When you see the amp hour (AH) rating on a battery, it can be deceiving. The amp hour may not apply to the full voltage listed but on an individual cell.
For example, I recently purchased a 12v lithium battery listed as 20 AH. However, the battery also listed as 76 watts. That means the AH rating is based on a 3.8v cell which equates to two of the lithium cells at 1.9v each. Note: this means this is actually a 11.4v battery but lists as 12v. So for the full 11.4v, the actual AH = 76/11.4 = 6.6AH. Next you have to apply the DoD (depth of discharge) that a battery can handle before the voltage significantly drops. For a lithium battery, this is ~ 80%. So the actual amount available is 6.66 x 80% = 5.3AH. I applied this battery to an 8 watt, 12v led light bulb (800 lumen output). Amps = 8 watts / 12v = 0.75amps. So the battery should last 5.3AH/ 0.75amps = 7.1hours. That is exactly what I got.
Now, applying this to an SLA (sealed lead acid) that you are discussing, the DoD is 50%. You also need the watt rating for the battery to
Correctly calculated the AH rating for the entire 12volts. Each cell is 2volts so the actual AH for the battery @12volts may be 100/6 x 50% = 8.3AH. If you are getting 45 minutes of run time, that would mean you have a 8.3AH/(0.75) = 11.1 amp load. Or 11.1amps x 12v = 133 watts.
By the way, when your 12v to 120v converter gets an input voltage below about 11volts, it will shut down to protect a lead acid battery. The converter wants a 14v input +/-. On my lithium battery that is not a concern so I added a buck boost electronic voltage regulator. I could the boost my voltage to 14v, hook it into a converter, and power a 120v load. The regulator and converter adds about 0.4 amps to the load so the equivalent 120 volt, 800 lumen bulb, my battery life reduced 50% to 4.5 hours. That is why using 12v loads with no converter is a more efficient way to use battery power.
