Miter Cut Angle Chart: Saw Settings for 3–12 Sided Frames

This page is your printable, offline-ready reference for miter cut angles. Rather than an interactive calculator, it gives you the complete table you can tape above your miter saw, plus the geometric reasoning behind every number, three fully worked shop examples, and a guide to the most common cutting mistakes. If you need to calculate an angle for an unusual polygon or an odd wall corner in real time, scroll to the bottom for a link to the interactive tool.

How to Read This Chart: Saw Setting vs. Complementary Angle

Before reaching for your saw, understand the two different angles that appear in every miter-cut conversation:

Interior corner angle (α) is the angle you see inside the finished joint — what you would measure with a protractor placed on the assembled corner. For a picture frame corner, α = 90°. For a hexagonal planter, α = 120°.

Miter saw scale setting (θ_saw) is the number you dial on your saw table. It is not the same as the interior corner angle. Standard miter saws are indexed so that 0° produces a perfectly square 90° crosscut. The scale measures how far you swing the saw away from square. The relationship is:

θ_saw = 90° − (α ÷ 2)

Which simplifies to the cleaner form used throughout this chart:

θ_saw = 180° ÷ n

where n is the number of equal sides in your polygon.

A second angle you may encounter on saw specifications is the complementary cut angle — the angle on the other side of the blade from the scale setting. For any saw angle θ_saw, the complementary angle is simply 90° − θ_saw. This matters only when your saw does not swing past 45° and you need to flip your work piece against a sacrificial sub-fence.

The interior angle formula, consistent with the Miter Angle Calculator, is:

Interior angle α = 90 × (n − 2) / n × 2 = (n − 2) × 180° / n

Complete Miter Cut Angle Chart (3 to 12 Sides)

Print this table, laminate it, and stick it above your chop saw. All values are rounded to two decimal places for practical precision.

Quick reminder: The saw scale column is the number you set on your miter saw’s angle indicator. The complementary column is useful when your saw cannot swing that far and you need to work from the opposite side of the blade.

Three Worked Examples

Example 1 — Standard 4-Sided Picture Frame

The project: You are assembling a rectangular picture frame from 2-inch hardwood moulding to surround a 20 × 16-inch print.

1. Look up n = 4 in the chart. Interior corner angle = 90.00°. Saw scale = 45.00°.
2. Set your miter saw to 45°. Clamp a stop block on the right side of the fence to guarantee all four pieces are cut to exactly the same length — this is more critical than the angle itself.
3. Cut both ends of each of the four pieces at 45°, mirroring the direction so that each piece tapers from wide to narrow (not both ends tapering the same way).
4. Assembly check: Dry-fit without glue and hold the frame up to a framing square. The outside corners should sit flush against the square’s inside faces. Any rocking indicates unequal piece lengths, not an angle error.
5. Total cuts: 8 (two mating cuts per corner × 4 corners).

Tip for picture frames: Use a band clamp (strap clamp) to pull all four joints tight simultaneously while the glue sets, rather than individual bar clamps that can skew the frame out of square.

Example 2 — 6-Sided Hexagonal Cedar Planter

The project: You want to build a garden planter from 2×6 cedar decking. A hexagon makes efficient use of a standard 8-foot board and is far more stable on uneven ground than a rectangular box.

1. Look up n = 6 in the chart. Interior corner angle = 120.00°. Saw scale = 30.00°.
2. Rotate your miter saw table to the 30° detent. If your saw only has detents at 22.5°, 30°, and 45°, you are in luck — 30° is a standard stop.
3. Rip your 2×6 boards to the desired height of the planter box (e.g., 16 inches tall). You will need six pieces of equal length.
4. Lock a stop block to guarantee identical lengths, then cut both ends of each board at 30°, mirroring the direction (one end left-leaning, the other right-leaning when viewed from above).
5. Dry-fit on a flat surface. Six boards × two 30° ends = twelve individual cuts totalling 360° of rotation, which closes a perfect hexagon.
6. For waterproofing, apply exterior wood glue and fasten with stainless-steel finish nails from inside. Avoid iron nails on cedar — they stain.

Visual check: If you have a digital angle finder such as those on our Interactive Angle Finder, place it against the assembled joint face. You should read 120° (or its supplement, 60°, depending on which face you measure).

Example 3 — 8-Sided Octagon Frame

The project: A custom framer building an octagonal mirror frame from 3/4-inch solid walnut moulding.

1. Look up n = 8 in the chart. Interior corner angle = 135.00°. Saw scale = 22.50°.
2. Set the saw to exactly 22.5°. Most quality miter saws include a detent at 22.5° specifically because octagons and hexadecagons are common in trim work.
3. Mill or purchase moulding stock. For an octagonal frame, all eight pieces must be identical in length, measured from the short point (the shortest dimension of each mitered piece). Calculate the short-point length from your desired outer frame dimension.
4. Cut 16 total miter cuts (two per piece × eight pieces). Because walnut is dense, lower the blade slowly and let the blade reach full RPM before contact — blade deflection at high feed rates can shift the effective cut angle by up to 0.5°.
5. Geometry check: Eight segments with 16 cuts at 22.5° = 8 × 2 × 22.5° = 360°. The frame closes exactly.

For non-standard shapes or irregular polygon dimensions, use the Triangle Angle Calculator to solve individual segment dimensions using the Law of Sines or Cosines before cutting.

Saw-Setting vs. Complementary Angle: When It Matters

Most powered miter saws swing from 0° to 45° on each side. This covers every polygon from a square (4 sides, 45° saw setting) up to shapes with very many sides (approaching 0°). However, three-sided equilateral triangles require a 60° saw setting — beyond the maximum swing of most saws.

The solution: use the complementary angle.

For a triangle (n = 3):

• Required saw scale: 60.00°
• Complementary angle: 90° − 60° = 30.00°

Clamp a sacrificial wooden auxiliary fence at exactly 90° against your main fence. Place your workpiece against this sub-fence and set the saw to 30°. The blade will cut through the workpiece at an effective 60° miter — the same result as setting the saw directly to 60° if it were mechanically possible.

This technique also applies to any angled cut that exceeds your saw’s maximum swing range. Identify the complementary angle, set the sub-fence, and cut from the opposite reference face.

5 Common Miter Cutting Mistakes

Understanding what goes wrong is as valuable as knowing the correct angles:

1. Confusing the Saw Scale with the Interior Corner Angle

The most frequent beginner error. For a hexagon, the interior corner is 120° but you cut at 30°, not at 120° or even 60°. Always derive your saw setting from the formula 180° ÷ n — never set the saw to the interior corner angle directly.

2. Cutting Segments to Unequal Lengths

Even a 0.5 mm variation in segment length across a 10-sided decagon will cause the final corner to miss by several millimetres. Unequal length is a more common source of gaps than an incorrect angle. Use a rigid stop block and measure from the fence, not from a tape measure applied individually to each piece.

3. Ignoring Blade Kerf

Each pass of a saw blade removes approximately 2.4–3.2 mm of material (the kerf). For regular polygon work, this is compensated by your stop block positioning, but if you are cutting pieces to an exact short-point dimension calculated from geometry, subtract half a kerf from each end’s measurement. On a 10-sided frame, uncorrected kerf can accumulate to a full 3–5 mm of total error across the assembly.

4. Skipping Saw Calibration

Factory detents shift during shipping and heavy use. Before any critical project, use a precision machinist’s triangle to verify that your saw blade stands truly perpendicular to the fence at the 0° detent. A 0.3° error at the detent translates to 0.6° of error per joint — enough to open a visible gap on a fine hardwood frame.

5. Not Testing on Scrap First

Always make two test cuts on identical scrap pieces of the same width and thickness as your finished material. Hold the mitered faces together and inspect the joint. Any gap at the front or back face tells you which direction to micro-adjust — you do not need to re-read the chart, just nudge the saw by 0.25° increments and retest.

When to Use the Interactive Calculator Instead of This Chart

This reference chart covers regular polygons with 3 to 12 equal sides — the shapes you will build most often in a woodworking or framing context. However, there are four situations where you should open the Miter Angle Calculator instead:

1. More than 12 sides. The calculator handles any integer from 3 to 100 sides, covering segmented turning blanks and decorative architectural rings.
2. Out-of-square real-world corners. Baseboard miters on walls that are not a true 90° require measuring the actual corner angle, dividing by two, and subtracting from 90°. The calculator accepts any corner angle, not just regular polygon values.
3. Instant verification on the job site. Rather than squinting at a laminated printout, enter the number of sides on your phone for an immediate readout.
4. Exploring polygon options. If you are deciding between a 7-sided and 9-sided frame for an art project, use the calculator to compare the saw settings before committing to a design.

For measuring actual corner angles on photos or blueprints, the Angle from Photo Tool lets you upload an image and measure directly on screen with no physical tools needed.

How We Calculate

Interior corner angles and miter saw settings across Angle Finder are derived from standard regular polygon geometry computed in double-precision floating-point arithmetic:

• Interior corner angle: α = 90 × (n − 2) / n × 2 = (n − 2) × 180° / n
• Miter saw scale angle: θ_saw = 180° / n
• Complementary angle: 90° − θ_saw
• Total cuts: 2 × n

Disclaimer: Woodworking and framing reference only. Timber moisture expansion, blade kerf deflection, and framing-square tolerances must be accounted for by making test cuts on scrap material before cutting finished stock.

Related Tools & Guides

Tools:

• Miter Angle Calculator — Interactive saw angle calculator for any polygon, including irregular corners.
• Triangle Angle Calculator — Solve triangular frame dimensions using SSS, SAS, and ASA rules.
• Roof Pitch Calculator — Convert rafter slopes to framing angles for hip-rafter and gable trim work.
• Angle from Photo Tool — Measure corner angles on blueprints and workshop photos.

Guides:

• Types of Angles — Geometric definitions of acute, right, obtuse, and reflex angles.
• How to Measure an Angle With a Protractor — Traditional and digital protractor techniques for the workshop.

Last updated: 2026-10-08