So ive memorised the 5 shapes which has helped with fret knowledge and finding the root notes of the chords around the neck. Is there a formula associated with it for working out arpeggios and scales within it?
Well, not associated with it specifically as such, because they are the same arpeggios regardless. Your basic starting point is the shapes themselves. G with the G shape, C shape on C, D shape on D etc... The arpeggios are linked into each other very nicely if you're using the "caged" aspect.

Scales would most likely be affected just by the starting point and starting finger. The C shape would start with your pinky, the G shape would be the ring or pinky, The D, E and A shapes would be with the index finger. The E and A shapes could also use the middle finger for the more traditional approach, the index using the 3 notes to the string approach.

Think like that instead of thinking that its different formulas. The formula remains the same, the shape, however, changes. And this is best done on self discovery rather than finding the tabbed version. Hope this helps
caged is a simplified way of finding chords, so it takes a very small amount of theory and applies it. it's quite difficult to work from this into more complex things because they require more theory.

all the notes in the caged chords are part of the arpeggios of those chords, but not every note from those arpeggios is in those chords. If you want to get to grips with scales and arps it may be worth diving in to the big wide world o' theory, starting with the crusade lessons that are on UG
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