I'm trying to make this circle for my pool to put 3" of sand in it
You can't figure this out without knowing how many boards your circle will have; once you choose the number of boards, just divide 360 by the number of bevels (one for each end of each board) and that's how far from 90° each end should be.
So, if you have 4 boards (a square):
- 4 * 2 = 8 bevelled ends
- 360° / 8 = 45°
- each end should have a 45° bevel on it:
If you have 20 boards:
- 20 * 2 = 40 bevelled ends
- 360° / 40 = 9°
- each end should have a 9° bevel on it, so each end should be cut 9° from perpendicular:
A couple of possible optimizations:
- When you're cutting a board to length with a (say) 9° bevel, you automatically create a second end with a 9° bevel in the opposite direction. So, flip the board over and then cut THAT board to length with the 9° bevel. Bingo: half as many cuts.
- Another alternative would be to leave one end of each board square (what I'm calling a 0° bevel), and then cut the other ends at twice the angle calculated above. Depending on the situation, this may mean less work.
(Just to be clear: what I'm calling a 9° bevel will result in a board whose end is cut almost perpendicular to the sides, not a board with an extremely sharp point on the end. Here's a page with more math for your calculations.)