See [1] for the theory.

I couldn't find a model/calculator that would help visualise typical COP values for particular climatic conditions. However, you'll find in your travels that a COP of ~2-2.5 is typically achieved for ambient (outdoor) temperatures of -15oC (for air sourced heat pumps).

If 300L of water at 15oC is filled into a tank and needs to be heated to 60oC within 2 hours during ambient temperature of -15oC, you get very approximately (no thermal losses considered):

- An output energy need of approximately (4190300(60-15))/(60*120)=~8kW (56MJ/2h)

- An input electricity need of approximately (8/2.2)=~3.6kW

Instead of a resistive heating hot water unit requiring 16kWh to do this job, you could use a heat pump hot water unit requiring 7.2kWh, cutting electricity use in half.

And this is for arguably the most extreme use case for a heat pump hot water unit where it's "cold started" right at the coldest moment in Winter in cool-temperate climates (such as SE Australia). Think for example, arriving at a ski chalet and having to turn on the hot water unit before someone can take the first hot shower.

On a more typical day of the year, perhaps with overnight ambient temperature of 10-15oC, the COP would rise to ~4, equating to an electricity consumption of 2kWh to heat the 300L of water. A lot of units will be set to heat during the warmest part of the day, let's assume an ambient temperature of 25-30oC, where a COP of ~5-6 is more typically achieved. However, there are obviously diminishing returns for COP of 4 vs 5.

In arctic climates, heat pumps are still used, but with a ground or aquifer source rather than ambient air source.[2]

[1] https://en.wikipedia.org/wiki/Coefficient_of_performance

[2] https://en.wikipedia.org/wiki/Ground_source_heat_pump

If 4.2 (or 4.1) is really the annual coefficient of performance (turn 1kWh electric energy into 4.2kWh heat energy) then this is a very good value.

Because heating water requires higher temperature differences (usually heat pumps get more inefficient then). And with an "ordinary" (propane) heat pump you get such high numbers only in summer time (>=20°C) and for water temperatures of max 50°C.

If I'm not mistaken, it means 1kWh of electricity moves 4.1kWh of heat into your hot water tank. Heat pumps are amazing.

I believe that for every joule of electricity used, 4 or 4.1 joules are pumped from the environment into the water. This is contrast to conventional water heaters which are bounded by an efficiency of 1, where, for example, burning gas directly heats the water with some heat leaking into the environment instead of the water.