WOODWORKING & JOINERY

Miter Angle Calculator: Miter Saw Angles for n-Sided Polygons

A miter angle calculator determines the saw blade cut angle required to join two pieces of wood or moulding at a seamless corner. For any regular polygon of n sides, each piece is cut at a miter saw angle of θ = 180° / n (e.g. 45° for a 4-sided frame, 30° for a 6-sided hexagon, and 22.5° for an 8-sided octagon).

Miter Angle Calculator: Miter Saw Angles for n-Sided PolygonsACTIVE

DEG (°)RAD (rad)

Quick Shape Presets:

Number of Equal Sides (n):

Miter Saw Scale Angle

45.00°

Angle to set on miter saw table

Interior Corner Angle

90.00°

Total angle inside each joint

Total Cuts Required

8 Cuts

2 cuts per side (2n total)

LOCAL COMPUTATION ONLYRESOLUTION: 0.01°

NO SERVER UPLOADS

How to Use This Tool

Enter the number of equal sides (n) for your multi-sided frame or polygon (minimum 3 sides).
Or click one of the quick preset buttons for common frames (Square, Hexagon, Octagon, etc.).
Read the Miter Cut Angle (the angle of the joint) and the Miter Saw Scale setting (the angle to set on your miter saw detent).
Note the total number of cuts required (2 cuts per joint across n joints = 2n cuts).
Click 'Reset Defaults' to return to a standard 4-sided picture frame.

Estimate only. Verify with professional tools for critical work. Always test cuts on scrap timber before cutting fine mouldings.

What the Miter Angle Calculator Does

The Miter Angle Calculator determines the precise blade angle settings required on a compound miter saw or sliding chop saw to construct regular multi-sided frames and polygons. By simply entering the number of sides ($n$), the calculator translates classical Euclidean polygon formulas into real-world miter saw scale settings.

Woodworkers, picture framers, finish carpenters, and metal fabricators use this tool to build triangular pediments, octagonal mirrors, hexagonal planters, segmented turning blanks, and custom architectural mouldings.

Formulas for Polygon Miter Angles

The mathematics behind miter joints rests on dividing total circular rotation (360°) across $n$ mating joints:

Interior Corner Angle

α = [(n - 2) × 180°] / n

The total enclosed angle inside each frame corner.

Joint Bisector

Bisector = α / 2 = [(n - 2) × 90°] / n

The angle of the joint relative to the length of the board.

Miter Saw Setting

θ_saw = 90° - Bisector = 180° / n

The angle indicator on your saw table.

Two Worked Practical Examples

Example 1: Building a 6-Sided Hexagonal Cedar Planter

Project: Build a 6-sided planter box from 2×6 cedar lumber (n = 6).

Determine Interior Corner Angle: α = (6 - 2) × 180° / 6 = 720° / 6 = 120.00°.
Calculate Miter Saw Setting: θ_saw = 180° / 6 = 30.00°.
Set up Miter Saw: Swivel the saw table to the 30° detent. Clamp a stop block to cut six pieces to exact matching lengths.
Cut both ends of each of the 6 boards at 30° (12 cuts total). When assembled, six 120° corners form a seamless closed hexagon.

Example 2: Trimming an Out-of-Square Drywall Corner (88.00°)

Problem: A finish carpenter measures an inside room corner that is slightly acute at 88.00° instead of a true 90.00°.

Divide the measured corner angle in half to find the joint bisector: 88.00° / 2 = 44.00°.
Calculate the required miter saw scale angle: 90.00° - 44.00° = 46.00°.
Adjust Saw Table: Set the saw to 46.00° (instead of the standard 45.00°).
Result: The joint closes tight along the outer face without the gap typically caused by standard 45° cuts on acute corners.

Miter Cut Angle Reference Table (3 to 12 Sides)

Standard polygon joint dimensions and corresponding miter saw table settings:

Sides (n)	Polygon Name	Interior Corner Angle	Joint Bisector	Miter Saw Setting	Total Cuts
3	Equilateral Triangle	60.00°	30.00°	60.00°	6
4	Square / Rectangle	90.00°	45.00°	45.00°	8
5	Regular Pentagon	108.00°	54.00°	36.00°	10
6	Regular Hexagon	120.00°	60.00°	30.00°	12
7	Regular Heptagon	128.57°	64.29°	25.71°	14
8	Regular Octagon	135.00°	67.50°	22.50°	16
9	Regular Nonagon	140.00°	70.00°	20.00°	18
10	Regular Decagon	144.00°	72.00°	18.00°	20
11	Regular Hendecagon	147.27°	73.64°	16.36°	22
12	Regular Dodecagon	150.00°	75.00°	15.00°	24

Common Mistakes in Miter Cutting

Confusing the Saw Scale with Joint Angle: Cutting a 6-sided hexagon requires setting the saw to 30°, not 60° or 120°. Remember that saw scales measure deflection from square.
Cutting Segments to Unequal Lengths: Even a 1/32-inch error in segment length prevents the final joint of a polygon from closing. Always use a rigid stop block.
Blade Flex (Deflection): Forcing a thin-kerf blade through dense hardwood causes the blade to wander, beveling the cut surface. Feed the blade slowly and evenly.

REFERENCE & SUPPORT

Frequently Asked Questions: Miter Angle

Practical guidance for calculating miter saw blade angles, polygon joints, and corner bisectors.

Why does my miter saw read 45° when cutting a 90° square corner?

Miter saw scales are calibrated relative to a square 90° crosscut. When the saw is set at 0°, the blade cuts perpendicular (90°) to the fence. Deflecting the blade by 45° cuts a 45° angle, which pairs with a matching 45° cut on the mating piece to form a 90° corner.

What saw angle do I cut for an 8-sided octagon?

Set your miter saw to 22.5°. An octagon has eight 135° interior corners. Bisecting each corner requires two 67.5° angles, which corresponds to setting your saw table to 22.5° (90° - 67.5° = 22.5°, or 180° / 8 = 22.5°).

How do I cut miter angles on an out-of-square wall corner?

Measure the actual interior angle with an angle finder or T-bevel, divide that angle by 2 to find the joint bisector, and subtract the result from 90° to determine your miter saw scale setting. For example, for an 88° corner: 88° / 2 = 44°, and 90° - 44° = 46° on your saw.

Why do my mitered frames have gaps even though my saw angle is accurate?

In multi-sided frames, unequal side lengths cause gaps just as readily as incorrect angles. If one segment is 1/16-inch longer than the others, the final corner cannot close. Always clamp a stop block to your miter saw fence to guarantee identical segment lengths.

How We Calculate

Miter saw scale angles are computed from regular polygon geometry using θ_saw = 180° / n and θ_corner = 90° × (n - 2) / n. Calculations execute entirely in client-side code with zero external transmission.

Last updated: September 2026

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