This is a question we get asked all the time. Usually, it depends on the loads, the capacity of the inverter should be not less than the appliances used on same time. Let’s say your largest load is a microwave. A typical microwave will draw between 900-1200w. With this load you would install a minimum of 1500w inverter. This size inverter will allow you to run microwave and have a little leftover for running small items like a phone charger, fan, etc.
On the other hands, you should consider discharge current that a lithium battery can deliver. YIY LiFePo4 battery with internal BMS system is capable of delivering a maximum discharge of 1C. Let’s take 48V100AH as an example, the discharge current is 100Amps. When calculating the amp usage of an inverter, you take the output wattage of the inverter and divide it by the low battery cut-off voltage and the inverter efficiency, i.e. 3000W/46V/0.8=81.52Amps.