Miter Angles

Segments and staves are used in woodworking to form circles, arches, cylinders and polygons. Once you decide on how many sides or segments your polygon will have, simply divide 360 degrees by the number of segments. Each segment and its radial lines form a triangle whose included angles total 180 degrees.

Divide 360 degrees by the number of segments desired, to find the included angle of the radial lines. Subtract this number from 180 degrees. Divide the result by two to find the miter angle to be cut on each end of a segment, or each side of a stave. This holds true for any number of segments.

Let us assume a pentagon, which, of course, has 5 sides. Divide 360 by 5, and you get 72 degrees. This is the included angle of the radial lines, and since a triangle has 180 degrees, the angles at each end of the segment are half of the difference between 180 degrees and 72 degrees. (360/5=72. 180-72=108. 108/2= 54) The angle at each end of the segment is 54 degrees, which is the miter angle at which you will cut each segment.

Table saw and miter saw angle scales are relative to the blade being perpendicular to the table or to the fence, so it is necessary to deduct the miter angle from 90 degrees in the above formula to arrive at the proper angle setting on the saw.

Notice that in a 3 piece project, the miter angle is 30 degrees, where a table saw or a miter saw generally will not tilt past 45 degrees. It is necessary to set the blade at 30 degrees and place the board vertically against the fence. There are some inherent dangers in doing this, as the board must be supported by some supplemental means. First, a tall fence is required to keep the board vertical. Second, a rail should be placed on top of the rip fence, and clamped to the work piece so the work piece is supported beyond the cut to prevent the work piece from dropping onto the trailing edge of the blade at the end of the cut. Alternatively, clamp two pieces together and readjust the rip fence accordingly.

A power miter saw can be used to make cuts less than 45 degrees by securing an auxiliary fence 90 degrees to the saw fence, but I don't advocate doing so unless the work piece is of sufficient length to provide adequate finger room for the operator. This is particularly useful when cutting complimentary angles such as for forming odd shapes in decking. Use an adjustable work stand to support the board when turned 90 degrees from the fence.

Set the blade angle for the required angle, and cut one end with the board against the auxiliary fence and the other end with the board against the saw fence over the top of the auxiliary fence. Doing so in this order allows the length to be controlled against the saw fence. Make your auxiliary fence from scrap 3/4" plywoo. ans place a second piece of 3/4" scrap on the other side of the blade to support the drop off.

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