Carnot Efficiency Calculator

Calculate the maximum theoretical efficiency of a heat engine between two temperatures.

Must be > cold temperature
e.g. room temperature = 293 K
Please check your inputs and try again.

Carnot Efficiency as a Thermodynamic Upper Limit

Carnot efficiency is the maximum efficiency any heat engine can achieve while operating between two fixed reservoir temperatures. It is not a prediction that a real engine will reach that efficiency. The Carnot cycle is reversible and has no friction, uncontrolled heat transfer, pressure drop, combustion irreversibility, or other losses that appear in real machines.

The formula depends only on the ratio of the cold and hot absolute temperatures. A heat engine absorbs heat Qh from a hot reservoir, produces work W, and rejects Qc to a colder reservoir. For a reversible Carnot engine, Qc/Qh = Tc/Th. Since efficiency is W/Qh = 1 − Qc/Qh, the temperature ratio gives the upper bound directly.

ηCarnot = 1 − Tc/Th    or    η% = (1 − Tc/Th) × 100%
SymbolMeaningWhy it matters / units
ThHot-reservoir temperatureKelvin; must be greater than Tc
TcCold-reservoir temperatureKelvin; determines unavoidable heat rejection
ηThermal efficiencyFraction of input heat converted to work
1 − ηMinimum rejected fraction for Carnot caseEquals Tc/Th

Temperatures must be in kelvins because the equation uses ratios measured from absolute zero. Increasing Th or lowering Tc raises the theoretical limit, but a 100% heat-engine efficiency would require Tc = 0 K or an equivalent impossible limit for a finite practical engine.

Worked Examples

Example 1: Steam turbine: Th=800K, Tc=300K
η = 1 − 300/800
Result: 62.5% max efficiency
Real steam turbines reach 35–45%
Example 2: Car engine: Th=900K, Tc=350K
η = 1 − 350/900
Result: 61.1% theoretical
Real engines: 20–35% due to irreversibilities
Example 3: Converting Celsius before using Carnot efficiency
Th = 500°C = 773.15 K, Tc = 25°C = 298.15 K → η = 1 − 298.15/773.15
Result: η = 61.4%
Using 500 and 25 directly would give 95%, which is wrong because Celsius temperatures cannot be used in the absolute-temperature ratio.
Example 4: Smaller temperature difference
Th = 600 K, Tc = 450 K → η = 1 − 450/600
Result: η = 25%
Even with a perfectly reversible engine, three-quarters of the incoming heat cannot become work when the reservoirs are this close in absolute temperature.

Common Mistakes

⚠️
Using Celsius directly in the ratio

Carnot efficiency requires absolute temperature. Convert with T(K) = T(°C) + 273.15 before dividing temperatures.

⚠️
Reversing hot and cold temperatures

The expression is 1 − Tc/Th, with Th greater than Tc. Reversing them produces a negative value that does not describe a heat engine operating between those reservoirs.

⚠️
Treating Carnot efficiency as expected real efficiency

The Carnot result is an upper bound for a reversible engine. Real engines operate below it because entropy is generated by friction, finite temperature differences, flow resistance, combustion, mixing, and other irreversible processes.

⚠️
Using a temperature difference instead of a temperature ratio

Efficiency is not (Th − Tc) by itself. Two engine pairs can have the same 300 K difference but different Carnot efficiencies because their absolute temperature ratios differ.

Frequently Asked Questions

Why can't efficiency reach 100%?
The second law of thermodynamics requires heat rejection to a cold reservoir. Even a perfect Carnot engine cannot convert all heat to work.
What is Carnot efficiency used for?
It sets the upper bound for any real heat engine. Engineers compare real efficiency to Carnot to assess how much room for improvement exists.
Why must Carnot temperatures be in kelvins?
The Carnot relation uses a ratio of absolute temperatures. Kelvin has a physically meaningful zero at absolute zero, so temperature ratios correspond to thermodynamic energy relationships. Celsius has an arbitrary zero and therefore cannot be used directly in Tc/Th.
Can a real engine ever exceed Carnot efficiency?
No, not when compared correctly between the same hot and cold reservoir temperatures. Exceeding the Carnot limit would violate the second law of thermodynamics. Real engines always include irreversibilities and therefore fall below the reversible limit.
What happens if the hot and cold reservoirs have the same temperature?
If Th = Tc, the Carnot efficiency is zero. There is no temperature difference to drive net heat flow through an engine, so no cyclic heat engine can extract net work from the two equal-temperature reservoirs.
Is Carnot efficiency the same as coefficient of performance?
No. Heat-engine efficiency measures work output divided by heat input and is below 1. Refrigerators and heat pumps use coefficient of performance, which compares heat moved with work input and can be greater than 1.

Formula Explorer connections

Interpretation: This relationship connects motion, force, momentum, work or energy in a mechanical system. Assumption: Choose a consistent reference direction and unit system. The model may assume constant acceleration, rigid bodies, negligible losses or an isolated system.

Center of Mass Calculator →Centripetal Acceleration Calculator →Centripetal Force Calculator →Physics Formula Explorer →