What are the mitre saw angles for a hexagon and an octagon?

Question

What are the mitre saw angles for a hexagon and an octagon?

Answer 1

hexagon 30

octagon 22.5

The way to figure this out is to divide 360 by the number of sides.  This gives you the "central" angle of an imaginary triangle centered at the center of the polygon.  The base of this triangle is one of the edges of your polygon.

Since the sum of angles of a triangle must be 180, subtract that number from 180 and divide by two.

For example, hexagon (6 sides) will have a 360/6 = 60 degree central angle.  180-60=120    and 120/2 is 60.  why not 30?!?!   Well because when you cut a board straight across, your saw or miter gauge reads 0 degrees, not ninety.  So you angle the blade to 30 to get a 60 degree cut.  Confusing, isn't it?

Answer 2

The angles total 360 degrees, so just do the division by six and eight.

Answer 3

When you do the math, an octagon will have angles at each corner of 45 degrees, the cut on each side is 1/2 of that so set the saw at 22 1/2 degrees. Same thing on the hexagon.  With most saws that are mass produced, the the angle is close but not exact, do several test cuts on scraps before you do the final cuts.

Answer 4

octagon is 22 1/2 cuts

hexagon is 30

if you figure your 360 divided by the number of sides, you'll get your angles, divide by 2 to get the miter