A miter angle splits a corner so two pieces meet cleanly. The right saw setting depends on the corner angle, the number of sides, and how the material sits against the saw. The arithmetic is short; the errors nearly always come from which angle the saw scale is reporting.
Simple Corners
For a square frame corner of 90 degrees, each mating piece is commonly cut at 45 degrees.
Treat the corner input as the included finished angle between the joined pieces. For two equal cuts, subtract that angle from 180 degrees and divide by two to get the miter setting from square.
The logic is that the two cut faces together have to close the gap between the pieces. Splitting the remainder evenly is what makes both pieces identical and the joint symmetrical.
Polygons and Trim
Regular polygons use equal outside angles, so the miter can be calculated from the number of sides alone. A hexagonal frame, an octagonal planter and a twelve-sided clock face all reduce to one division.
Trim work is harder because walls are rarely square. A corner that measures 91 degrees instead of 90 needs 44.5 degrees on each piece, and the half-degree shows as a visible gap on the outside of the joint.
- 4 sides: 180 / 4 = 45 degrees per cut.
- 5 sides: 180 / 5 = 36 degrees per cut.
- 6 sides: 180 / 6 = 30 degrees per cut.
- 8 sides: 180 / 8 = 22.5 degrees per cut.
- 12 sides: 180 / 12 = 15 degrees per cut.
Miter Angle Formula
Both formulas below return the cut angle measured from square — the angle most mitre-saw scales show as a deflection away from a 90-degree crosscut.
If your saw scale is labelled the other way, use the complement instead. Establish which convention applies before cutting stock you cannot replace.
Simple corner: miter cut from square = (180 - included corner angle) / 2
Simple corner complement = included corner angle / 2
Regular polygon: miter cut angle = 180 / number of sides
Saw complement angle = 90 - miter cut angle
Worked Example
A four-sided frame has 90 degree corners, so each miter cut is (180 - 90) / 2 = 45 degrees.
A 120 degree included corner uses (180 - 120) / 2 = 30 degrees for the miter cut from square. A six-sided regular frame has the same included corner and uses 180 / 6 = 30 degrees — the two formulas agree, as they should.
Now take an out-of-square wall measuring 93 degrees. The cuts become (180 - 93) / 2 = 43.5 degrees each. Cutting both at 45 would leave roughly 3 degrees of gap spread across the joint.
Miter, Bevel, and Compound Cuts
A miter rotates the blade across the face of the board. A bevel tilts the blade through the thickness. They are independent settings that solve different parts of a joint.
A flat picture frame needs only a miter. Crown moulding that sits at an angle against both wall and ceiling needs both at once — a compound cut — and the required settings are not the same as the wall angle.
This guide and the calculator cover flat miters and regular polygons. Compound crown settings depend on the moulding's spring angle and need a separate calculation.
Why Test Cuts Are Not Optional
Saw calibration drifts, blades deflect under feed pressure, fences move, and material is rarely perfectly straight. A calculated angle is a starting point, not a guarantee of fit.
Cut two offcuts at the computed setting, hold them together, and check the closed joint against a reliable square or against the actual opening. Adjust once, then cut the real stock.
- Measure the actual corner rather than assuming it is square.
- Calculate the cut angle for that measured corner.
- Confirm which angle your saw scale reports.
- Cut two scrap pieces at the setting and close the joint.
- Adjust the setting if the joint shows a gap, then cut project stock.
Common Mistakes
Most miter failures are not arithmetic failures. They are assumptions about the corner or the saw scale.
- Confusing miter angle with bevel angle.
- Assuming a wall or carcase corner is exactly 90 degrees.
- Setting the complement because the saw scale uses the other convention.
- Applying a flat-miter number to compound crown moulding.
- Cutting all pieces before test-fitting the first joint.
- Ignoring that stock thickness variation changes how a mitred corner closes.
Common questions
Why do miters need test cuts?
Real corners, saw calibration, blade deflection, and material movement can all affect the final fit.
Is a miter angle the same as a bevel angle?
No. A miter turns across the face of the material, while a bevel tilts through the thickness.
Why does my saw show 45 when the calculator says 45 but the joint still gaps?
Either the corner is not actually 90 degrees, or the saw scale is reading the complement rather than the cut angle, or the saw is out of calibration. Measure the real corner first, then confirm the scale convention with a scrap test cut.
Does this cover crown moulding?
No. Crown sits at a spring angle against wall and ceiling, so it needs a compound miter and bevel pair that this flat-miter calculation does not produce.
Sources
- Wood Handbook, Chapter 6: Commercial Lumber, Round Timbers, and Ties · USDA Forest Service, Forest Products Laboratory
Documents the surfacing and dimensional variation in commercial stock that makes test-fitting a mitred joint necessary rather than optional.
- Saw Blade Glossary · Rockler Woodworking and Hardware
Defines blade terminology, including kerf, used when a mitred joint has to account for the material the cut removes.