Miter Angle Calculator

Three different questions get asked with the same three words, and the reason mitres gape is usually that the wrong one got answered.

A frame or box with equal sides

Walk around the outside of any closed shape and you turn through 360 degrees in total. A shape with n equal sides turns 360/n at each corner, and that turn is shared between the two pieces meeting there. So each piece is cut at 180/n.

A square picture frame: 180 ÷ 4 = 45 degrees. A hexagon: 30. An octagon: 22.5. A five-sided planter: 36. The formula never changes and it does not care how long the sides are, only how many there are.

Note what this does not depend on: the shape being regular in the sense of equal side lengths. A rectangle and a square both take 45 degree mitres, because both turn 90 degrees at each corner.

A corner that is not 90 degrees

Walls are rarely square. Older houses are frequently a degree or two out, and the gap that opens at the front of a mitre is exactly that error made visible.

Measure the actual angle between the two surfaces, then cut each piece at half of it. A 92 degree corner takes two 46 degree cuts. A 178 degree near-straight run takes two 89s.

One complication: most mitre saws read from 90 rather than from zero, so the scale shows the complement. For a 45 degree cut the scale reads 45 because 90 minus 45 is also 45, which conceals the issue neatly until the first non-square corner. The calculator gives both numbers.

To measure a corner without an angle finder, hold two offcuts against each wall, overlapping, scribe along both, and measure the angle between the scribed lines with a protractor. A digital angle finder costs little and removes the guesswork.

Crown moulding, which is a different problem entirely

Crown does not sit flat against the wall. It leans, bridging the corner between wall and ceiling at what is called the spring angle, most commonly 38 or 45 degrees. That tilt means the blade has to swing and tilt at once, and the two settings do not come from halving anything.

The relationships come from spherical trigonometry:

miter = arctan( sin(slope) × tan(corner ÷ 2) )
bevel = arcsin( cos(slope) × cos(corner ÷ 2) )

where slope is 90 minus the spring angle. For a standard 38 degree crown at a plain 90 degree corner, that gives a miter of about 31.6 degrees and a bevel of about 33.9. Neither is a number anybody would guess, which is why crown has its reputation.

The alternative to compound cutting is to cut crown "nested": stood upside down against the saw fence in the same orientation it will occupy on the wall, with the fence acting as the ceiling. Then it is a simple mitre at half the corner angle, and no bevel at all. This works and is how many finish carpenters prefer to do it, but it only works on a saw with enough fence height for the moulding, which rules out larger profiles.

Inside and outside corners

For an inside corner, the pieces meet with their long points at the back. For an outside corner, the long points are at the front. The angle is the same; the orientation on the saw reverses. Marking which face is "up" before cutting saves an astonishing amount of material.

Many finish carpenters do not mitre inside corners at all. They cope: one piece runs square into the corner, the second is cut to the reverse profile of the first with a coping saw and fitted over it. A coped joint absorbs seasonal movement and a slightly out-of-square wall without opening, which a mitred inside corner does not.

Why a joint still opens after the maths is right

Angles are only half of it:

• The saw fence is out. Check it with a square rather than trusting the factory detent.
• The stock is not flat. A bowed piece contacts at one edge and gapes at the other regardless of the angle.
• The blade is deflecting. Cutting fast in hardwood pushes a thin blade sideways, leaving a cut that is not square to the table.
• The wall is not flat near the corner, which is common where drywall compound has built up.

Cut a test joint in offcuts before touching finished stock. Two scrap pieces cost nothing and tell you in ten seconds what a full-length piece of moulding tells you expensively.