Can somebody please explain what the radius means?
At home I have a Vintage Stratocaster with the fingerboard radius 184 mm, and I want to buy an American Deluxe, but it has a fengerboard radius of 241 mm.
What does it mean, and does it make any difference to my playing or the sound?
it's how much of a curve the fretboard has. basically, if you continued the curve of the fretboard, the radius is how far it would be to the center of the imaginary circle. so bigger number means flatter fretboard. it won't make any difference to the sound, and it won't be a huge jump for playing. just takes some getting used to.
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I am Michael!
The functional difference is that necks with smaller radii are usually easier to do barre chords on (your fingers take to a curved surface better) but flatter fretboards are easier to get low action on and easier to do bends on.
Hi, I'm Peter
The more curved the fretboard (lower radius) the more comfortable it is to chord, but you'll "fret out" on big bends more often.

Flat fretboards mean you won't fret out .
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^I'd let a pro look at it. Once you get into the technicalities of screws...well, it's just a place you don't want to be, friend.