That depends on several factors:
- Will the inverter be installed in a vehicle?
- How many watts does the appliance consume?
- How long do you want to run the appliance?
If you are installing in a vehicle, you can run the appliance for a very long time simply by running the engine. That way the alternator will be putting power back into the battery. You may need to run the engine at a high idle in order for the alternator to generate sufficient power.
If you are not installing in a vehicle, or you do not want to run the engine, then battery size will depend on how many watts the appliance consumes and for how long. Here is a simple formula:
Reserve Capacity = Running Time x Watts / 4.348
Running Time = How long the appliance will run (in hours) Watts = The watts of the appliance
After you calculate the required Reserve Capacity, simply purchase a battery with the appropriate Reserve Capacity rating. To get a higher Reserve Capacity, you can connect several batteries in parallel. The Reserve Capacities will add up.