = 1 − T_c/T_h depends on the ratio of two temperatures, and that ratio only makes physical sense on an absolute scale. Celsius lets temperatures go negative, which would give nonsensical efficiencies above 100% or below zero. Kelvin starts at absolute zero, where all thermal motion stops, so every kelvin temperature is positive and ratios behave properly. Forgetting this conversion is one of the most common errors I see — students plug in 100 °C and 25 °C instead of 373 K and 298 K, and end up with wildly wrong answers.

No, never. Carnot efficiency is the absolute upper bound for any heat engine working between two given temperatures, and the second law of thermodynamics forbids exceeding it. If anyone claims otherwise, they've either ignored hidden energy inputs or run afoul of the laws of physics. Real engines always fall short because of irreversibilities — friction, viscous losses, finite-time heat transfers, leaks. Modern combined-cycle gas plants reach about 60% efficiency, which is impressive given how close that is to their Carnot limit. Beating Carnot would mean building a perpetual motion machine of the second kind.

From energy conservation: Q_cold = Q_hot − W. Whatever heat enters minus the useful work done equals the heat dumped to the cold reservoir. So an engine that absorbs 1200 J and produces 400 J of work must reject 800 J as waste heat. Equivalently, Q_cold = Q_hot × (1 − η). This rejected heat is exactly why power stations need cooling towers, rivers, or ocean inlets — there's always a thermodynamic tax that has to leave the system. A higher-efficiency engine rejects less of its input, but always something.

Plug in the hot reservoir temperature and the cold reservoir temperature, both in kelvin, and the calculator returns η_Carnot = 1 − T_c/T_h. For a steam engine running between 600 K (boiler) and 350 K (condenser), η_max = 1 − 350/600 ≈ 0.417, or 41.7%. That's the theoretical best — real engines achieve maybe two-thirds of this in practice. The bigger the gap between hot and cold reservoirs, the higher the ceiling. That's why high-temperature combustion chambers and very cold sinks both raise efficiency, and why this calculation matters for power plant design.