Science & engineering · Thermodynamics
Carnot efficiency calculator.
The theoretical ceiling for any heat engine between two temperatures.
Inputs
Result
Enter temperatures.
What is Carnot efficiency?
The Carnot efficiency is the highest fraction of heat any engine can turn into work while operating between a hot reservoir at Th and a cold reservoir at Tc: e = 1 − Tc / Th, with both temperatures in kelvin. Carnot's principle states that no engine working between two reservoirs at constant temperatures can have a greater efficiency than a reversible engine. Work out = e × Qh and waste heat Qc = Qh − work.
Worked example. A Carnot engine with efficiency 0.60 and a cold reservoir at 300 K needs Th = 300 / (1 − 0.60) = 750 K. With 500 J of heat in it gives 300 J of work and rejects 200 J (OpenStax Example 4.2).
Real engines run below this limit because of friction, heat leaks and finite-rate processes. Fill in either the hot temperature or the efficiency and leave the other empty.
Frequently asked questions
What is the Carnot efficiency formula?
e = 1 − Tc/Th, with Th and Tc the absolute temperatures of the hot and cold reservoirs.
Can a real engine reach Carnot efficiency?
No. It is an upper bound for any engine between those two temperatures, reached only by an ideal reversible engine.
How do I raise the maximum efficiency?
Raise the hot temperature, lower the cold temperature, or both. The formula depends only on the ratio of the two absolute temperatures.
Why kelvin and not Celsius?
The ratio Tc/Th only has meaning on an absolute scale. The tool converts Celsius and Fahrenheit for you and rejects values at or below absolute zero.
Sources
Checked
Formula, Carnot's principle and the worked example are from the source above. Runs entirely in your browser. Nothing you type is sent or stored.
Scope
Education reference. Carnot efficiency is a theoretical limit and does not predict the efficiency of any real engine, power plant or refrigerator.