Carnot Efficiency Calculator
Maximum theoretical efficiency of a heat engine between two temperatures, plus the ideal COP of a fridge and a heat pump.
Results
What this tool does
Only the temperature difference matters, and it has to be measured from absolute zero, which is why a hot source buys so much more than a cold sink. Run in reverse the same limit gives the best coefficient of performance a fridge or a heat pump could manage — always greater than one, because they move heat rather than make it.
Formula
η = 1 − T cold ÷ T hot (absolute temperatures)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
th | Hot side temperature | °C |
tc | Cold side temperature | °C |
pw | Power | kW |
qa | Heat actually supplied | kW |
wa | Work actually produced | kW |
EF | Efficiency | % |
WO | Power | kW |
QR | Power | kW |
CP | Coefficient of performance | — |
HP | Coefficient of performance | — |
RE | The efficiency you are actually getting | % |
SL | How much of the theoretical limit that is | % |
QJ | Heat thrown away | kW |
Worked example
- Hot side temperature350 °C
- Cold side temperature30 °C
- Power100 kW
- Heat actually supplied0 kW
- Work actually produced0 kW
- Efficiency51.3520 %
- Power51.352 kW
- Power48.648 kW
- Coefficient of performance0.9473
- Coefficient of performance1.9473
- The efficiency you are actually getting0.0000 %
- How much of the theoretical limit that is0.0000 %
- Heat thrown away0.0000 kW
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Temperatures below absolute zero (−273.15 °C) do not exist physically. The converter will still show the arithmetic result.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
Frequently asked questions
Why can no real engine reach this figure?
Because the Carnot cycle assumes every step happens infinitely slowly and with no friction, no turbulence and no heat leaking anywhere it should not. Those assumptions are what make it the ceiling: it is not a target to aim for but a limit that says no arrangement of parts, however clever, can do better between those two temperatures. Real steam plants reach roughly half of it.