Carnot efficiency formulas and interpretation
Carnot efficiency is the upper theoretical efficiency limit for a heat engine operating between two reservoirs.
Temperatures must be converted to an absolute scale before division.
How to use the Carnot efficiency calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
Maximum efficiency equals one minus the cold-to-hot absolute temperature ratio.
η = 1 − T_c / T_h- η — Carnot efficiency
- Maximum theoretical efficiency (%)
- T_h — Hot temperature
- Hot-reservoir absolute temperature (K)
- T_c — Cold temperature
- Cold-reservoir absolute temperature (K)
Reservoir example
A heat engine operates between 500 K and 300 K.
- Hot reservoir
- 500 K
- Cold reservoir
- 300 K
- η = 1 − 300 / 500
- η = 0.40
Result: The maximum theoretical efficiency is 40%.
A real engine will operate below this reversible limit.
Understanding your results
Interpreting the result
The result is an ideal upper bound, not a prediction of actual engine performance.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.