Calculator
Plotly Graph
The chart compares heating output against electrical input. When temperatures are available, it also shows the ideal Carnot reference line.
Formula Used
1) Direct Heat Pump COP
COP = Qhot / W
Qhot is the heat delivered to the heated space. W is the electrical work input. COP is dimensionless.
2) Ideal Carnot COP for Heating
COPCarnot = Thot / (Thot - Tcold)
Both temperatures must be in Kelvin. This formula gives the theoretical upper limit, not the real installed system performance.
3) Required Input Power
W = Qhot / COP
Use this when you know the needed heating load and the target COP, and you want the electrical input estimate.
4) Heating Output from Input Power
Qhot = COP × W
Use this when you know input power and expected COP, and you want the approximate heating delivery rate.
How to Use This Calculator
- Select a calculation mode based on the value you need.
- Choose the heat, power, and temperature units you want.
- Enter delivered heat and electrical input for direct COP.
- Enter hot and cold temperatures for ideal Carnot COP.
- Enter target COP with heat or power for reverse calculations.
- Optionally add operating hours and electricity rate for cost estimates.
- Press Calculate to show the result above the form.
- Review the chart, summary metrics, and download CSV or PDF if needed.
Example Data Table
These example scenarios help you compare common heating conditions and check expected COP behavior.
| Scenario | Heat Delivered (kW) | Electrical Input (kW) | Hot Temp (°C) | Cold Temp (°C) | Actual COP |
|---|---|---|---|---|---|
| Cold Climate Split System | 12.00 | 3.20 | 35 | 5 | 3.7500 |
| Mild Climate Ducted Unit | 10.50 | 2.60 | 38 | 10 | 4.0385 |
| Retrofit Radiator Upgrade | 14.80 | 4.40 | 45 | 7 | 3.3636 |
| Low Lift Ideal Reference | 9.00 | 2.00 | 30 | 15 | 4.5000 |
Frequently Asked Questions
1) What does COP mean for a heat pump?
COP means coefficient of performance. It compares heating output to electrical input. A COP of 4 means the system delivers four units of heat for every one unit of electricity consumed.
2) Is a higher COP always better?
Usually yes, because a higher COP means better heating efficiency. Still, real equipment choice should also consider installation quality, temperature range, defrost behavior, maintenance, and seasonal operating conditions.
3) Why does the Carnot formula use Kelvin?
Thermodynamic temperature formulas use absolute temperature. Kelvin avoids negative or shifted scales and keeps the ideal COP equation physically correct for comparing hot and cold reservoirs.
4) Why is actual COP lower than Carnot COP?
Real systems have compressor losses, fan power, refrigerant pressure drops, heat exchanger limits, frosting, and control losses. Carnot COP is a theoretical ceiling, not an expected field result.
5) Can a heat pump COP be greater than 1?
Yes. Heat pumps move heat instead of creating all of it directly from electricity. That is why COP values above 1 are normal and often much higher under favorable temperature conditions.
6) How does outdoor temperature affect COP?
As the outdoor source gets colder, the temperature lift grows. That usually lowers COP because the system must work harder to move heat into the warmer indoor space.
7) Which units matter in the direct COP method?
Heat and power units must be consistent after conversion. This calculator handles kW, W, and BTU/hr for heat, then converts values internally before calculating the dimensionless COP.
8) Can I use this calculator for seasonal comparisons?
Yes, for quick comparisons. Enter realistic loads, temperatures, hours, and energy prices. For full seasonal analysis, combine many operating points rather than relying on one single condition.