1) Measure or estimate the average power consumption of your system in Watts. You need to provide this many Watts for 7x24 hours so multiply to get 1 week power consumption in units of Watt hours. This link provides some guidance:

https://www.pidramble.com/wiki/benchmar ... onsumption. As an example 2 W for a Pi3 implies 336 Watt hours.

2) Battery banks are typically a different voltage than required by the Pi, so a suitable power converter will be required. There will be a conversion efficiency factor for this, typically on the order of 75% for a switching converter. Divide the Pi power by that efficiency to get the power at the battery. For the example above we have 336 Wh / 0.75 = 448 Wh minimum at the battery.

3) Batteries are specified in units of Amp Hours. Multiply this by the nominal voltage of the battery to get Watt hour capacity of the battery. You'll need one that can provide at least the capacity from step 2.

4) Recognize that batteries lose capacity with age, temperature, etc and that there is some (sometimes a lot of) shading of the nominal battery specifications and double the capacity from step 3.

5) If this absolutely positively has to work, test and measure the system components carefully to see if they match the specified performance under your specific operating conditions.