Also, you didn't make it clear whether the "width" will be the narrowest dimension (flat to flat) or the widest dimension (corner to corner). I'm guessing since you want to rotate the table that it has to be able to rotate within a 4 foot diameter without hitting anything.
Here's a solution for 4' corner to corner:
Divide the octagon into 8 triangles. 360 degrees / 8 = 45 degrees
Now bisect a triangle to form a right triangle: 45 / 2 = 22.5 degrees.
OK, so the hypotenuse of the right triangle is two feet. The short side will be 2 x sin(22.5) = 2 x .3827 = .7654 feet
Double that number to get the width of one side of your octagon: 2 x .7654 = 1.531 feet 1.531 x 12 = 18.37 inches; 1' 6-3/8"
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