Miter Angle Calculator

Free Online Miter Angle Calculator

This miter angle calculator works out the exact angle you need to set on a miter saw, miter box, or protractor before you cut two pieces that will meet at a corner. It covers three common situations: a regular polygon like a hexagon or octagon, a corner joint where you already know the corner or interior angle, and a multi-piece joint where more than two pieces meet at a single point, such as spokes on a wheel or rays in a sunburst pattern.

You don't need to work through any trigonometry yourself. Pick the mode that matches your project, type in your numbers, and the calculator instantly returns the miter angle, along with the corner angle, the interior angle, and a diagram showing exactly how the pieces meet. If you also enter the board's width, it adds the cut length along the mitered face too.

Miter angles come up constantly in woodworking, framing, trim carpentry, and metal fabrication, and small mistakes here are one of the most common reasons a joint ends up gapping instead of closing flush. Getting the number right before you cut saves material and time.

What Is a Miter Angle?

A miter angle is the angle each piece is cut at so that two (or more) pieces meet flush at a corner, with the cut running across the face or width of the material rather than through its thickness. It's different from a bevel angle, which tilts the saw blade to cut through the material's thickness instead, and from a compound cut, which combines both a miter and a bevel in one cut.

The key relationship to remember is this: the miter angle is always half of the corner angle. If two boards need to turn through a 90° corner, each board is mitered at 45°, and when the two 45° faces are joined, they form the full 90° turn.

The Core Miter Angle Formula

Every miter angle calculation in this tool comes back to one relationship:

• Miter Angle = Corner Angle ÷ 2
• Corner Angle = 360° ÷ Number of Sides (for a regular polygon)
• Corner Angle = 180° − Interior Angle (if you measured the interior angle instead)
• Cut Length along the mitered face = Board Width ÷ cos(Miter Angle)

How to Use This Calculator

If you're building a shape with equal sides, like a picture frame, gazebo, planter box, or segmented ring, use Polygon Sides. Enter (or tap a preset for) the number of sides, and the calculator works out the corner angle and miter angle automatically, since a regular polygon always splits 360° evenly across all of its corners.

If you already know the angle of the corner itself, whether that's a standard 90° square corner, an odd angle from an as-built wall, or an obtuse outside corner like a deck edge, use Corner / Interior Angle. This mode also accepts an interior angle instead — the angle you'd measure with a protractor inside the finished joint — and converts it to a corner angle for you, since the two always add up to 180°.

If more than two pieces meet at a single point, like the spokes of a wheel, rays in a sunburst pattern, or the ribs of a fan or gazebo roof, use Multi-Piece Joint. Enter the total angle being filled (360° for a full circle, 180° for a flat run across a straight line) and how many equal pieces divide it, and the calculator splits the angle evenly and returns the miter angle for each piece.

In any mode, entering the board's width is optional but adds one more useful number: the cut length along the mitered face itself, which runs longer than the board's actual width because the blade travels on a diagonal.

Worked Example: Picture Frame Corner

A standard picture frame has four 90° corners. Using the formula, each piece is mitered at 90° ÷ 2 = 45°. Set both boards to 45° on the miter saw, cut, and the two faces meet to form a clean 90° corner. On a 2.5-inch-wide frame piece, the cut face itself measures 2.5 ÷ cos(45°) = 3.54 inches, longer than the board is wide since the blade travels the diagonal.

Worked Example: Hexagon Planter Box

Building a six-sided planter box means each corner has a corner angle of 360° ÷ 6 = 60°. The miter angle for each piece is then 60° ÷ 2 = 30°. Every one of the six boards gets cut at 30° on both ends, and the six pieces close up into a perfect hexagon. Change the number of sides to 8 for an octagon and the calculator returns a 22.5° miter instead, following the exact same logic.

Worked Example: 8-Spoke Wheel or Sunburst

Say you're building a sunburst mirror frame or a decorative wheel with 8 spokes radiating out from a center point, filling the full 360° circle. Using Multi-Piece Joint with a total angle of 360° and 8 pieces, each piece takes up 360° ÷ 8 = 45° of the circle, and the miter angle on each edge of every spoke is 45° ÷ 2 = 22.5°. Cut all 16 edges (2 per spoke) at 22.5° and the spokes close up cleanly around the center.

Miter Angle Chart for Common Regular Polygons

A quick reference using Miter Angle = (360° ÷ Sides) ÷ 2:

• 3 sides (equilateral triangle) → 60° miter
• 4 sides (square) → 45° miter
• 5 sides (pentagon) → 36° miter
• 6 sides (hexagon) → 30° miter
• 7 sides (heptagon) → ~25.7° miter
• 8 sides (octagon) → 22.5° miter
• 9 sides (nonagon) → 20° miter
• 10 sides (decagon) → 18° miter
• 12 sides (dodecagon) → 15° miter

Miter Angle Chart for Common Corner Angles

A quick reference using Miter Angle = Corner Angle ÷ 2, for corners that aren't part of a regular polygon:

• 90° square corner (inside a room, most furniture) → 45° miter
• 120° obtuse outside corner (common on decks and bay-style layouts) → 60° miter
• 135° obtuse outside corner → 67.5° miter
• 60° acute corner → 30° miter
• 45° acute corner (sharp point trim) → 22.5° miter

Corner Angle vs. Interior Angle: Don't Mix Them Up

This is the single most common source of a wrong miter setting. The corner angle is the angle the material turns through as it changes direction, measured from the outside of the joint. The interior angle is the angle you'd measure with a protractor standing inside the finished corner, looking at the inside face. The two always add up to 180°.

A standard square corner has a 90° corner angle and also a 90° interior angle, which is why this particular case doesn't cause confusion. But for anything other than a perfect right angle, plugging the wrong one into the miter formula gives a completely different, wrong answer. This calculator's Corner / Interior Angle mode has a toggle specifically so you can enter whichever one you actually measured, without having to convert it in your head first.

Where Miter Angles Are Used

Miter joints and miter angle calculations show up across a wide range of projects and trades:

• Picture frames, mirrors, and door and window casing, almost all built from clean 45° miters at square corners.
• Baseboard, crown molding, and other trim, which typically use 45° miters at inside and outside corners, plus compound cuts for angled trim.
• Furniture making, including boxes, tabletops, and cabinet face frames with mitered corners for a seamless look.
• Segmented woodturning and bowl-making, where staves are mitered at precise polygon angles so a ring of pieces closes into a perfect circle.
• Fencing, decking, and gazebos, where rail ends and roof rafters are mitered to follow a corner, an angle change, or a multi-sided layout.
• Metal fabrication and welding, where angle iron, tubing, and framing members are mitered to form clean corner joints.
• Decorative work like sunburst mirrors, fans, and spoked patterns, where several pieces meet at a single center point.

Tips for a Clean, Tight-Fitting Miter Joint

The math gets you the angle. A few habits get you the fit:

• Cut a test piece from scrap first at your calculated angle and check the fit before cutting your finished material.
• Account for the saw's kerf, the small amount of material removed by the blade, by marking and cutting on the waste side of your line.
• Double-check whether your saw or miter box reads angles from the 90° (square) position or from 0° (parallel to the fence); this calculator's angles are measured from square, matching most miter saws.
• For polygons with more than four sides, cut and dry-fit all the pieces before gluing any of them, since a small error compounds around the full shape.
• Clamp narrow or thin stock rather than holding it by hand; mitered cuts put more sideways force on the blade than a plain square crosscut.
• Use a sharp, fine-tooth blade for miters; a dull or coarse blade tends to chip the edge right where the tight point of the miter needs to be clean.

Common Mistakes to Avoid

Most poorly fitting miter joints trace back to one of a handful of avoidable mistakes:

• Entering the interior angle where the corner angle was expected, or the other way around — remember they add up to 180°.
• Forgetting that the miter angle is half the corner angle, not the corner angle itself.
• Mixing up outside corners and inside corners, which use the same formula but are easy to enter backwards on an as-built job.
• Not accounting for blade kerf on tight, high-precision joints such as small picture frames or segmented rings.
• Assuming every multi-sided shape is regular; an irregular polygon has a different angle at each corner and needs each one measured or calculated separately, not just divided evenly.