Hi we dealt with Inverter battery sizing and calculation in the full course and I will ask you to refresh or take the course here.
In Lecture 3.3, we gave this example which I will reproduce here:
A house in Lagos, Nigeria has the following electrical appliance usage:

• 1 x 10 Watt LED bulb used 4 hours per day.
• 1 x 70 Watt fan used for 2 hours per day.
• 1 x 75 Watt refrigerator that runs 24 hours per day with compressor run 12 hours and off 12 hours.

We will power the system with 12 Vdc, 80Wp PV module.
1. Calculate the daily power consumption

 

Total appliance use = (10 W x 4 hours) + (70 W x 2 hours) + (75 W x 24 x 0.5 hours)

 
= 1,080 Wh/day

Total PV panels energy needed
= 1,080 x 1.3 (this is the energy lost in the system)

 
= 1,404 Wh/day.

2. Inverter sizing
Total Watt of all load = 10 + 70 + 75 = 155 W
To avoid overloadof inverter, the inverter should be considered 25-30% bigger size.
    The inverter size should be at least 195 W or greater.
4. Battery sizing
Total appliances use = (10 W x 4 hours) + (70 W x 2 hours) + (75 W x 12 hours)
Nominal battery voltage = 12 V
Days of autonomy = 2 days
    Battery capacity = [(10 W x 4 hours) + (70 W x 2 hours) + (75 W x 12 hours)] x 2
(0.85 x 0.6 x 12)
Total Ampere-hours required 352.94 Ah Approx 400Ah
    So the battery should be rated 12 V 400 Ah for 2 day autonomy.
Do you understand?

Ok, you should also watch this video to get further clarification.