The math is easy. the formula for an octagon from a square is:

L – {L(.2071)2}/2

Where L is the length of the side of the square and .2071 is constant. You can simplify the formula if you break it into two pieces:

L(.2071)2 = LO

Where LO is the length of the octagon side. Plug that into the formula above and you get:

L-LO/2

tells you how far from each corner of the square to set the posts.

Example for this gazebo:

L=144"

144" – {144"*.2071*2}/2 = 42.1776"

or

144*.2071*2 = 59.6448 (length of the side of the octagon LO)

144-59.6448/2 = 42.1776

Don’t bother trying to measure out to 4 decimal places LOL! Just round it to two or three places and convert to a fraction.

If you want to skip ahead and see the finished product I posted a picture of it here

Where are the band-aids?---Pro Libertate!