Miter angles for common corners and frames
These follow directly from the bisection rule and regular-polygon geometry; the saw-setting column applies to scales that read 0° at a square cut.
| Situation | Corner angle | Miter angle | Saw setting (from square) |
|---|---|---|---|
| Standard wall corner | 90° | 45° | 45° |
| Out-of-square corner | 88° | 44° | 46° |
| Bay window wall (135°) | 135° | 67.5° | 22.5° |
| Square/rectangular frame (n=4) | 90° | 45° | 45° |
| Hexagonal frame (n=6) | 120° | 60° | 30° |
| Octagonal frame (n=8) | 135° | 67.5° | 22.5° |
- Miter saw scales differ: most compound miter saws read 0° at a square crosscut (use the saw-setting column), while protractors and some layout tools measure the full cut angle from the workpiece edge. Confirm which convention your tool uses before cutting.
- This calculator covers flat miters. Crown molding installed 'nested' against the fence uses the same numbers, but cutting crown flat on the saw table requires compound (miter + bevel) settings derived from the crown's spring angle — a separate calculation.
What is a miter angle?
A miter joint joins two pieces at a corner by cutting each piece at half the corner angle, so the two cut faces meet in a seam that bisects the corner. The everyday case is a 90° corner — each piece is cut at 45° — but real rooms are rarely perfect: an out-of-square corner measuring 88° needs two 44° cuts, and a bay-window wall meeting at 135° needs two 67.5° cuts. Cutting each piece at exactly half the measured corner angle is what makes the seam close without a gap.
Closed frames follow the same principle applied around a polygon. A frame with n equal sides has interior corner angles of 180 − 360/n degrees, so each end of each piece is cut at half that: (180 − 360/n) ÷ 2. A rectangular picture frame (n = 4) needs 45° cuts, a hexagonal frame (n = 6) needs 60° cuts, and an octagonal frame (n = 8) needs 67.5° cuts.
How to use this miter angle calculator
- For a corner joint, measure the actual corner angle with a protractor or angle finder and enter it — do not assume 90°.
- Leave the number of pieces at 2 for a corner joint, or enter the number of sides for a closed frame (the corner-angle input is ignored for frames, which use the polygon geometry).
- Read the miter angle — the angle of the cut measured from the edge of the workpiece.
- If your saw's scale reads from square (0° = straight crosscut), use the saw-setting figure instead: 90° minus the miter angle.
The formula behind miter angles
A miter joint bisects the corner: each of the two pieces is cut at the corner angle divided by 2. For a closed frame of n equal sides, the interior angle of a regular polygon is 180 − 360/n degrees, and each cut is half of that. The saw setting reported is the complement (90° − miter) for saws whose scale reads zero at a square crosscut.
Worked examples: a standard 90° corner needs two cuts of 90 ÷ 2 = 45°. A hexagonal frame (n = 6) has corners of 180 − 360/6 = 120°, so each end is cut at 120 ÷ 2 = 60° — which is a 30° setting on a from-square saw scale.
Common mistakes
- Assuming room corners are exactly 90° — drywall corners are commonly a degree or two off, and splitting the measured angle is what closes the joint.
- Confusing the miter angle with the saw setting — a 60° miter is a 30° setting on a saw scale that reads from square; cutting at the wrong one leaves a 30° gap.
- Dividing 360 by the number of sides and using that as the cut angle — 360/n is the exterior/central angle, not the cut; the cut is half the interior angle.
- Using flat-miter numbers for crown molding laid flat on the saw — crown cut flat needs compound miter-and-bevel settings that depend on its spring angle.
Frequently asked questions
What miter angle do I cut for a 90 degree corner?
Cut each piece at 45° — half of the 90° corner angle. On virtually all miter saw scales this is the marked 45° detent.
What angle do I cut for a 135 degree corner?
Half of 135° is 67.5° per piece. On a saw whose scale reads from a square crosscut, that is a 22.5° setting — a marked detent on many saws precisely because 135° corners (bay windows, octagons) are common.
What miter angle for a 6-sided frame?
A regular hexagon has interior corners of 180 − 360/6 = 120°, so each piece end is cut at 60° (a 30° from-square saw setting). Both ends of every piece get the same cut.
Why doesn't my 45° miter close on a real wall corner?
Because the corner is not exactly 90°. Measure the actual corner with an angle finder and cut each piece at half the measured value — an 88° corner needs 44° cuts. For inside corners on baseboard, many finish carpenters cope the joint instead of mitering, precisely because coping tolerates out-of-square walls.
What is the difference between a miter and a bevel?
A miter is an angled cut across the width of the board (the saw swings left or right); a bevel is an angled cut through its thickness (the blade tilts). Flat trim corners need only a miter; crown molding cut flat needs both at once — a compound cut.
References
- Standard Euclidean geometry — interior angle of a regular n-gon: 180° − 360°/n; a mitered joint bisects the corner angle.
- Miter saw manufacturer manuals (e.g., DeWalt, Makita, Bosch) — saw scale conventions, detents at 22.5°/31.6°/45°, and compound-cut settings for crown molding.
- Finish-carpentry trade references (e.g., Gary Katz, Finish Carpentry) — mitering vs. coping practice for trim corners.