I assume you are talking about a Geo Heat pump system versus a conventional HP system.

If correct you need to know the rated COP for each system to make the calculation. A good dealer can provide this info.

When you get that, I can provide a link. Of course you need to know electric rate.

IMO

And do not forget the cost of money.

Brickeye is correct.

Not only operational cost but also upfront cost, maintenance, cost of money, etc...

And of course, it is most dependent on climate.

In Wisconsin, a geothermal might save 50% compared to conventional while in central NC, the quoted number is 20%.

Geothermal saves very little when the ambient temp is 35-95. So how long you spend under 35 (or over 95) really affects how much geo helps.

I think so many times geo is compared to oil or straight electric which is completely unfair. The other comparison is old "conventional" heat pump. Like when "a geothermal system is the equivalent of removing 2 cars from the road" - maybe compared to oil heat in a large, leaky, and northern house.