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Carnot Heat Engine Efficiency Calculator

Carnot's Theorem establishes the Second-Law thermodynamic upper bound on thermal efficiency η for any heat engine operating between a hot source at absolute temperature T_H and cold sink at T_C.

η (%) = (1 - T_C / T_H) × 100
Pick which value you want to calculate (or type into any field):Solving for: η (%) — Carnot Thermal Efficiency
Calculated

Maximum theoretical work output per unit heat input (%)

199
%

Heat sink absolute temperature in Kelvin (27 °C = 300.15 K)

12,000.00
unit

Heat source absolute temperature in Kelvin

505,000.00
unit
Calculated Result · Carnot Thermal Efficiency (η (%))
62.5

Step-by-Step Calculation

01Canonical Law: η (%) = (1 - T_C / T_H) × 100
02Given Inputs (Base Units): T_C (K) = 300, T_H (K) = 800
03Solve for η (%) (Carnot Thermal Efficiency): η (%) = 62.5

Carnot's Theorem establishes the Second-Law thermodynamic upper bound on thermal efficiency η for any heat engine operating between a hot source at absolute temperature T_H and cold sink at T_C.

Real-World Reference Values

Combined-Cycle Gas Turbine (CCGT)62% – 64% Real Efficiency

T_H ≈ 1,700 K firing temperature (~82% Carnot limit)

Supercritical Steam Rankine Plant42% – 47% Real Efficiency

T_H ≈ 873 K (600 °C) steam conditions

Geothermal Binary ORC Plant10% – 16% Real Efficiency

Constrained by low T_H ≈ 420 K (150 °C) brine

20-Row Comparison Table

Carnot Thermal Efficiency (η (%)) · Cold Reservoir Temperature (K) (T_C (K))

Carnot Heat Engine Efficiency Calculator — Cold Reservoir Temperature (K) → Carnot Thermal Efficiency
#Cold Reservoir Temperature (K) (T_C (K))Carnot Thermal Efficiency (η (%))Δ %
0175.1125 90.6109 +44.98%
02101.4151 87.3231 +39.72%
03127.7178 84.0353 +34.46%
04154.0204 80.7475 +29.20%
05180.323 77.4596 +23.94%
06206.6257 74.1718 +18.67%
07232.9283 70.884 +13.41%
08259.2309 67.5961 +8.15%
09285.5336 64.3083 +2.89%
10300 Current62.5 0.00%
11338.1388 57.7326 -7.63%
12364.4414 54.4448 -12.89%
13390.7441 51.157 -18.15%
14417.0467 47.8692 -23.41%
15443.3493 44.5813 -28.67%
16469.652 41.2935 -33.93%
17495.9546 38.0057 -39.19%
18522.2572 34.7178 -44.45%
19548.5599 31.43 -49.71%
20574.8625 28.1422 -54.97%
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Frequently Asked Questions

Why must T_C and T_H be in absolute Kelvin rather than Celsius?+

Thermodynamic entropy ratios (dQ/T) are defined strictly relative to absolute zero (0 K = -273.15 °C).

Why can no heat engine ever reach 100% Carnot efficiency?+

Achieving η = 100% would require either a cold sink at absolute zero (T_C = 0 K, forbidden by the Third Law) or an infinite hot source temperature.

Which improves efficiency faster: raising T_H by 50 K or lowering T_C by 50 K?+

Lowering the cold sink temperature T_C by ΔT always yields a larger percentage gain in Carnot efficiency than raising T_H by the same ΔT.