It depends on what you have now and what backup heat comes with the system. Efficiency (HSPF2) describes operating cost, not panel capacity. A compressor may draw less than an older air conditioner, or it may not; the backup strips, if present, are a new or larger resistance load. A 100-amp all-gas house might take a heat pump with modest or no strips and still struggle if you also add a charger. A 200-amp service usually has more options.
Contractor pages titled “panel upgrade for a heat pump or EV charger” exist because the two projects collide. If both are in your plan, read the 100-amp and 200-amp combination pages and put both loads on one sheet. The optional-method examples there are educational, not approval.
Use the panel calculator for capacity and the operating-cost calculator for the bill question — they are not the same question.
This is not a permit calculation, a utility approval, or a substitute for a licensed electrician, HVAC contractor, or the authority having jurisdiction. Panel Headroom is an independent educational site. It is not a utility, a certification body, or a contractor. Electrical and generator work that is done incorrectly can cause fire, shock, or carbon monoxide poisoning. Use the adopted electrical code and manufacturer instructions; pull permits where required.