Choose a calculation mode, enter values, and submit. Fields update automatically.
- COPHP = Qh / W (heat delivered divided by work input).
- W = Qh − Qc (energy balance for the cycle).
- COPHP = Q̇h / P (rate form using power values).
- COPCarnot = Th / (Th − Tc) with absolute temperatures.
- COPreal ≈ η × COPCarnot when using an efficiency factor.
All temperatures are converted to kelvin for Carnot calculations. Energy units are converted to joules, and power units to watts, so comparisons remain consistent.
- Select a calculation mode that matches your available data.
- Enter values and choose units for each field.
- Click Calculate to display results above the form.
- Use Download CSV or Download PDF for reporting.
- For temperature mode, keep Tₕ > T꜀ and avoid very small ΔT.
If you are comparing systems, keep the same operating conditions (source temperature, delivery temperature, and load) to make COP values meaningful.
| Scenario | Inputs | Method | Output COP | Notes |
|---|---|---|---|---|
| Space heating cycle | Qₕ = 12 kWh, W = 3 kWh | Qₕ & W | 4.0 | Qc = 9 kWh extracted |
| Measured heat flows | Qₕ = 18 kWh, Q꜀ = 14 kWh | Qₕ & Q꜀ | 4.5 | W = 4 kWh |
| Rated capacity | Q̇ₕ = 7.2 kW, P = 2.4 kW | Q̇ₕ & P | 3.0 | Common for datasheets |
| Ideal reference | Tₕ = 35°C, T꜀ = 5°C, η = 0.45 | Carnot | ≈ 4.6 | Ideal COP ≈ 10.2 |
Heat Pump COP in Practice
Coefficient of performance (COP) expresses how effectively a heat pump moves heat compared with the work you supply. A COP of 4 means 4 units of heat are delivered for every 1 unit of input energy. Because COP depends on temperatures, load, and equipment design, this calculator provides multiple methods so you can work from measured heat, rated power, or thermodynamic temperatures.
Typical COP Ranges You Can Expect
For air-source systems, steady-state heating COP often falls around 2.0–4.5 depending on outdoor conditions. Ground-source (geothermal) systems commonly operate around 3.0–5.0 because source temperatures are more stable. These ranges are not guarantees; frosting cycles, defrost power, and auxiliary heaters can reduce realized performance.
Why Temperature Lift Controls COP
The temperature lift is the difference between the delivery temperature (hot side) and the source temperature (cold side). In Carnot mode, COPCarnot = Th/(Th − Tc), so a smaller ΔT produces a higher theoretical COP. For example, at Th = 308 K and Tc = 278 K, COPCarnot ≈ 10.3; if ΔT doubles, the ideal COP roughly halves.
Energy vs Power Inputs: What the Numbers Mean
If you measure energy over a billing period, use Qh and W (or Qh and Qc). If you are comparing equipment nameplates, use the rate form COP = Q̇h/P with kW. The result is still dimensionless; you can mix units as long as the numerator and denominator represent the same time basis.
Unit Conversions Built Into This Tool
The calculator converts energy to joules and power to watts internally. Supported energy units include J, kJ, MJ, Wh, kWh, and Btu. Supported power units include W, kW, and horsepower. Conversions help prevent common errors such as dividing kWh by kW (which introduces an unintended hour factor).
Interpreting Derived Values Qc and W
When you enter Qh and W, the tool estimates extracted heat as Qc = Qh − W. When you enter Qh and Qc, it computes work as W = Qh − Qc. If computed work becomes zero or negative, the inputs are inconsistent for a heat pump cycle.
Using η to Estimate Real COP
Real equipment cannot reach the Carnot limit due to compressor inefficiency, pressure drops, finite heat exchanger approach temperatures, and control losses. The efficiency factor η (0–1) provides a practical bridge: COPreal ≈ η × COPCarnot. Values like 0.35–0.55 are often used for rough screening when detailed maps are unavailable.
Engineering Checks Before You Export
For professional reporting, record operating conditions with the COP: source temperature, supply/return temperatures, flow rates, and whether auxiliary resistance heat was active. If you compare two systems, normalize to similar Th, Tc, and load. Use the CSV export for audit trails and the PDF report for quick documentation.
Frequently Asked Questions
1) What is a “good” COP for heating?
A “good” COP depends on climate and temperature lift. Many air-source units deliver around 2–4 in winter conditions, while ground-source systems can be higher. Compare COP at similar temperatures.
2) Why can COP be higher than 1?
Because a heat pump moves heat rather than creating it. Input work drives a refrigeration cycle that transfers heat from a source to the heated space, so delivered heat can exceed electrical input energy.
3) How is heat pump COP different from refrigerator COP?
Heat pump COP uses delivered heat Qh in the numerator, while refrigerator COP uses extracted heat Qc. They are related by energy balance: Qh = Qc + W.
4) Should I use energy mode or power mode?
Use energy mode for metered totals over time (kWh). Use power mode for instantaneous or rated values (kW). Both yield the same dimensionless COP when data are consistent.
5) Why does Carnot COP get very large sometimes?
If Th and Tc are close, ΔT becomes small and COPCarnot rises sharply. In reality, approach temperatures and losses limit performance, so use η to estimate realistic values.
6) What makes my calculated COP look too low?
Common causes include auxiliary resistance heating, defrost cycles, incorrect unit pairing, or using output heat that excludes fan/pump power. Verify that all inputs represent the same measurement boundary.
7) Can I compare COP values from different datasheets?
Only if the test conditions match. Check source temperature, delivery temperature, and standards used. Seasonal metrics (like SCOP) incorporate part-load behavior and may differ from steady-state COP.