A real simple rule of thumb I use for how much something will draw from the battery through an inverter is 10X its 120 vac amperage draw and then add 15-20% to that for the inverter's non-perfect efficiency. 10X because it requires ten times the amperage at 12 volts as it does at 120 volts to do the same amount of work (watts).
So if something draws 6 amps at 120vac, it's going to draw 60+ amps at 12 volts. Then do the amp-hour calculation based on the battery's amp-hour rating and you can come up with a reasonably good estimate at how long the battery will last.
