Two different questions
The inverter size is about power: how many watts can be drawn at one moment. The battery size is about energy: how many watt-hours you need to get through the outage.
People mix these up. A big inverter on a small battery runs everything for a short time. A big battery on a small inverter can only run a few things, but for long.
Step 1: list what you want to keep running
Walk through the house and decide what must work during an outage. Most households keep lights, Wi-Fi router, TV, fridge, phone chargers and perhaps a laptop. Big heating loads such as a geyser, stove, oven, kettle and air-conditioner use a lot of power and drive the cost up quickly. Many homeowners leave those on the grid circuit or plan them separately.
For each item, find the watts on the label or in the manual. If it only shows amps, multiply amps by 230 for a rough figure.
Step 2: inverter size in watts
Add up the watts of everything that could run at the same time. Then allow for appliances with a start-up surge. A fridge compressor, a pool pump or a washing machine motor can draw several times its running power for a second or two. Check that the inverter can handle that surge, not only the running total.
Leave some headroom. Running an inverter at its limit all day is hard on it.
Step 3: battery size in watt-hours
For each item, multiply watts by the hours you expect to run it during an outage. Add the totals. That is the energy you need.
Worked example. Lights 100 W for 4 hours is 400 Wh. Router 15 W for 4 hours is 60 Wh. TV 100 W for 3 hours is 300 Wh. Fridge 150 W running about half the time over 4 hours is 300 Wh. Phone and laptop chargers 100 W for 2 hours is 200 Wh. The total is 1,260 Wh.
Now add a margin. A battery should not be run flat, and lead-acid in particular lasts far longer if you use only part of it. Check the usable capacity, which is lower than the label on many batteries. If a battery gives 80% usable, you need about 1,575 Wh of rated capacity for this example. Some installers add more again to cover longer outages.
What else changes the answer
- Outage length. Load-shedding schedules and unplanned outages can both run longer than you expect.
- Solar panels. Panels refill the battery during the day, so a bigger array helps when outages are back to back.
- Lithium or lead-acid. Usable capacity differs between them.
- Single phase or three phase supply to the house.
- Future loads, such as a pool pump or an electric car charger.
Let an installer check your numbers
Take your list to a qualified installer. They will check surge loads, the DB board layout and which circuits go on the backed-up side. A good quote shows the inverter rating in watts, the battery capacity in watt-hours and the usable portion, so you can compare quotes properly.
The job behind this: Inverters and battery backup.