How do I calculated the outputted AC voltage of an H-Bridge inverter
The power inverter schematic you've posted uses U1 and U2 to drive Q1 to Q4, to put whatever supply voltage there is, in this case 12v, alternately forwards and backwards across the load. As the load is differentially driven, I prefer to call this +/- 12v. Some folks like to call it 24 v peak to peak, which while correct I find can cause confusion.

The logic inverter HC4049 is a low power device, completely unrelated to a power inverter, so you won't find any joy in its datasheet.

 Your overall system diagram is labelled oddly. Your battery is followed by (what appears to be labelled) a 'Rectifier Circuit'. You would use a high frequency power inverter at this point, to drive the transformer you've marked 'AC'. After the transformer comes a box labelled '...  Ah! the penny drops, I've just noticed the arrow.

Your overall system diagram is drawn right to left, sredaer (nertsew tsom dna) hsilgnE fo tou lleh eht sesufnoc hcihw &lt;-. Please draw diagrams so the major signal flow is left to right, even if you've put a direction arrow on it.