Thermal Efficiency Calculator — Heat Engine η
Find how efficiently a heat engine converts absorbed heat into useful work. Enter heat input and heat rejected (or work output) to get the thermal efficiency η and see the energy split.
Known quantities
J
J
Fraction of absorbed heat converted to useful work
40%
efficiencyUseful work W
40%
Rejected heat Qc
60%
- 1
Net work W = Qh − Qc
1,000 − 600 = 400 - 2
Thermal efficiency η = W ÷ Qh × 100
400 ÷ 1,000 × 100 = 40
How does this calculator work?
Thermal efficiency η = W/Qh = (Qh − Qc)/Qh, where Qh is heat absorbed from the hot source, Qc is heat rejected to the cold sink, and W is useful work output. Enter any two of these three quantities to get efficiency and the full energy split. No real engine can reach 100%.
Formula
How this is calculated
A heat engine operates between a hot reservoir and a cold sink. In each cycle it absorbs heat Qh from the hot source, converts part of it into net work W, and rejects the remainder Qc to the cold sink. The first law demands Qh = W + Qc, so W = Qh − Qc. Thermal efficiency η = W / Qh measures the fraction of the input heat that becomes useful work; it ranges from 0 (no work produced) to 1 (impossible 100 % conversion forbidden by the second law).
You can supply either the pair (Qh, Qc) or the pair (W, Qh) — the calculator derives the missing quantity. Real engines always have η well below 1 due to irreversibilities such as friction, heat losses, and finite temperature differences. The theoretical maximum is the Carnot efficiency η_Carnot = 1 − T_c/T_h, achievable only with reversible processes — use the Carnot efficiency calculator to find that upper bound.
This calculator makes no assumptions about the working fluid or cycle type — the formula is universal. The energy-split donut shows how much of Qh is converted to work versus wasted as Qc.
Frequently asked questions
The second law of thermodynamics (Kelvin–Planck statement) prohibits a heat engine from converting all absorbed heat into work in a cycle — some heat must always be rejected to a cold sink. The maximum achievable efficiency is the Carnot efficiency, set by the absolute temperatures of the two reservoirs.
Thermal efficiency η = W/Qh is the actual measured ratio of work to heat input for a real engine. Carnot efficiency η_c = 1 − T_c/T_h is the maximum theoretical efficiency for any engine operating between the same two temperature reservoirs. Real engines always have η < η_c due to irreversibilities.
Refrigerators and heat pumps are rated by COP (coefficient of performance), not thermal efficiency. For a refrigerator COP = Qc/W, and for a heat pump COP = Qh/W. This calculator is designed for heat engines that produce work from heat.
Also known as
TG we-Calculate Editorial Team. (2026). Thermal Efficiency Calculator — Heat Engine η [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/thermal-efficiency-calculator
TG we-Calculate Editorial Team. "Thermal Efficiency Calculator — Heat Engine η." TG we-Calculate. 2026. https://we-calculate.com/calculator/thermal-efficiency-calculator.
TG we-Calculate Editorial Team, "Thermal Efficiency Calculator — Heat Engine η," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/thermal-efficiency-calculator
@misc{wecalculate_thermal_efficiency_calculator, title = {Thermal Efficiency Calculator — Heat Engine η}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/thermal-efficiency-calculator}}, year = {2026}, note = {TG we-Calculate} }
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