Every miter is a corner divided by two — and every ruined trim board is that division done wrong. This Miter Angle Calculator works in two modes: enter a polygon’s number of sides (picture frames, planters, columns) or any measured corner angle (rooms that are not quite square), and get the exact miter saw setting for each piece.
Worked Examples: A Hexagon and a Not-Quite-Square Room
Polygon mode. A regular polygon’s interior angle is (n − 2) × 180 / n, and each joint is two pieces splitting that angle, so the saw setting is (n − 2) × 90 / n. A hexagon (n = 6): interior 120°, miter 60° per piece. The family table writes itself: triangle 30°, square frame 45°, pentagon 54°, octagon 67.5°, dodecagon 75° — note the direction of travel, because it inverts most beginners’ intuition: more sides means a bigger saw angle and a shallower-looking joint, approaching a straight board as the polygon approaches a circle. Corner mode. A measured corner of 90° bisects to 45° per piece, but real rooms confess angles like 88° or 92° once you measure them with a digital angle finder or a bevel gauge — and the calculator’s whole value is the unglamorous one: an 88° corner needs 44° settings, and cutting 45s for it leaves a joint open at the back by a full degree’s worth of wedge, the gap that caulk companies’ profits are built on. Measure the corner, halve the truth, cut the halves: the discipline sounds trivial and is violated on most DIY trim jobs because the corner was assumed square. A related confession belongs to crown molding and any stock tilted in the saw (compound cuts): those need the miter and bevel pair computed from the spring angle — a different, trigonometric problem this page deliberately does not fake; flat stock, frames and polygon work are its honest territory, and it says so rather than hand you a confident wrong number for the crown.
Reading the Saw: What the Number on the Dial Means
The calculator reports the miter angle the way a miter saw’s scale reads it: degrees away from a square (90°) crosscut, so 0° is a straight cut and 45° is the classic picture-frame setting. Confusion enters because geometry texts measure the same cut from the board’s edge instead — the complement. A frame joint’s “60° miter” in polygon language is the 60° saw setting this page reports for a hexagon; the cut face itself makes 30° with the board’s long edge, and plans drawn either way have ended friendships in workshops. The safe practice: this page speaks saw-dial, always — set the saw to the printed number, and verify with the test-cut ritual below before the good stock goes on the fence. Two saw realities complete the picture. Detents (the click-stops at 0, 15, 22.5, 31.6, 45) are conveniences, not calibrations; a saw whose 45 detent is truly 44.6 will open every frame’s fourth corner by the accumulated error, which is why frame-makers tune the saw against a square and a test frame, not against the printed scale. And blade deflection on hard stock at steep settings adds its own fraction of a degree — cut the miters slightly long, dry-fit the whole frame, and sneak up on final length, because a miter joint shortened past its mark cannot be lengthened by any tool in the building.
The Test-Cut Method and Closing the Frame
Professionals treat the calculated angle as a hypothesis and prove it with scrap, and the proof is fast enough that skipping it is never rational. Cut two test pieces at the computed setting, hold them together against the actual corner (or assemble a full test frame for polygon work), and read the joint: open at the toe means the angle is too large, open at the heel means too small, and the correction is half the observed error at the saw — because each piece contributes half the joint’s angle, the same bisection that built the number. For polygon frames, assemble three sides and measure across the open side against the computed width; a frame that will not close is announcing cumulative error while there is still time to care. Glue-up technique respects the same geometry: mitered corners are end-grain joints and inherently weak and glue-starved, so size the end grain with a first thinned coat, then assemble with band clamps (frames) or strap clamps (boxes) that pull all corners simultaneously rather than sequentially — sequential clamping walks the error into the last corner, where it has nowhere left to hide. None of this contradicts the calculator; it completes it. The number gets you to the neighbourhood, the test cut signs the lease, and the frame closes.
Bisecting a Corner Without Instruments
The calculator halves a number; the number itself can be won without a digital finder, and the low-tech methods are older than the saw. The bevel-gauge transfer: set a sliding bevel against the actual corner, lock it, carry it to the saw, and split the angle by eye against a protractor or by the paper method. The paper bisection: trace the corner onto paper, fold the sheet so the two traced lines coincide — the crease is the bisector, geometrically exact — and measure the crease’s angle once, or set the saw directly from the folded template. The two-board method for baseboards: overlap two scrap offcuts in the corner, scribe the overlap, and the marked wedge is the corner’s own testimony. Each method honours the same principle the calculator enforces — the joint is built from the corner as it is, not as the framing square hoped it would be. For polygon work with no corner to measure, the frame’s closure itself becomes the instrument, which is why the test-assembly ritual in the previous section is not superstition but metrology: a hexagon that closes on scrap has certified its 60° more convincingly than any dial.
From Artwork to Cut List: Frame Arithmetic
A picture frame shows the miter and the measurement working together. Frame a 16 × 20-inch print with molding 2 inches wide: each piece’s outside (long-point) length is the artwork dimension plus twice the molding width — the horizontals cut at 20 inches long-point (16 + 2 + 2) and the verticals at 24 inches (20 + 2 + 2), each end at the calculator’s 45° for a four-sided frame, with the rabbet’s overlap of the print handled by sizing the frame’s inside to the print minus a small reveal allowance on each side. The general rule is worth keeping in the form the frame shop uses it: long-point length = inside dimension + 2 × molding width, for any rectangular frame at 45°; at other polygon angles the added amount is width × (the cotangent relationship of the joint), which is why polygon frames are priced from drawings, not rules of thumb. Cut all four pieces from the same molding stick to keep grain and profile continuous, mark the long points before cutting (the short point is the inside dimension exactly), and dry-assemble before glue — the frame is the cheapest polygon you will ever test a miter setting on, and its fourth corner will grade the saw without mercy.
Common Mistakes
Assuming the corner is 90° because the house is new (or old — both lie). Halving the supplement: for an inside corner of 88°, some divide 92° and cut 46° — the corner’s own angle is what bisects. Confusing saw-dial degrees with edge-measured degrees (the complement trap). Trusting detents over a test cut. Cutting all four frame sides to final length before proving the angle. And attempting crown molding’s compound angles with a flat-miter number — crown needs its own miter/bevel computation from the spring angle, a different tool for a different geometry.
Related Tools
Continue with the Spindle Spacing Calculator, the Feet and Inches Calculator, the Inches to Fraction Calculator, or browse the full Construction Calculators hub.
Frequently Asked Questions
What angle do I cut for a hexagon?
60° on the saw for each piece: interior angle (6 − 2) × 180 / 6 = 120°, split between two pieces. An octagon takes 67.5°, a pentagon 54°, a square 45°.
How do I find the miter for a corner that is not square?
Measure the actual corner (a digital angle finder or bevel gauge), enter it in corner mode, and cut half of it on each piece: an 88° corner takes 44° settings. Never assume 90°.
Why does my fourth frame corner always gap?
Accumulated error: four joints multiply any per-cut error, and a saw detent a fraction off delivers its verdict on the last corner. Prove the setting with a test frame, tune the saw, and cut pieces slightly long until the frame proves itself.
Is the calculator’s angle the saw setting or the angle on the wood?
The saw setting — degrees from a square crosscut, the way the saw’s own scale reads (0° = straight cut, 45° = classic frame miter). The cut face’s angle to the board’s edge is the complement.
Can I use this for crown molding?
Not directly — crown sits tilted (a spring angle) and needs a compound miter-plus-bevel pair computed from that tilt. This calculator covers flat stock, frames and polygons; crown is a separate computation.
What if the joint is open at the back?
The setting is too large for the true corner (or the corner is under 90°). Reduce each piece’s angle by half the observed error and re-test with scrap — each joint’s error is shared equally by its two pieces.