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I'm trying to make this circle for my pool to put 3" of sand in it

  • Hello, and welcome to Stack Exchange. How many boards will your (mostly) circle have? – Daniel Griscom Jun 5 '16 at 13:38
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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:

Rectangle with beveled corners

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:

20-sided polygon

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.)

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    I could add to this good answer that the bevel for 20 boards will apply to any length boards. Just make certain that all the boards are the same length. – Michael Karas Jun 5 '16 at 18:31
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    If you do decide to go with 20 boards to make the 28' diameter circle you will need to make each board about 4' 5 3/16" length on the outside (long side). If you want to make a more rounded circle of course more boards would be required. For example of you chose to go with 36 boards the bevel would be 360 / (2 * 36) = 0.5°. The outside length for 36 boards would be 2' 5 3/8". This latter choice would leave little waste if starting with 8' boards. The 20 sided design would require starting with 10' boards and there would be over a foot of waste from each board if cutting two per board. – Michael Karas Jun 5 '16 at 19:15

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