Heat Engine Efficiency Calculator
Compute a heat engine’s thermal efficiency from the heat it absorbs and either the work it does or the heat it rejects.
Given inputs
J
J
Fraction of heat input converted to useful work: 0.35
35%
efficiencyUseful work W
35%
Rejected heat Qc
65%
- 1
Rejected heat (Qc = Qh − W)
1,000 − 350 = 650 - 2
Thermal efficiency (η = W ÷ Qh × 100)
350 ÷ 1,000 × 100 = 35
How does this calculator work?
A heat engine’s thermal efficiency is η = W / Qh = 1 − Qc / Qh, where Qh is heat absorbed, W is work output, and Qc is rejected heat, linked by Qh = W + Qc. Enter Qh plus either W or Qc; the calculator returns efficiency as a fraction and percent along with the missing energy.
Formula
How this is calculated
A heat engine takes in heat Qh from a hot reservoir, converts part of it into useful work W, and dumps the remainder Qc into a cold reservoir. Energy conservation over one complete cycle requires Qh = W + Qc, since the working substance returns to its initial state and stores no net energy.
Thermal efficiency is the ratio of what you get (work) to what you pay for (heat input): η = W / Qh. Substituting the energy balance gives the equivalent form η = 1 − Qc / Qh. This calculator accepts either pair of known values: given Qh and W it finds Qc = Qh − W; given Qh and Qc it finds W = Qh − Qc. Efficiency is reported both as a dimensionless fraction and as a percentage.
All energies must use the same unit (joules here, though any consistent unit works since the ratio is unitless). Qh must be positive. For a physically valid engine 0 < W < Qh, so efficiency lies between 0 and 1; the second law forbids η = 1. If you enter W greater than Qh or a negative Qc, the implied rejected heat becomes negative, signalling inconsistent inputs.
Frequently asked questions
The second law of thermodynamics requires every cyclic heat engine to reject some heat Qc to a cold reservoir, so W is always less than Qh and η = W/Qh stays below 1.
This is the actual (real) efficiency computed from measured energies. Carnot efficiency, 1 − Tc/Th, is the theoretical maximum set only by reservoir temperatures; a real engine’s η is always at or below it.
Only consistency matters. Because efficiency is a ratio of energies, any unit works as long as all three quantities share it. The fraction and percentage are unitless.
Also known as
TG we-Calculate Editorial Team. (2026). Heat Engine Efficiency Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/heat-engine-efficiency-calculator
TG we-Calculate Editorial Team. "Heat Engine Efficiency Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/heat-engine-efficiency-calculator.
TG we-Calculate Editorial Team, "Heat Engine Efficiency Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/heat-engine-efficiency-calculator
@misc{wecalculate_heat_engine_efficiency_calculator, title = {Heat Engine Efficiency Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/heat-engine-efficiency-calculator}}, year = {2026}, note = {TG we-Calculate} }
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