You might, if you care about cleaner power for electronics and for a modern furnace control board. Conventional open-frame generators can produce a rougher waveform than inverter models, and manufacturers market inverter generators specifically for sensitive electronics. A furnace board, a modem, or a laptop is the usual reason homeowners ask. That is a real quality-of-power concern. It is not a promise that only an inverter will work, and this page will not invent a maximum THD percentage as if it were a national requirement.
What you can do without a made-up number: read the generator’s published waveform or THD statement, read any notes in the furnace manual about generator or UPS use, and prefer a listed inverter or “clean power” unit when the backup set includes controls and electronics. A transfer switch or interlock does not change the waveform; it only changes how the power enters the house. A cheap modified-sine UPS in front of the furnace is a different product discussion for the HVAC technician, not a wiring recipe from this site.
Size running and starting watts first with the calculator — an inverter generator still has to cover the 1/3 hp furnace fan and the refrigerator surge in the essentials example. Place the unit outdoors, 20 feet from the house, as the CPSC page describes.
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.