I am making a small barrel out of 1X4’s. 11.5 diameter. I am dividing the circumference by 12=3.013 inches for each board cut on 15 degrees. When I am finished the 12 points will be about 1/8" higher than the flat spot on each board. Will my 11.5 inches be on the high spot or the low spot? I plan to actually cut it slightly oversize anyway and then sand it down but the closer I can get the better.
Do you want the interior diameter or the exterior diameter to be 11.5?
What you’ve calculated is the arc length of 1/12 of a 11.5 diameter circle, which isn’t quite what you want in either case.
For just about any regular geometric shape like a dodecagon you can search on “dodecagon formula” and bring up your choice of websites providing helpful info like this dodecagon calculator and others like this one containing the formulas. One of them probably includes formulas for inscribed and circumscribed circles in a dodecagon.
Those calculators are cool. I ended up just measuring it with a ruler and compass.