It takes about 45 amp-hours of 12-volt service to cook a meal.
I'm curious about the "cook a meal" metric. Is that heating up a can of chili or preparing a three course meal with dessert? Not that I commonly do the latter on board. Probably what would help would be boiling a 70 degree quart of water and using an amp hour gauge on the battery (or even a Kill-a-Watt meter at the inverter). The Kill-a-Watt wouldn't take into account the effectiveness of the inverter, but it would give us some real numbers to work with. My calculation is that onboard induction cooking will take less than 45 amp-hours per day.
I'm replacing my propane with induction right now. Just pulled the stove out and I'm working on a new countertop. I'll probably start another thread as this one went FAR afield into $10,000 battery banks and crossing the Atlantic under electric propulsion, neither of which I care about.
But as to actually cooking with electricity vs. propane, I'm guessing that rolomart doesn't have a pure sine wave inverter. Those would be a $100-300 more than what he paid at Harbor Freight. From that I'm also guessing that his hot plate is resistance, not induction, as modified sine wave inverters don't run induction plates, or if they do, run them very ineffectively. Inexpensive inverters also tend to have 80-90% efficiency in converting DC to AC. I found a PSW inverter that has 93% efficiency with a remote switch to eliminate any standby losses. It is hard to get any apples to apples on propane vs. induction, but electric to electric should be possible.
One of the issue for me was the lack of an oven. In an earlier post I suggested that a Coleman stovetop oven could be used with induction. My experiments failed. I put a piece of mild steel on the induction stove top under the oven, thinking that it would get hot enough to throw off sufficient heat to heat the oven +350. Nope. Induction burners have a safety feature (dammit) that limits the temperature to 450-500, not nearly as hot as a Coleman stove (open flame) or electric resistance (glows red hot at +900F) in order to get a stove top oven hot enough. My induction top would get the steel just hot enough to start glowing, but then shut down for 5-10 minutes. I tried various things, including a fiberglass welding mat between the stove top and steel (to fool the temp sensor), but I was always foiled by the safety feature before the oven got hot enough. I could only maintain about 250 and that required resetting the induction burner each time after a safety shutdown and cooling period. I suppose I could eliminate the overheat safety feature to be like propane.
My present experiments involve the use of a Dutch oven on an induction stovetop. Most people aren't aware that the terminology came about because the English used "Dutch" as a pejorative. Dutch courage (aka, liquor), Dutch talent (aka, a poorly tied knot), Dutch auction (aka, sucker pricing). So I acknowledge that a Dutch oven is a workaround to a real oven. But, having been a professional chef, workarounds are often part of the job. It appears that I can do on 2 burners what requires 3 or 4 by unprofessional "toast burners."
The success or failure of my experiments will be updated.
Anybody interested in a vintage Magic Chef three burner propane stove without thermocouples? Original condition. I'm not sure it has even ever been cleaned. In my crazy induction stove top oven experiments, I did actually manage to burn something on the induction glass stove top. But the propane stove is a monument to burnt crap, crumbs, and popcorn. And that's just the top.
It wasn't just dust bunnies that I found in the 4" air space under the propane oven. I'll try to post a picture later.