#1
Is a 12 inch fretboard radius considered a thin or a thick neck?
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#2
Radius has nothing to do with neck thickness or width. Radius is the cruve of the front of the fretboard (and the fretwire); something like a 7.25" radius is very rounded and most people find it easier to play chords and such on, while a radius like 16" is very flat and many people find this easier to play faster lead runs on. A flatter radius also helsp with string bending; on a very cruved fretboard, when you bend a note upwards it can "fret out" and buzz.

A 12" radius is just a touch flatter than average. For reference, most modern Fender necks have a radius of 9.5" while the necks of most guitars from brands like Jackson and Ibanez have a radius of 16".
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#3
Neither. Fretboard radius only deals with the fretboard and denotes how curved the surface of the board is. Neck thickness is described separately.
#4
Oh ok thanks guys. Sorry, I just got a little confused there
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