There are three things here at play, when thinking of losses in the use of inverters:
1. When an inverter is switched on and providing power to the main voltage, but no power is used, then often such power usage (sometimes referred to as resting current) is a few amps (as measured that battery
is supplying). Generally this resting current
is getting larger as the capacity of the inverter increases. Such power use can add up quite a bit over 24 hours.
2. Many inverters have a sleep mode, to reduce such resting current
. In fact the main power is disconnected, and as soon as something is plugged in, then power is restored. They need at least 5 to 15 watts appliance connected to the mains to switch the power on, ie a small phone charger
at times might not be able to switch the power on. Such level of minimum power can be adjusted on some inverters.
Resting current can be that way reduced to 200 mAmp to 1 Amp. Still over 24 hours quite a drain on the house batteries
3. Lastly there is the efficiency factor, as previously mentioned often around 80%, although the spec of some inverters offer 93-95% efficiency. That means, if a main appliance is using 200 watts, then with an efficiency of 80%, the batteries
has to supply 100-80=20% more power to provide that 200 watts. So the battery
is supplying 200+40=240 Watts. For a 12 volt battery that is an extra 40 watts, 40:12=3.3 amps.
Note that loss of efficiency is generally not linear with power use.
One can measure measure those losses and efficiency easily, with an amp meter in series with the battery supply of the inverter and using a incandescent globe (remember those?) connected to the inverter. Comparing that to the power used by the globe.