Thermal Efficiency Calculator

Background.

Thermal efficiency answers the bluntest question you can ask of an engine, boiler, or power cycle: of the heat you paid for, what fraction came back as the output you wanted? The definition is a plain ratio, η = W_useful / Q_in, and this page turns two measured energies into that percentage.

The measurements must share one boundary and one time interval — that discipline is where real efficiency figures are won or lost. Count the fuel's full heating value in but only shaft work out, and a petrol engine lands near 30%; quietly switch the output to “heat delivered to the cabin plus shaft work” and the number inflates past any fair comparison. The calculator treats the inputs as your declared boundary and does the arithmetic; the declaring is your job, and the model-scope note beside the result says so.

Typical magnitudes are worth memorising as sanity anchors: spark-ignition car engines 25–35%, modern diesels around 40%, simple-cycle gas turbines 35–40%, combined-cycle plants up to about 64%, home gas boilers 85–95% (a boiler's output is heat, so it escapes the work-conversion penalty entirely). A figure that beats these classes by a wide margin usually signals a boundary error, not a breakthrough.

The deep ceiling is Carnot's: no heat engine operating between a hot source at T_h and a cold sink at T_c can exceed η = 1 − T_c/T_h. A gas turbine breathing 1,500 K combustion gas against a 300 K ambient is capped at 80% before a single irreversibility is counted — real machines then lose their share to friction, finite-rate heat transfer, and exhaust enthalpy.

What is thermal efficiency calculator?

Thermal efficiency is the dimensionless ratio of useful energy delivered to heat energy supplied, over the same boundary and the same interval, expressed here as a percentage. For a heat engine the useful term is net work; for a furnace or boiler it is delivered heat. It is a first-law bookkeeping figure — it tells you what fraction of the input survived as intended output, and by subtraction how much left as waste heat, but it does not by itself say where those losses occur.

How to use this calculator.

1. 01Fix the boundary first: decide what counts as the machine, over which interval you are accounting, and stick to it for both numbers.
2. 02Enter the useful energy out — shaft work for an engine, delivered heat for a boiler — in joules (kWh work too, as long as both inputs use the same unit).
3. 03Enter the heat input over the same interval; for fuel, that is mass burned times heating value, and stating which heating value (higher or lower) matters at the few-percent level.
4. 04Read the percentage and place it against the typical range for the machine's class — 30% is respectable for a petrol engine and disastrous for a boiler.
5. 05If the result tops 100%, do not celebrate: some input energy crossed your boundary uncounted, or the output includes energy that was never part of Q_in.

The formula.

The first law guarantees the energy budget balances: Q_in = W_useful + Q_rejected. Efficiency takes the ratio of the term you want to the term you paid for, η = W_useful/Q_in, and multiplying by 100 states it as a percentage — the calculator's only two operations, done in Decimal arithmetic with a single rounding at the end. The second law then bounds what the ratio can be for any cyclic heat engine: η ≤ 1 − T_c/T_h (temperatures in kelvin), the Carnot limit, reached only by a reversible cycle operating infinitely slowly. The gap between a machine's measured η and its Carnot ceiling is the engineer's loss budget: exhaust enthalpy, incomplete combustion, friction, and heat leaking around the working fluid. Note what the ratio deliberately excludes — it says nothing about power (a slow engine can be efficient and useless), emissions, or cost per joule.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, University Physics Volume 2, section 4.5, The Second Law of Thermodynamics.
2. [2]Çengel and Boles, Thermodynamics: An Engineering Approach, 10th ed. (PRINT).
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.