Carnot Efficiency Calculator
Temperature unit
Try an example
Carnot efficiency, the most any heat engine can convert to work
61.4%
η = 1 − Tc / Th = 1 − 298.15 K / 773.15 K = 0.6144
Of every 100 J of heat taken from the hot side, at most 61.4 J can become work and at least 38.6 J must be rejected to the cold side. Real engines lose more to friction and to heat flowing across finite temperature differences.
The same temperatures run in reverse
COP 1.63
Heat pump limit: Th / (Th − Tc). At most 1.63 units of heat delivered per unit of work.
COP 0.628
Refrigerator or air conditioner limit: Tc / (Th − Tc), heat removed per unit of work.
The smaller the temperature gap, the higher the COP, which is why heat pumps work best in mild weather and with low-temperature heating such as underfloor systems.
Calculate the Carnot efficiency, the highest share of heat any engine can turn into work between two temperatures, and the matching limits on the coefficient of performance of heat pumps, refrigerators and air conditioners, with temperatures in °C, °F or kelvin.
Formula
Worked Example
In kelvin the temperatures are 838.15 K and 303.15 K, so η = 1 − 303.15 ÷ 838.15 = 0.638. Real steam power plants convert roughly 35–45% of their heat to electricity, because of friction and heat flowing across finite temperature differences.
Frequently Asked Questions
Why must the temperatures be in kelvin?
The efficiency depends on the ratio of absolute temperatures. Dividing Celsius values gives nonsense: 25 °C over 500 °C would suggest 95% efficiency, while the correct figure from 298.15 K over 773.15 K is 61.4%.
Can a real engine reach the Carnot efficiency?
No. It is the limit for a perfectly reversible engine, set by the second law of thermodynamics. Friction, heat leaks and the temperature differences needed to move heat at a useful rate keep every real engine below it.
What does the Carnot limit mean for heat pumps?
Run in reverse, the same temperatures cap the coefficient of performance at T_h ÷ (T_h − T_c). Heating to 35 °C from −5 °C outdoors allows at most a COP of 7.7. Real heat pumps typically achieve 2 to 4, but the formula shows why they work better when the gap is smaller, in milder weather and with low-temperature radiators or underfloor heating.