surely one can run a mini-fridge on a large, thousand dollar camping battery for a couple of days

That becomes a pretty simple calculation. The battery will have a certain number of Watt-Hours of capacity at full charge. The fridge will draw a certain number of Watts. It’s basic arithmetic from there.

The unknown here is how much time the fridge spends running, vs how much time it spends sitting there. No idea, and the answer will depend entirely on how often it is opened, how much stuff is put into the fridge that isn’t already cold, etc.

Put a WAG on it of 50%.

Going back to the battery you listed when this started, it says a “whopping” 777 watt-hours. At 120v, that is 6.5 amp-hours. Figure your mini-fridge draws two amps. That gives you 3:15 of continuous use. If you figure a 50% factor for how often the fridge runs, you’ll get 6:30 in wall clock time.

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