What gauge wire from batteries to inverter

pianotuna wrote:
I'll have to tell my 700 watt heater that it has no inrush the next time it refuses to operate on a 750 watt inverter. I'll threaten to spank it.

You are correct. A typical heater circuit can have up to 25% increase in inrush current due to to heater element having a much lower resistance when cold until it reaches operating temp. It's not as much as an inductive motor startup current but it's still there.