COP Calculator: Coefficient of Performance from Watts, EER or HSPF

What COP tells you

The coefficient of performance compares how much heat a machine moves with how much energy it consumes, using the same units on both sides. Electric resistance heat has a COP of exactly 1: one kilowatt in, one kilowatt of heat out. A heat pump moves heat from outdoors rather than making it, so it typically delivers 2 to 4 units of heat per unit of electricity, a COP of 2 to 4. That ratio is why heat pumps cost less to run than baseboard heaters.

COP is the international, unit-free measure. US ratings such as EER, SEER and HSPF mix BTU and watt-hours, which is why they come out about 3.4 times bigger than COP.

Formulas

COP = Heat output ÷ Energy input (same units)
COP = BTU/h output ÷ (Watts input × 3.412)
COP = EER ÷ 3.412  ·  Seasonal COP ≈ SEER ÷ 3.412 or HSPF ÷ 3.412
EER = COP × 3.412

EER is measured at one test condition, so EER ÷ 3.412 gives a COP at that point. SEER and HSPF are seasonal averages; dividing them by 3.412 gives an average seasonal COP, not the COP at any one moment. The 2023 SEER2, EER2 and HSPF2 ratings use a tougher test with higher duct static pressure, so their values are lower than the old ratings for the same equipment, but the conversion to COP is the same division.

Worked example

A heat pump delivers 36,000 BTU/h of heat while drawing 3,500 W:

1. Convert input to BTU/h: 3,500 × 3.412 = 11,943 BTU/h.
2. COP = 36,000 ÷ 11,943 = 3.01.
3. Equivalent EER: 36,000 ÷ 3,500 = 10.29 BTU/h per watt.
4. So the heat pump delivers about 301% as much heat as a resistance heater using the same electricity.

For the rating conversion, an EER of 10 is 10 ÷ 3.412 = 2.93 COP. These numbers match the calculator's defaults.

Typical COP values

These are typical ranges for current equipment; the manufacturer's extended performance data gives the exact figure at each temperature. COP falls as the outdoor temperature drops because the heat pump has to lift heat across a bigger temperature difference. See heat pump efficiency by temperature.

Using COP to compare running costs

Because COP is unit-free, cost per unit of heat is simply the electricity price divided by COP. At 15 cents per kWh, resistance heat costs 15 cents per kWh of heat, while a heat pump at COP 3 costs 5 cents. To compare with gas, convert therms to kWh (1 therm ≈ 29.3 kWh) and divide by furnace efficiency. The heat pump running cost page and the BTU conversion calculator walk through the numbers.

When checking a heat pump in heating mode, measure output carefully: the airflow and temperature rise across the indoor coil (BTU/h = 1.08 × CFM × ΔT) divided by measured power gives a field COP. Defrost cycles lower the real-world average in cold, humid weather.

COP in cooling vs heating

A heat pump has two COPs, one for each mode. In cooling, the useful output is the heat removed from the house. In heating, the useful output is the heat delivered to the house, which includes the energy used by the compressor itself, since that ends up as heat in the refrigerant. As a result, the heating COP of a heat pump at a given temperature lift is roughly one higher than its cooling COP at the same lift.

That is also why the theoretical limit, the Carnot COP, is written differently for each mode. For heating it is the indoor temperature divided by the temperature difference, using absolute temperatures. Heating a 70 °F house from 30 °F outdoors gives an ideal heating COP above 13; real equipment reaches around a quarter of that because of compressor losses, fan power, heat-exchanger temperature differences and defrost. The useful takeaway: the smaller the temperature gap the heat pump has to bridge, the higher its COP. Low-temperature distribution, such as larger ducts or radiant floors, and a well-insulated house both raise real-world COP.

Frequently asked questions