Article — Miter Angle Calculator
Miter Angle Calculator: Cuts for Corners, Polygons, and Crown Molding
The miter angle is half the corner angle. For a standard 90° corner, two boards each cut at 45° meet flush. For a regular polygon, the miter is 180° divided by the number of sides — square 45°, pentagon 36°, hexagon 30°, octagon 22.5°. Compound miters for crown molding use both miter and bevel: a 90° wall corner with 38° spring molding (the US standard) needs miter 31.62° and bevel 33.86° set together on a compound miter saw.
This calculator solves all three cases. The simple corner mode handles any measured wall angle (drywall corners are rarely exactly 90°). The polygon mode covers picture frames, planters, gazebos, and segmented rings from 3 to 100 sides. The compound mode handles crown molding installed against the wall-ceiling intersection at any spring angle.
How miter angle is calculated
For two boards joining at a corner, the miter cut on each board equals half the corner angle. The logic is geometric: the two cuts together must span exactly the corner. If a corner measures 100°, each board needs a 50° cut from its long edge so the two cuts together fill the 100° gap. Most outside corners on rooms are 90°, which is why 45° miters are the universal default for picture frames, baseboards, and door casing.
The saw setting is not always the same as the miter angle. Miter saws measure rotation from a square (90°) cut. A 45° miter is set as 45° on the saw because 90 − 45 = 45 — the two coincide only for 90° corners. For a 60° corner (where each miter is 30°), the saw is set to 60° from square (because 90 − 30 = 60), and many beginners cut these the wrong way.
Miter angle for regular polygons
For an n-sided regular polygon, the miter angle on each piece is (360 ÷ n) ÷ 2, which simplifies to 180 ÷ n. The exterior angle at each vertex equals 360 ÷ n, and that angle is split evenly between the two adjacent pieces. A square has exterior angle 90° at each corner, split into two 45° miters. A hexagon has 60° exterior angles, split into 30° miters.
For complex polygons the math is identical: a 12-sided clock frame uses 15° miters (180 ÷ 12), and a 16-segment turned ring uses 11.25° (180 ÷ 16). Once you go above 12 sides, cumulative error becomes the dominant concern — a 0.1° error per cut, multiplied across 32 cut ends, throws the closure off by more than 3° and leaves visible gaps. Precision saws with digital readouts are mandatory above n = 8.
Triangle (3) 60°Square (4) 45°Pentagon (5) 36°Hexagon (6) 30°Octagon (8) 22.5°Decagon (10) 18°Dodecagon (12) 15°Compound miter angle for crown molding
Crown molding sits sprung against the wall — not flat, not perpendicular, but tilted at a specific spring angle. The two US standards are 38° and 45° spring (printed on the back of the molding). Cutting crown to wrap a corner means the saw must rotate in the horizontal (miter) AND tilt in the vertical (bevel). The formulas for both are trig functions of the wall corner angle and the spring angle.
For a 90° wall corner with 38° spring crown — the most common combination in US homes — the miter is 31.62° and the bevel is 33.86°. Many compound miter saws have these two values stamped as detents on the miter and bevel scales because they are the only crown angles 95% of carpenters ever cut. For 45° spring, the values are miter 35.26° and bevel 30° — also stamped as detents on quality saws.
Miter angle vs bevel angle
Miter is the horizontal rotation of the saw blade. Bevel is the vertical tilt. A standard miter saw rotates left and right (miter); a compound miter saw also tilts the blade left and right of vertical (bevel). A simple miter cut — say, a 45° on a picture frame — uses miter only, with the blade vertical. A compound cut sets both at once.
For trim work and simple casework, miter alone is enough. Compound cuts are required for crown molding, hopper joints (angled boxes like flower planters with sloped sides), and complex casework where pieces meet at angles that are neither vertical nor horizontal. A dual-bevel compound miter saw (tilts left and right) is the modern standard because it handles every cut without flipping the workpiece.
Measuring real corner angles
The biggest source of error in real-world miter cuts is assuming every corner is exactly 90°. Drywall taping rarely produces a true 90° — most interior corners run 88° to 92°, and exterior corners on framed walls often vary by 1 to 3°. A 1° error on a 5-inch-wide piece of trim shows as a 1.4 mm gap (one-sixteenth of an inch) — visible from across the room on stain-grade work.
Use a digital angle finder or a sliding bevel gauge to measure the actual corner before cutting expensive trim. Digital angle finders cost $25 to $80 and resolve to 0.1°. Set the gauge in the corner, read the angle, divide by 2 for the miter, and cut a test piece in scrap before committing to a 10-foot stick of premium trim.
The compound miter angles for crown molding (31.62° / 33.86° for 90° walls with 38° spring) are derived from a single trig identity discovered by 19th-century carpenters working without tables. The formulas only became widely known after the 1980s when the first inexpensive compound miter saws shipped with the angles printed in the instruction manual. Before then, most carpenters cut crown "in position" (held against a fence at spring angle) using only the miter scale.
Miter saw detents and settings
Quality miter saws have factory-set detents at the most common miter angles: 0° (square), 15°, 22.5°, 31.62°, 45°, and sometimes 60°. The 22.5° detent is for octagon corners; 31.62° is for crown molding miter at 38° spring. Hitting a detent gives positive feedback and locks the saw at exactly that angle — much more reliable than reading a scale and trying to land precisely on a mark.
For non-detent angles, professional carpenters often use a digital miter scale (overlay on the saw base) or a separate digital angle finder placed against the blade. Reading angles off a printed scale alone is good to about 0.5°; with a digital readout, 0.1° is achievable. The accuracy needed depends on the trim — paint-grade casework can hide 1°, stain-grade and oak frames cannot.
- Simple miter = corner angle ÷ 2
- Polygon miter = 180° ÷ n (number of sides)
- Square frame = 45° miters on all four corners
- Hexagon = 30° miters (planters, table tops)
- Octagon = 22.5° miters (gazebos, stop signs)
- Crown 38° spring at 90° = miter 31.62° / bevel 33.86°
- Crown 45° spring at 90° = miter 35.26° / bevel 30°
- 1° corner error = 1.4 mm gap on 5-inch trim
Common miter angle mistakes
The first mistake is assuming corners are 90°. Always measure. The second is confusing inside and outside corners — they take complementary cuts, and the saw direction reverses. The third is setting the saw to the corner angle instead of the miter angle (90° corner needs a 45° saw setting, not a 90° setting). The fourth, most common with crown molding, is cutting the molding flat when it should be sprung in position.
Crown molding cuts come two ways. In position: hold the molding upside down and backwards against the saw fence at its spring angle, then cut with only the miter set (45° for a 90° corner). Compound: lay the molding flat on the saw table and set both miter and bevel. Both produce the same cut, but mixing the methods on one project guarantees mistakes. Pick one and stick with it for the whole installation.
The fifth mistake is cutting one piece per corner instead of marking the matching cut on the adjacent piece before moving the saw. Miter saws drift slightly between cuts — cutting both halves of a joint without changing the saw setting produces a tighter match than re-setting the angle for each piece.
For picture frames and small boxes, cut all four (or six, or eight) pieces in a single saw session without changing settings. Dry-fit the assembly. If a gap shows up, do not adjust the miter angle — instead, take 1 mm off the gap side of the offending piece with a sanding block and the joint closes. Adjusting the miter throws off the next corner.