# Heat Pump COP Calculator

> Work out a heat pump’s coefficient of performance from heat output and electrical input, compare it with the Carnot limit and estimate yearly running cost.

Category: Energy & environment · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/heat-pump-cop-calculator

COP is heat delivered divided by electricity used: a COP of 3 gives 3 kWh of heat per kWh of electricity. The Carnot limit shows the theoretical best for your temperatures.

Also called: Coefficient of performance calculator, Heat pump efficiency calculator.

## Inputs
- Heat output (unit kW; default 8)
- Electrical input (unit kW; default 2.5)
- Output (flow) temperature (unit °C; default 35)
- Source temperature (outdoor air or ground) (unit °C; default 5)
- Heat needed per year (unit kWh; default 10000; optional)
- Electricity price per kWh (default 0.25; optional)
- Currency

## Results
- Coefficient of performance (COP)
- Carnot (ideal) COP
- Share of the Carnot limit achieved
- Electricity per year at this COP
- Running cost per year at this COP

## Formula

```
COP = Heat output ÷ Electrical input;  COP(Carnot) = T_hot ÷ (T_hot − T_cold) in kelvin;  Electricity per year = Heat needed ÷ COP
```

Where:
- T_hot: output temperature + 273.15
- T_cold: source temperature + 273.15

## Worked example
1. COP = 8 ÷ 2.5 = 3.2.
2. Carnot COP = 308.15 ÷ (35 − 5) = 10.27, so the unit reaches 3.2 ÷ 10.27 = 31.15% of the ideal.
3. Yearly electricity = 10,000 ÷ 3.2 = 3,125 kWh × 0.25 = 781.25.

**Result:** Delivering 8 kW of heat from 2.5 kW of electricity is a COP of 3.2, so 10,000 kWh of heat costs about 781 a year.

## What the result means

COP falls as the gap between source and output temperature grows, which is why low flow temperatures (larger radiators, underfloor heating) improve efficiency. A single COP measurement is a snapshot; the seasonal average (SCOP) is what sets yearly cost.

## Assumptions and limits
- The COP entered applies to the whole year when estimating running cost.
- Defrost cycles, backup heaters and pump energy reduce real seasonal efficiency.

## Questions

### What is the difference between COP and SCOP?

COP is measured at one set of conditions; SCOP (seasonal COP) averages performance across a heating season and is the better guide to annual cost.

### Can COP be higher than the Carnot COP?

No. If a measurement exceeds it, the heat or power readings are wrong.

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- [Home Electricity Bill Calculator](https://calculators.geekmidst.com/calculators/home-electricity-bill-calculator)
- [Carbon Emissions Calculator](https://calculators.geekmidst.com/calculators/carbon-emissions-estimate-calculator)
- [Temperature Converter](https://calculators.geekmidst.com/calculators/temperature-converter)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/heat-pump-cop-calculator