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Miter Angle Calculator

Construction

Find the exact miter angle to cut pieces for any regular polygon frame, box, or planter. Enter the number of sides to get the precise saw angle instantly.

320

Miter Angle

45

This calculator computes your Miter Angle from the values you enter.

Inputs
Number of Sides
Outputs
Miter Angle

What is a Miter Angle?

A Miter Angle Calculator determines the exact saw angle needed to cut pieces so that they join cleanly into a closed, regular polygon — whether that's a simple 4-sided picture frame, a hexagonal planter box, or an octagonal gazebo frame. The primary keyword here — miter angle calculator — addresses one of the most common questions in woodworking and DIY carpentry: what angle do I set my miter saw to for this shape?

The tool uses a single input, the number of sides in your target shape, and instantly returns the miter angle in degrees. This works because any regular polygon's exterior corner geometry follows a fixed mathematical relationship: 180 degrees divided evenly across the number of sides. No measuring, protractors, or angle charts are required — just enter the side count and cut.

Whether you're building a frame, a box, a planter, or a multi-sided structure, getting the miter angle right the first time avoids wasted material and mismatched joints, which is especially valuable when working with expensive hardwood or trim stock.

How to use this Miter Angle calculator

  1. Identify your target shape. Count how many sides your finished frame, box, or structure will have — a rectangle has 4, a hexagon has 6, an octagon has 8, and so on.

  2. Enter the Number of Sides using the slider or number field, from a minimum of 3 (triangle) up to a maximum of 20 sides.

  3. Read the Miter Angle result in the highlighted card — this is the angle in degrees to set on your miter saw for every cut in the project.

  4. Set your saw to the calculated angle, and cut a pair of test scraps first to confirm the joint closes cleanly before cutting your final material.

  5. Cut all pieces at the same angle on both ends, since a regular polygon uses identical miter cuts throughout — there is no need to alternate angles between pieces.

  6. Dry-fit the full assembly before gluing or fastening, checking that all corners close without gaps.

Formula & Methodology

The calculator applies the standard regular-polygon miter geometry formula:

> Miter Angle = 180° ÷ Number of Sides

This works because the sum of a regular polygon's exterior angles always totals 360 degrees, split evenly across all corners, and the miter cut at each joint is half of that exterior angle contribution per piece — which simplifies to 180 divided by the number of sides for the angle set on a standard single-bevel miter saw.

Worked examples:

- 4 sides (square frame): 180 ÷ 4 = 45°
- 6 sides (hexagon): 180 ÷ 6 = 30°
- 8 sides (octagon): 180 ÷ 8 = 22.5°
- 12 sides: 180 ÷ 12 = 15°

This formula assumes a regular polygon — equal side lengths and equal interior angles. For irregular shapes or compound angles (where the frame or box also has sloped, non-vertical sides), an additional bevel angle calculation is required alongside the miter angle from this tool. Always verify with a test cut, since saw calibration can drift slightly from its printed scale over time.

Frequently Asked Questions

For a standard 4-sided (square or rectangular) picture frame, the miter angle is 45 degrees. This comes from dividing 180 degrees by the number of sides (4), which produces four corners that each sum to a full 90-degree angle when two mitered pieces meet. This is the most common miter setting used on any miter saw.
For a 6-sided hexagon frame, divide 180 by 6 to get a miter angle of 30 degrees. Each piece is cut at 30 degrees on both ends so that six pieces join to form a closed hexagonal shape with 120-degree interior corners. Enter 6 into the Number of Sides field to confirm this instantly.
This calculator assumes a regular polygon, meaning all sides and angles are equal. Irregular polygons — where side lengths or corner angles differ — require calculating each corner's angle individually, since the simple 180 divided by sides formula only holds for regular shapes. Most picture frames, boxes, and planters use regular polygon geometry, so the formula applies in the vast majority of DIY projects.
The miter angle is the horizontal angle you set on the saw's miter gauge to cut the end of a board at a rotation across its face — this is what this calculator computes. A bevel angle is a separate, vertical tilt of the saw blade used for compound cuts, such as when building a box with sloped sides. Simple flat frames only need the miter angle; compound cuts need both angles set together.
Many miter saws are labeled by the angle from a 90-degree straight cut rather than the full corner angle, so some carpenters set the saw to 90 minus the miter angle, or work directly from the miter angle depending on the saw's scale convention. Always check a scrap piece first, since saw angle scales vary between brands. This calculator gives you the true miter angle needed at each cut end for a closed regular polygon.
Hexagonal (6-sided) and octagonal (8-sided) planter boxes are the most popular shapes after simple rectangles, prized for their visual interest and stability. An octagon uses a 22.5-degree miter angle (180 divided by 8), while a hexagon uses 30 degrees. Both are achievable on any standard miter saw without needing a specialty jig.
Crown molding on a standard rectangular room uses the same 45-degree miter angle as any 4-sided frame for standard 90-degree corners, but it also requires a bevel angle because the molding sits at an angle against the wall and ceiling. This calculator gives the correct miter component; consult a crown molding angle chart or compound miter table for the matching bevel angle.
An 8-sided octagon frame requires a miter angle of 22.5 degrees, calculated as 180 divided by 8. Each of the eight pieces is cut at 22.5 degrees on both ends, and the pieces join to form 135-degree interior corners around the closed octagon shape.
As a regular polygon gains more sides, it more closely approximates a circle, and each individual corner turn becomes gentler. Since the miter angle is 180 divided by the number of sides, more sides means a larger denominator and therefore a smaller angle. A 20-sided polygon needs only a 9-degree miter angle per cut, reflecting its very gentle, nearly circular curve.
Yes, the same regular-polygon miter formula applies to larger structural projects like gazebo roof framing, octagonal decks, or multi-sided sheds. For an 8-sided gazebo, use the 22.5-degree result from this calculator on the framing members, then verify structural spans separately with a framing or beam calculator since larger builds carry real load requirements.
A miter saw (manual or power) with a reliable angle scale is the standard tool, paired with a speed square or protractor to verify the saw's setting before cutting. For high-precision work, cut a test piece first and check the joint fit with a combination square, since even a half-degree of error compounds across multiple corners in a closed polygon.
Small errors compound quickly in a closed polygon — a half-degree of error per cut on an 8-sided frame can leave a visible half-degree gap when all eight corners are assembled. For visible joinery like picture frames, aim for cuts within a quarter degree of the calculated miter angle, and always dry-fit the full assembly before gluing.
Also known as
miter cut angle calculatorpicture frame angle calculatorpolygon miter angle calculatorbox joint angle calculatorcompound angle cutting calculator