Formula & Calculator
Coefficient of Performance (COP)
Rates the efficiency of a heat pump or refrigeration system as the ratio of useful output to energy input.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| COP | Coefficient of performance (dimensionless efficiency ratio) | dimensionless |
| Q | Useful thermal output (heating or cooling energy) | kWh (or kJ) |
| W | Work/energy input (electrical or mechanical energy consumed) | kWh (or kJ) |
What it means
The Coefficient of Performance (COP) is the ratio of useful heat or cooling output to the work input for heat pumps and refrigerators. COP = Useful Output / Work Input. For a heat pump, COP > 1 means it delivers more thermal energy than the electrical energy consumed, because it moves heat from a low‑temperature source to a high‑temperature sink. Example: A heat pump with heat output 3 kW and electrical input 1 kW has COP = 3. This is much more efficient than resistive heating. COP is a key metric for evaluating the efficiency of heat pumps and refrigeration systems.
Worked example
Coefficient of Performance – Practical Example
Real‑World| Parameter | Value |
|---|---|
| Useful output | 12 kWh |
| Work input | 3 kWh |
| Formula | COP = Useful Output / Work Input |
Common mistakes
Watch for unit mismatches (W vs kW, single- vs three-phase) and remember to include power factor or efficiency where the formula requires it.Applications
Coefficient of Performance (COP) = Useful Heat/Cooling Output / Work Input measures the efficiency of heat pumps and chillers. COP values are typically 2‑4, meaning more energy delivered than consumed. Engineers use it to select and compare heat pump systems. This is a key metric for sustainable HVAC solutions.
- Heat pump and chiller selection
- Energy efficiency analysis and savings
- Geothermal and air‑source heat pump design
- Building decarbonisation and electrification
- Educational understanding of heat pump efficiency