An inverter rating and a battery capacity describe different jobs. Understanding the difference makes quotations much easier to compare.
kW: what can run together
An inverter must support simultaneous demand and the starting requirements of connected equipment. A motor may need a brief surge beyond its normal running demand. Ask whether the quoted rating is continuous output and whether the proposed system supports the actual motor load.
kWh: how much energy is available
Battery capacity describes stored energy. Usable energy can be less than the nameplate capacity because of the permitted discharge range, reserve settings, temperature, ageing and conversion losses. A larger inverter does not automatically give longer backup.
A useful estimate, with limits
Backup hours are approximately usable battery energy divided by average supported load. If 4 kWh is available to the loads and the average load is 0.5 kW, the simplified estimate is eight hours. Actual runtime changes with appliance cycles and settings. Ask for a written runtime estimate for your essential circuits.
Further reading
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