Multiply daily watt-hours by days of autonomy, then divide by bank voltage and depth of discharge. A system using 3,000 Wh per day, needing 2 days of backup, on a 48V lithium bank at 80% depth of discharge, requires (3,000 × 2) ÷ (48 × 0.80) = 6,000 ÷ 38.4 = 156 Ah — about 6 kWh of usable storage, or two 100Ah batteries. The calculator above returns amp-hours, usable and total kWh, and the number of 100Ah batteries.
Two numbers drive battery bank size: how much energy you use per day and how many days you must run without sun. Depth of discharge then decides how much of the bank is actually usable — you cannot drain any battery to zero without destroying its lifespan. Building depth of discharge into the math is why a "6 kWh" load needs a bank rated well above 6 kWh of nameplate capacity.