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I only know it for sure for a circle with diameter equal to 1. The perimeter of a polygone with n sides inscribed in a circle with diameter 1 is equal to n times sin (pi/n), so for a hexagon it is 6 times sin (pi/6) = 3.0000.
For circles having another diameter, I would intuitively say that the formula becomes diameter times n times sin (pi/n).
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