I'm looking to calculate the angle I need to cut on square tiles that will be arranged around the edge of a circular pool.
Given that radius is 7' and that tile width is 12", how many tiles are needed to close the full circle, when distance between each tile is 1/4". At what angle does each tile need to be cut on both sides, so that when laid in a circle, sides of the tiles are parallel to each other? Can somebody point me in how to calculate this?
Best Answer
For your circle & tiles:
12-1/4 inches if you leave the tile full-width at the outside edge - tile plus grout.
2 pi R is circumference - 43.923 feet. 527.79 inches.
Divide by 12.25 to get number of tiles. 43.084 - depending on the project, you either figure 43 is close enough (0.27 inch grout line rather than 0.25) or you use 44 tiles and trim more off them (not full width at edge - 11.745" at outer edge.)
360 degrees in a circle divided by number of tiles = the angle of cut
360 degrees divided by 43 = 8.37 degrees per tile, to make symmetric, cut 4.185 degrees on each side. For 44 tiles, 8.18, 4.09.
To get fussy (the 43/44 may be near enough to make it matter) you could check with the fact that the edge of the tile is not really "the circumference of the circle" but a chord making up a polygon inscribed in the circle. Chord length = 2 * r * sin (c/2) where c is the "central angle" - so c/2 is 4.185 or 4.09 degrees for 43 or 44 tiles, respectively. Looks like it might make it 0.26 rather than 0.27 inch grout line for 43.
In real life, start from opposite sides and work to the point where you have one tile left on each side - check the fit of that as constructed and trim to fit as needed, since getting grout lines precisely repeatable to the 100th of an inch is unlikely in practice.