Physics
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Carnot Efficiency Calculator.
Calculate ideal reversible heat-engine efficiency from hot and cold absolute temperatures.
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This page applies only the stated idealized equation and explicit inputs; verify specialized engineering, medical, or safety decisions against applicable standards.
Use Cases
Benchmarking real engines
Compare the efficiency of an actual heat engine against the ideal Carnot limit to see how close it comes to reversible operation.
Example: If a steam turbine operates between 500 K and 300 K, its Carnot efficiency is 40%, so a real turbine might achieve 30%.
Educational demonstrations
Illustrate the second law of thermodynamics by showing how efficiency depends on the temperature difference between reservoirs.
Example: Increase the hot reservoir temperature from 400 K to 600 K (cold at 300 K) and see efficiency rise from 25% to 50%.
Frequently Asked Questions
- What is Carnot efficiency?
- Carnot efficiency is the maximum theoretical efficiency of a reversible heat engine operating between two temperatures. It is calculated as 1 minus the ratio of the cold reservoir temperature to the hot reservoir temperature, both in Kelvin.
- Why must temperatures be in Kelvin?
- The Carnot efficiency formula requires absolute temperatures (Kelvin) because it is based on thermodynamic temperature ratios. Using Celsius or Fahrenheit would give incorrect results, as they are not absolute scales.
- Can a real engine achieve Carnot efficiency?
- No, real engines always have lower efficiency due to irreversibilities like friction and heat losses. Carnot efficiency serves as an upper limit and a benchmark for comparing real engine performance.
Tips & Common Mistakes
Tips
- Ensure both temperatures are in Kelvin. If you have Celsius, add 273.15 to convert.
- The cold reservoir temperature must be lower than the hot reservoir temperature; otherwise, the efficiency will be zero or negative.
- Use this calculator to explore how increasing the hot temperature or decreasing the cold temperature improves ideal efficiency.
- Remember that Carnot efficiency is a theoretical maximum; real engines will always have lower efficiency.
Common Mistakes to Avoid
- Using Celsius or Fahrenheit instead of Kelvin, which leads to incorrect efficiency values.
- Entering the cold temperature higher than the hot temperature, resulting in a negative or zero efficiency.
- Assuming that Carnot efficiency is achievable in practice, when it is only an ideal limit.
Last updated: August 13, 2026