We don't frequently lose power here, but I was thinking it might be a nice starting point if I picked up an MPPT that could also charge batteries from the grid and began building something that could power the house for around an hour. The calculations seem pretty straightforward, but the amount of battery power I came up with feels ridiculously low so I thought I'd ask for verification.

So on to the math! Based on an average power bill of around 3,000kWh/month, I divided by 30 days and 24 hours to come up with around 4167W of power. Looking on Amazon I am finding 12V 100Ah LifePO4 lithium batteries which provide 1280Wh (under ideal conditions, of course)... so if my math is correct that means I would only need four of these batteries to power the house for a full hour? Surely that can't be right???

I also ran across some pages suggesting the calculations for lithium are different than for lead-acid batteries, but I would think the only thing that matters here is the listed Wh capacity of the batteries?

If the math IS correct, that's still a lot of juice to deal with. I think ideally I would run the batteries in series at 48V. I found a Victron charge controller rated at 150V/45A which would give a little room for surges (4167W / 120V = 35A of average usage), but I would still need the equipment to do the switch-over from mains, and prevent backflow into the mains (or does the switch only provide one connection at a time, preventing this problem?).

Still a lot to consider, but if I were to get this initial setup in place then I should be able to simply start adding solar panels as time and funding allows. Please let me know if I'm on the right track or if I'm making a fundamental mistake in my math. Thanks!