A short lesson
Amp-hours are not the whole story
Amp-hours describe charge capacity. Multiplying amp-hours by battery voltage converts that rating to watt-hours, a more useful measure when a load is rated in watts.
A 12 V, 100 Ah battery contains a nominal 1,200 Wh. If you plan to use 50% of its capacity and an inverter is 90% efficient, about 540 Wh reaches the load. A steady 500 W load therefore has an idealized runtime of about 1 hour and 5 minutes.
Runtime estimates are planning numbers, not guarantees. Motors and compressors may also need a brief startup surge that is much higher than their running power.