Joinery Angle Calculator
Calculate miter and bevel angles for polygon miters and compound joints. Enter the number of sides and optional tilt angle to find exact saw settings.
About this calculator
Every regular polygon's miter angle follows directly from its interior geometry: Miter Angle is 180 degrees divided by Number of Sides, so a 4-sided frame needs a 45-degree miter, a 6-sided hexagon needs 30 degrees, and a 12-sided dodecagon needs only 15 degrees -- more sides always means a smaller miter angle, since the same 360-degree turn is being split into more, narrower wedges. Because a miter saw is calibrated from square (0 degrees) rather than from the polygon's own interior angle, Miter Angle is also the number you actually dial on the saw -- a hexagon frame is a 30-degree saw setting, an octagon is 22.5 degrees, not their complements. Number of Sides is the only input that moves Miter Angle and Interior Angle: it drives both directly through polygon geometry, and it also sets the baseline that Tilt Angle then modifies for compound joints.
Tilt Angle only matters once it's above zero -- at Tilt Angle = 0 the Compound Miter equals the flat Miter Angle and Compound Bevel is 0, but tilting the workpiece (as for a splayed basket, a raked picture frame, or an angled table leg) trades some of that miter angle for a bevel angle via the compound-miter trigonometric identity, so the two compound outputs move in opposite directions as Tilt Angle increases: Compound Bevel rises from zero while Compound Miter falls away from the flat value. Interior Angle -- the angle inside each corner of the finished polygon -- rises toward 180 degrees as Number of Sides grows, which is exactly why a near-circular polygon has almost-flat corners and a triangle has the sharpest ones.
Inputs
Results
Miter Angle / Saw Setting
30°
How to Use This Calculator
- Enter Number of Sides and Tilt Angle.
- Review Miter Angle / Saw Setting (°) -- the number to dial on the saw.
- Use Interior Angle (°) and Compound Miter (°) to inform your decision.
- Use the chart to visualize the results and explore different scenarios by adjusting inputs.
How the result changes with Number of Sides
| Number of Sides | Miter Angle / Saw Setting |
|---|---|
| 3 | 60° |
| 4.5 | 40° |
| 9 | 20° |
| 15 | 12° |
What each input means
- Number of Sides
- Number of sides for the polygon (e.g., 4=square, 6=hexagon, 8=octagon)
- Tilt Angle
- Tilt angle in degrees for compound miters (0 for flat miters)
How this is calculated
Worked example, using the default values
- Identify Input ParametersNumber of Sides = 6, Tilt Angle = 0 = 2 input(s) provided
- Calculate Miter AngleMiter Angle30 = 30
- Calculate Interior AngleInterior Angle120 = 120
- Calculate Compound MiterCompound Miter30 = 30
Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
How is Miter Angle calculated from Number of Sides?
Miter Angle is 180 divided by Number of Sides. A square (4 sides) needs a 45-degree miter, a hexagon (6 sides) needs 30 degrees, and an octagon (8 sides) needs 22.5 degrees. The relationship is inverse: adding sides always shrinks the required miter angle, because the same full turn around the polygon is being divided into more corners.
What does the calculator do differently once Tilt Angle is above zero?
Below a nonzero Tilt Angle, Compound Miter equals the flat Miter Angle and Compound Bevel stays at 0. Once Tilt Angle rises above zero, the compound-miter trigonometric formulas redistribute the flat miter angle between a (smaller) Compound Miter and a (nonzero) Compound Bevel -- the saw setting a workpiece actually needs when it's also tilted, as on a splayed basket or angled table leg.
Is Miter Angle the number I actually set on my miter saw?
Yes. Because a miter saw reads 0 degrees at a square crosscut, the angle you dial in is the polygon's own miter angle (180 / Number of Sides) -- for a hexagon that's 30 degrees, not its complement of 60 degrees. Earlier versions of this calculator reported a separate "Miter Saw Setting" equal to 90 minus Miter Angle, which was the angle between the cut and the board's long edge, not a saw dial value; it has been removed to avoid confusion, since above an octagon it produced numbers outside the physical range of most consumer miter saws.
Does the Interior Angle output change if I only adjust Tilt Angle?
No. Interior Angle is computed purely from Number of Sides via the standard polygon formula ((sides-2) x 180 / sides) and never references Tilt Angle at all, so tilting the workpiece for a compound joint has zero effect on the reported Interior Angle -- only Compound Miter and Compound Bevel respond to Tilt Angle.
Related Calculators
The questions that sit next to this one — chosen by subject, including calculators filed under a different category.
Dovetail Joint Calculator
Calculate pin count, tail spacing, and layout for hand-cut dovetail joints. Enter board width, pin size, and angle for exact joint layout.
WoodworkingBoard Foot Calculator
Calculate board feet from lumber dimensions. Enter thickness, width, length, and quantity to determine total board footage for your woodworking project.
Finish CarpentryCrown Molding Calculator
Linear feet and miter angles for rooms with corners.
WoodworkingCabinet Material Calculator
Estimate the number of 4×8 sheet goods and edgebanding feet needed for your cabinet project. Accounts for standard cabinet parts and waste factor.
More in Crafts, Hobbies & Games.