# Carnot Efficiency Calculator

URL: https://speedycalculator.com/calculators/physics/carnot-efficiency/
Last updated: 2026-10-25

> The Carnot efficiency calculator finds the maximum possible efficiency of a heat engine operating between a hot and a cold temperature, η = 1 − T_cold ÷ T_hot (in kelvin).

## Inputs

- Hot reservoir temperature (K, °C, °F)
- Cold reservoir temperature (K, °C, °F)

## Results

- Maximum efficiency
- Carnot COP (heat pump)

## Formula

```
η = 1 − T_c ÷ T_h
```

## Explanation

No real engine can beat the Carnot limit, which is why power plants aim for very high steam temperatures.

### How to use the Carnot Efficiency Calculator

- **Hot reservoir temperature**
- **Cold reservoir temperature**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Convert both temperatures to kelvin and subtract their ratio from one.

### Inputs explained

FieldWhat to enterHot reservoir temperatureUnits: K, °C, °FCold reservoir temperatureUnits: K, °C, °F

### What each result means

- **Maximum efficiency** = (1 - [Cold reservoir temperature]÷[Hot reservoir temperature]) × 100
- **Carnot COP (heat pump)** = [Hot reservoir temperature] ÷ ([Hot reservoir temperature] - [Cold reservoir temperature])

### Example values

How the main result changes when **Hot reservoir temperature** changes and everything else stays at the example values above:

Hot reservoir temperature (K)Maximum efficiency (%)436.5830.56654.8653.71873.1565.281,091.4472.221,309.7376.851,746.382.64

## Worked example

Inputs — Hot reservoir temperature: 873.15 K; Cold reservoir temperature: 303.15 K.

Results — **Maximum efficiency = 65.28 %**; Carnot COP (heat pump) = 1.532.

## FAQ

**Why use kelvin?**
The formula needs absolute temperature.

**How efficient are real power plants?**
Typically 33–45% for steam plants and up to about 60% for combined-cycle gas plants.

**What formula does the Carnot Efficiency Calculator use?**
η = 1 − T_c ÷ T_h.