# Coefficient of Performance Calculator (COP)

URL: https://speedycalculator.com/calculators/physics/performance-coefficient/
Last updated: 2026-10-30

> The coefficient of performance calculator finds the COP of a refrigerator or heat pump from the heat moved and the work input, or the ideal (Carnot) COP from the hot and cold temperatures.

## Inputs

- Device
- Method
- Heat moved (Q_c for fridge, Q_h for heat pump) (kW, W, kWh)
- Work / electrical input (kW, W, kWh)
- Hot side temperature (°C, °F, K)
- Cold side temperature (°C, °F, K)

## Results

- Coefficient of performance
- Equivalent EER (BTU/Wh)

## Formula

```
Refrigerator: COP = Q_c/W = T_c/(T_h − T_c) (ideal) · Heat pump: COP = Q_h/W = T_h/(T_h − T_c) (ideal)
```

## Explanation

Heat pumps and refrigerators move heat rather than create it, so their COP can be well above 1: a heat pump with COP 3.5 delivers 3.5 kWh of heat for each kWh of electricity. The smaller the temperature lift, the higher the COP.

### How to use the Coefficient of Performance Calculator

- **Device**
- **Method**
- **Heat moved (Q_c for fridge, Q_h for heat pump)**
- **Work / electrical input**
- **Hot side temperature**
- **Cold side temperature**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the device and method and enter the values.

### Tips

- Use absolute temperature (K) in gas laws and efficiency formulas.
- Temperature differences are the same in K and °C.
- Heat = mass × specific heat × temperature change when no phase change occurs.
- Phase changes need latent heat at a constant temperature.

### Common mistakes to avoid

- Using °C in pV = nRT.
- Forgetting latent heat during melting or boiling.
- Confusing heat capacity (J/K) with specific heat (J/(kg·K)).

### Inputs explained

FieldWhat to enterDeviceChoose one: Refrigerator / air conditioner, Heat pump (heating)MethodChoose one: Heat and work, Ideal (from temperatures)Heat moved (Q_c for fridge, Q_h for heat pump)Units: kW, W, kWhWork / electrical inputUnits: kW, W, kWhHot side temperatureUnits: °C, °F, KCold side temperatureUnits: °C, °F, K

### Example values

How the main result changes when **Heat moved** changes and everything else stays at the example values above:

Heat moved (Q_c for fridge, Q_h for heat pump) (kW)Coefficient of performance1.758.80432.638.80433.58.80434.388.80435.258.804378.8043

## Worked example

Inputs — Device: Heat pump (heating); Method: Ideal (from temperatures); Hot side temperature: 35 °C; Cold side temperature: 0 °C.

Results — **Coefficient of performance = 8.8043**; Equivalent EER (BTU/Wh) = 30.0402.

## Key terms

- **Heat pump**: Device moving heat from cold to hot using work.

## FAQ

**Can COP be greater than 1?**
Yes – heat pumps move more heat than the work they use.

**Why does COP fall in cold weather?**
The temperature lift increases.

**What is a typical heat pump COP?**
3–4.5 in mild conditions.

**How is EER related?**
EER = 3.412 × COP for cooling.

**What formula does the Coefficient of Performance Calculator use?**
Refrigerator: COP = Q_c/W = T_c/(T_h − T_c) (ideal) · Heat pump: COP = Q_h/W = T_h/(T_h − T_c) (ideal).


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)