Carnot Efficiency Calculator
The theoretical efficiency limit of reversible heat engines — no real engine can exceed it.
η = 1 − Tc / ThTh = hot-reservoir temperature, Tc = cold-reservoir temperature — both in Kelvin (absolute temperature). Entering °C directly is the classic mistake: 1 − 20/500 = 96% is wrong; the correct value is 62.08%.
Mode 1 — Efficiency from two reservoir temperatures
Physical requirement: Th > Tc > 0 K. If Tc ≥ Th, it is not a heat engine (no work can be extracted).
Mode 2 — Required hot-reservoir temperature (Th)
Formula: Th = Tc / (1 − η) — for a target efficiency η and a known cold temperature Tc.
η = 100% is impossible: it would require Tc = 0 K (absolute zero, unattainable) or an infinite Th.
Mode 3 — Allowed cold-reservoir temperature (Tc)
Formula: Tc = Th × (1 − η) — for a target efficiency η and a known hot temperature Th.
Solar panels are NOT heat engines — they do not convert heat into work through a thermal cycle, so Carnot efficiency does not apply to them. The theoretical limit of a single-junction solar panel is the Shockley–Queisser limit (~33.7%).
Verified examples
| Case | Th | Tc | Carnot η |
|---|---|---|---|
| Anchor: 500 °C / 20 °C | 773.15 K | 293.15 K | 62.08% |
| Gasoline engine (preset) | 2500 K | 350 K | 86.00% |
| Steam power plant (preset) | 800 K | 300 K | 62.50% |
| Body temperature vs. room | 310 K | 300 K | 3.23% |
Mode 2 — for η = 80% with Tc = 300 K, Th = 1500.00 K is required. Mode 3 — for η = 86% with Th = 2500 K, the maximum Tc is 350.00 K.
The Kelvin trap: plugging in raw °C gives 1 − 20/500 = 96% — completely wrong. Always convert to Kelvin first.
Frequently asked questions
What is Carnot efficiency?
Carnot efficiency is the highest theoretical efficiency limit any heat engine operating between two temperature reservoirs can reach. The formula is η = 1 − Tc/Th, with Th and Tc in Kelvin. Example: a hot reservoir at 500 °C (773.15 K) and a cold reservoir at 20 °C (293.15 K) give η = 62.08%. No heat engine can exceed this value.
Why must temperatures be in Kelvin instead of Celsius?
The Carnot formula is derived from thermodynamics using absolute temperature. Plugging in Celsius raw gives a completely wrong result: 1 − 20/500 = 96%, when the correct answer is 62.08%. This calculator automatically converts °C/°F to Kelvin before computing.
How do I calculate the hot-reservoir temperature needed for a target efficiency?
Rearrange the formula: Th = Tc/(1 − η). Example: for 80% efficiency with a 300 K cold reservoir, Th = 300/(1 − 0.8) = 1500.00 K is required. Use Mode 2 in this calculator.
How do I calculate the cold-reservoir temperature from the efficiency and hot temperature?
Use Tc = Th × (1 − η). Example: for 86% efficiency with Th = 2500 K, the maximum cold temperature is Tc = 2500 × 0.14 = 350.00 K. Use Mode 3.
What is the Carnot efficiency limit of a gasoline engine?
With combustion temperatures around 2500 K and exhaust temperatures around 350 K, the Carnot limit is 1 − 350/2500 = 86.00%. Real gasoline engines only reach about 25–30% because of friction, irreversible heat transfer, and other losses.
What is the Carnot efficiency limit of a steam power plant?
With steam around 800 K and a condenser around 300 K, the limit is 1 − 300/800 = 62.50%. Real steam power plants operate in the 33–40% range.
Are solar panels limited by Carnot efficiency?
No. A solar panel is not a heat engine — it does not convert heat into work through a thermodynamic cycle — so the Carnot formula does not apply to it. The theoretical limit of a single-junction solar cell is the Shockley–Queisser limit, about 33.7%.
Can Carnot efficiency reach 100%?
Only if the cold reservoir reaches absolute zero (0 K) or the hot reservoir is infinitely hot. Absolute zero is unattainable (third law of thermodynamics), so 100% efficiency is physically impossible.
Why are real engines always below the Carnot limit?
The Carnot limit applies to fully reversible cycles. Real engines suffer irreversibilities: mechanical friction, heat transfer across finite temperature differences, incomplete combustion, and heat leaks — all of which push efficiency below the theoretical limit.
What is the Carnot cycle?
The Carnot cycle is an idealized thermodynamic cycle consisting of two isothermal processes (constant temperature) and two adiabatic processes (no heat exchange), all reversible. It defines the maximum possible efficiency, not a buildable engine design.
What is the difference between thermal efficiency and Carnot efficiency?
Thermal efficiency is the ratio of net work to heat input in a real engine (W_net/Q_in) — the value actually achieved. Carnot efficiency is the theoretical upper bound for the same reservoir temperatures — the value that cannot be exceeded.
Which temperature units does this calculator support?
Celsius (°C), Fahrenheit (°F), and Kelvin (K). All inputs are converted to Kelvin first — this correct conversion is what separates the 62.08% result from the 96% trap.
Free tool by NRTechStudio