How to Calculate Compound Miter Saw Settings Using the Miter Angle and the Bevel Angle

Sometimes when you engage in woodworking projects, you're going to have to make compound cuts -- that is, cutting a piece of wood at an angle to both horizontal and vertical axes. When two workpieces are designed to fit together at a given angle from the horizontal, the flat angle between the joints will correspondingly decrease. You need to know how to calculate this angle when making cuts with a compound miter saw.

Scientific calculator
Workpiece diagram
Compound miter saw

Instructions

- 1
  Determine the number of sides the whole workpiece has. For example, assume you want to create crown molding for a hexagonal room. You need to know your flat miter cut angle, or the deviation from a perpendicular cut; the easiest way to calculate it is to divide 180 by the number of sides the room has. In a six-sided room, the flat miter angle is 30 degrees. Label this as "A."
- 2
  Determine the bevel angle, the angle at which the piece deviates from a horizontal plane. Assume, for example, that you want your crown molding to form a 30-degree angle with the ceiling. Label this bevel angle as "B."
- 3
  Plug A and B into the formula "arctan(tan(A) * cos(B)." Doing this gives you "arctan(tan(30) * cos(30)." Arctan is the inverse of a tangent, or "tan-1" on a calculator. If you entered the formula correctly, you should get 26.565 degrees as the miter angle.
- 4
  Plug A and B into the formula "arcsin(sin(A) * sin(B)." Like arctan, arcsin is the inverse of the sine function, or "sin-1." You should get 14.478 degrees as the bevel angle.

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