DC battery cable and fuse size for an inverter
Undersized battery cable gets hot and can start a fire. Enter the inverter's continuous watts, the battery voltage and the one-way cable run to get the fuse rating and the minimum copper cable, sized by ampacity and by voltage drop (the larger wins).
Basis
Current = watts / (volts x efficiency). Fuse = 125% of that current, rounded up to a standard rating (2023 NEC 240.6(A)). Cable by ampacity: Table 310.16 copper, chosen column, must carry the fuse rating. Cable by voltage drop: 2 x length x current x resistance / 1000, resistance from Chapter 9 Table 8 (copper, 75 C). Copper only, single conductors up to 500 kcmil. Marine and welding cable is rated differently from NEC building wire; follow the cable maker's ampacity table and the inverter manual, and use the larger cable when in doubt. Load is the inverter's continuous rating, not its surge.
Next: AC wire and breaker size, voltage drop, home battery size.