Angle math

Miter angle calculator for regular polygons

Six-sided box, eight-sided picture frame, twelve-sided lampshade — the math is the same. Each miter is half of the angle between adjacent sides, and getting it wrong by a degree compounds across every joint until the last one won’t close.

The formula

miter_angle = 180 / n

n is the number of sides. For a regular hexagon (n=6), each miter is 30°, so the saw is set to 30° off the fence. For an octagon (n=8), miter is 22.5°. For frame stock with miters at both ends, both faces get cut at the same angle.

Example: octagonal picture frame

n = 8 sides, miter = 180 / 8 = 22.5°. Saw fence is set to 22.5°. Eight pieces, sixteen cuts, all identical. Dead On draws the polygon at scale and shows the cut angle and the saw fence setting in the same view, so you can sanity-check the geometry before you tilt the saw.

Why it matters

A 1° error on each of eight miters compounds to an 8° gap at the last joint — visible from across the room. The math is unforgiving, but it’s also the same every time. Lock it in once and it’s right forever.

Step-by-step

  1. 1

    Pick number of sides

    3 to 24 sides covers everything from triangles to lampshades.

  2. 2

    Read the miter angle

    180 divided by the number of sides — the saw fence setting.

  3. 3

    Set the saw

    Most miter saws and table saw sleds read in degrees off square. Dial it to the calculated number.

  4. 4

    Cut a sample first

    Test on a scrap, dry-fit two pieces — the corner should close to a hairline before you commit to the run.

  5. 5

    Cut all pieces with the same setup

    Don’t move the fence between cuts. Identical setup, identical pieces, joint that closes.

Skip the math. Build the diagram.

Dead On does the miter angle calculator and 12 other woodworking calculators with visual diagrams, offline, on every Apple device signed into your Apple ID.

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Frequently asked questions

What’s the miter angle for a hexagon?

30°. Six sides, 180/6 = 30° per cut, set right off the fence.

What about an octagon?

22.5°. Eight sides, 180/8 = 22.5°. The same angle whether you’re cutting picture frame stock or a stop-sign blank.

Does Dead On handle irregular polygons?

Yes. The Pro version supports custom angle sequences for irregular shapes — useful for trapezoid frames or asymmetric layouts.

How do I cut a 3-sided object (triangle)?

60° per cut. 180/3 = 60. That’s a steep cut for most miter saws — some require a sled or a sliding compound miter to reach it.

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