ConverterHub

Carnot Efficiency Calculator

Find the Carnot efficiency of a heat engine.

How it is calculated

The Carnot efficiency is η = 1 − Tc / Th, shown as a percentage. Th is the absolute temperature of the hot source and Tc that of the cold sink, both in kelvin. It is the upper limit for any heat engine working between those two temperatures; real engines come out lower.

The tool requires Tc to be greater than zero and Th to be greater than Tc; equal temperatures, a hotter cold side or a zero or negative value give no result. The inputs are not converted for you: values must already be in kelvin (K = °C + 273.15). Efficiency is shown to two decimals. The formula covers only the thermodynamic ceiling and does not account for friction, heat losses or the practical cycle used.

Worked example

A heat engine takes heat at 800 K and rejects it at 300 K. Divide the temperatures: 300 / 800 = 0.375. Subtract from 1: 1 − 0.375 = 0.625. As a percentage the maximum possible efficiency is 62.50%. Even a perfect engine between these temperatures wastes 37.5% of the heat it takes in.

Try this example →

Common mistakes

  • Entering Celsius or Fahrenheit. 800 °C and 300 °C are 1,073.15 K and 573.15 K, which give about 46.6%, not 62.5%.
  • Swapping hot and cold. Hot must be the larger value, otherwise no result appears.
  • Treating the figure as what a real engine delivers. A car engine or power plant reaches only a part of the Carnot limit.
  • Entering 0 for a cold side near room temperature. Zero kelvin is absolute zero; room temperature is about 293 K.
  • Raising efficiency only by cooling the cold side and forgetting how hard that is. The ratio, not the difference, sets the limit, so 600 K to 300 K and 1,200 K to 600 K give the same 50.00%.

About this calculator

The Carnot efficiency, η = 1 − Tc/Th, sets the theoretical maximum efficiency of any heat engine operating between a hot reservoir at absolute temperature Th and a cold reservoir at Tc, both measured in kelvin. Sadi Carnot derived this limit in 1824 from an idealized reversible cycle of isothermal and adiabatic steps, proving that no real engine — regardless of its working fluid or mechanical design — can exceed it without violating the second law of thermodynamics.

Mechanical and thermal engineers use the Carnot limit as a benchmark to judge how close a real engine, turbine or refrigeration cycle comes to its theoretical best, since actual efficiencies are always lower due to friction, heat leakage and irreversible processes. Power plant designers apply it to justify raising boiler temperatures for higher efficiency, and physics students use it to build intuition for the second law before studying real cycles like Rankine or Otto.

Was this helpful?

You can pick up to 3 reactions.

Comments (0)

  • Be the first to comment.

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators