# How to Calculate a Compound Miter

By James T Wood ; Updated September 15, 2017

#### Things Needed

• Scientific calculator
• Tape measure or T-square
• Carpenter's protractor

When making a miter cut, you're often dealing with material and installation surfaces that aren't completely flat. Compound miter saws help to account for this by allowing you to adjust both the miter (the angle at which the pieces of material will fit together) and the bevel (the angle of the pieces relative to the mounting surface). For example, if you're installing crown molding into a 90-degree corner, you know you want a miter of 45 degrees so the two pieces of molding will fill the corner. But the bevel also needs to be set correctly to make sure the molding lines up correctly when it's installed to the wall.

Measure the corner(s) for which you're cutting the molding (or framing or trim). Using a carpenter's protractor, align the arms with each surface and note the angle. Most corners will be 90 degrees. Half of the corner angle is your "flat miter" number. You can use the same calculations for a 90-degree inside or outside corner--you'll just have your off-cut on the opposite side. For example, if the off-cut is to the right for an inside corner, it'll be to the left for an outside corner, with all the miter and bevel settings being the same.

Measure the molding for three dimensions. The wide, flat surface on the back of the molding is the "width." Note that dimension. Measure the distance the molding projects out from the vertical surface (such as the wall). Measure the distance the molding drops from the horizontal surface (such as the ceiling). You now have three numbers: width, projection and drop. In this example, let's say the width is 5 inches, the drop is 3 inches and the projection is 4 inches.

Calculate your true miter setting by dividing the projection by the width. Then find the tangent of the flat miter and multiply those two numbers. In our example, that would be four divided by five, which equals 0.8, while the tangent of 45 degrees is one. So the product of 0.8 and one is 0.8. Then take the inverse tangent (arc tangent or tan^-1) of that product. In this example that would yield a miter of 38.6 degrees.

Find the bevel setting by dividing the drop by the width, then find the sine of the flat miter and multiply those two numbers. In our example, that would be three divided by five, which equals 0.6, while the sine of 45 is 0.7. So the product of 0.6 and 0.7 is 0.42. Then take the inverse sine (arc sine or sin^-1) of that product. In this example that would yield a bevel of 25.1 degrees.

#### Tip

The formulas look like this: Miter = InvTan [Tan(FlatMiter)_Projection/Width] Bevel = InvSin [Sin(FlatMiter)_Drop/Width]

Test your settings on scrap lumber to make sure things will fit correctly.