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
| Field | What to enter |
|---|---|
| Device | Choose one: Refrigerator / air conditioner, Heat pump (heating) |
| Method | Choose one: Heat and work, Ideal (from temperatures) |
| Heat moved (Q_c for fridge, Q_h for heat pump) | Units: kW, W, kWh |
| Work / electrical input | Units: kW, W, kWh |
| Hot side temperature | Units: °C, °F, K |
| Cold side temperature | Units: °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 performance |
|---|---|
| 1.75 | 8.8043 |
| 2.63 | 8.8043 |
| 3.5 | 8.8043 |
| 4.38 | 8.8043 |
| 5.25 | 8.8043 |
| 7 | 8.8043 |
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)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.
Frequently asked questions
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).