Carnot Efficiency Calculator (Heat Engine, Heat Pump COP)
By Santaji GadepatilinUpdated November 3, 2026
No heat engine working between two temperatures can beat the efficiency of an ideal reversible Carnot cycle, η = 1 − T_c/T_h, and no refrigerator or heat pump can beat the Carnot COP. This Carnot efficiency calculator gives all three limits from the reservoir temperatures, together with the maximum work from a heat input — the benchmark for judging real chiller capacity and COP.
How to use the Carnot efficiency calculator
Enter the hot and cold reservoir temperatures and, optionally, the heat input rate. The calculator returns the Carnot efficiency, the maximum power output, and the ideal coefficients of performance for a refrigerator and a heat pump working between the same temperatures.
Carnot efficiency formula
η = 1 − Tc ÷ Th · W = η × Qh
COPref = Tc ÷ (Th − Tc) · COPHP = Th ÷ (Th − Tc)
Example
An engine takes 100 kW of heat at 500 °C (773.15 K) and rejects heat at 30 °C (303.15 K):
- η = 1 − 303.15 ÷ 773.15 = 60.79%
- Maximum work = 0.6079 × 100 = 60.79 kW
- Carnot COP as a refrigerator = 303.15 ÷ 470 = 0.645; as a heat pump = 773.15 ÷ 470 = 1.645
Carnot efficiency with a 25 °C cold sink
| Hot temperature | Carnot efficiency |
|---|---|
| 100 °C | 20.1% |
| 200 °C | 37.0% |
| 300 °C | 48.0% |
| 400 °C | 55.7% |
| 500 °C | 61.4% |
| 600 °C | 65.9% |
| 800 °C | 72.2% |
| 1000 °C | 76.6% |
| 1500 °C | 83.2% |
Ideal heat pump and refrigerator COP (delivering heat at 35 °C)
| Cold source | Hot side | Carnot COP (heating) | Carnot COP (cooling) |
|---|---|---|---|
| -20 °C | 35 °C | 5.60 | 4.60 |
| -10 °C | 35 °C | 6.85 | 5.85 |
| 0 °C | 35 °C | 8.80 | 7.80 |
| 5 °C | 35 °C | 10.27 | 9.27 |
| 10 °C | 35 °C | 12.33 | 11.33 |
| 15 °C | 35 °C | 15.41 | 14.41 |
Notes
- Efficiency improves by raising Th or lowering Tc; that is why gas turbines run hot and power plants want cold cooling water.
- A smaller temperature lift gives a much higher heat-pump COP, which is why underfloor heating (low flow temperature) suits heat pumps.
Frequently asked questions
What is the Carnot efficiency formula?
η = 1 − T_c ÷ T_h, with both temperatures in kelvin. It is the highest efficiency any heat engine can reach between those two temperatures.
Why must temperatures be in kelvin?
The formula uses a ratio of absolute temperatures. The calculator converts °C or °F to kelvin for you; entering 500 °C and 30 °C means 773.15 K and 303.15 K.
How efficient are real power plants compared with Carnot?
Typically 50–70% of the Carnot limit. A steam plant with 550 °C steam and 30 °C cooling water has a Carnot limit near 63% but achieves about 35–45%; combined-cycle gas plants reach about 60%.
What is the Carnot COP of a heat pump?
COP = T_h ÷ (T_h − T_c). Heating to 35 °C from 0 °C outside gives an ideal COP of 8.8; real heat pumps achieve about 3–4.5 because of compressor and heat-exchanger losses.