To calculate the amp-hours (Ah) of a battery, you need to know the total Load and its Backup-hours (Wh). The formula for calculating Ah is
Assume Total Load- 500 watt
Battery= Load*Backup Hour
=500*4
=2000/12
=166.66 AH
Battery Required= Approx 180 AH( As per availability and future upgradation)