I thought I would write this up as a little tutorial for those who want a grasp of basic electrical theory. I am only going to talk in terms for dc circuits, ac circuits do weird things when inductors and capacitors are part of the circuit, think speaker crossovers.
Ohms Law states that the current(I) flowing through a circuit is equal to the voltage(E) applied to the circuit divided by the resistance(R) of the circuit.
Now, we're going to make the Ohms Law wheel. Draw a circle. Cut it in half horizontally, then cut the bottom half in half vertically. In the top half, put, "E (P)". In the bottom left quarter put, I (I). In the bottom right quarter put, "R (E). The letters in parenthesis are for Watts Law, which I'll get to in a bit.
Now, we have a circuit drawing 4 amps with 12v feeding the circuit. To find the resistance of the circuit, cover the R, the letters E and I give you the formula for finding it in this case E divided by I. So, 12/4= 3 ohms.
Now, a watt is a watt is a watt, ac or dc, it doesn't matter. Using the 400w inverter as our example, to find out how much current is used at 12 v, or available at 120v. The available current for you to use with whatever you plug into the inverter would be 400/120= 3.33 amps. The current needed to give you those 3.33 amps would be 400/12= 33.33 amps. Here we see that we need 10x the current at 12v to give us what we need at 120v.
These formulas assume Ideal conditions, not taking into account for the resistance in the wire or connectors used. and will probably not match up perfectly with an ohm meter or an amp probe, but they will be real close to our calculations.
Hope this helps,

Larzzzz