About the Miter Angle Calculator
This miter angle calculator gives the saw setting for joining two pieces at an angle. In polygon mode, enter how many sides your frame, planter, gazebo or table top has and it returns the miter angle for every cut, the interior angle of each corner, the short-point length of each piece for your stock width and the total length of stock to buy. In corner mode, enter any corner angle — a 135° bay window, an out-of-square wall — and it splits the angle evenly between the two pieces.
It is for woodworkers, trim carpenters and DIYers building picture frames, octagon planters, hexagon shelves, segmented bowls or wrapping baseboard around odd corners. The miter angle is given the way most miter saws are marked: 0° is a square cut and 45° is the setting for a four-sided frame.
These are flat miters, cut with the blade square to the face of the board. Crown molding and pieces that tilt (like a splayed box) need a bevel as well; use a compound miter calculator for those. Measure real corners with an angle finder rather than assuming 90° — walls are rarely perfect.
With the default inputs, the miter saw setting (each cut) is 22.5 °. Change any value above to recalculate instantly.
How to use the miter angle calculator
- 1Choose polygon mode for a frame with equal sides, or corner mode for a single joint.
- 2Enter the number of sides, or measure the corner angle with an angle finder.
- 3For frames, enter the outside length of each side and the width of your stock.
- 4Set your miter saw to the miter angle shown and make a test cut on scrap.
- 5Cut each piece with opposing miters so the long points face outward.
Formula and method
Two pieces meeting at a corner each take half of the angle that is “missing” from a straight line. For a corner of θ degrees, that is (180 − θ) ÷ 2 per piece, which is the number to set on a miter saw whose 0° position is a square cut. For a regular polygon the interior angle is 180 × (n − 2) ÷ n, so the formula simplifies to 180 ÷ n: 45° for a square, 30° for a hexagon and 22.5° for an octagon. The same miter works for an outside corner of 360 − θ.
The angle measured from the board’s edge (the angle a protractor shows on the workpiece) is 90° minus the saw setting. When the outside, long-point edge of each piece is L, the inside short-point edge is shorter by the stock width times the tangent of the miter angle at each end, so short side = L − 2·w·tan(miter). The total stock is simply n × L before saw kerfs and waste.
- n
- Number of sides
- θ
- Corner angle between the pieces (°)
- L
- Long-point (outside) length of each piece
- w
- Stock width
Worked examples
Octagon planter with 12-inch sides
An octagon has interior angles of 180 × 6 ÷ 8 = 135°, so each cut is 180 ÷ 8 = 22.5°. With 2-inch stock the short edge is 12 − 2 × 2 × tan 22.5° = 10.343 in (about 10-5/16), and eight sides need 96 in of stock.
Hexagon shelf, 10-inch sides from 1½-inch stock
A hexagon’s corners are 120°, so the saw is set to 30°. The short edge is 10 − 2 × 1.5 × tan 30° = 8.268 in, and six pieces need 60 in of stock.
Baseboard around a 135° bay-window corner
The two pieces must close a 135° corner, leaving 45° to split between them, so each is cut at 22.5°. Measure the real angle first; a 133° corner would need 23.5° per piece.
Frequently asked questions
What angle do I cut for an octagon?+
Set the miter saw to 22.5° for every cut. An octagon’s interior angles are 135°, and each of the two pieces at a corner takes half of the remaining 45°. Eight pieces at 22.5° on both ends form a closed octagon.
What is the miter angle for a hexagon?+
A hexagon needs 30° miters on both ends of all six pieces. The general rule for any regular polygon is 180 divided by the number of sides: 60° for a triangle, 45° for a square, 36° for a pentagon and 30° for a hexagon.
How do I find the miter angle for an odd corner?+
Measure the corner with an angle finder or bevel gauge, subtract it from 180 and divide by 2. A 100° corner needs 40° miters and a 95° corner needs 42.5°. For outside corners, measure the inside angle of the wall and use the same formula.
Why is my miter saw angle different from the protractor angle?+
Miter saws read 0° for a square (90°) cut, while a protractor on the board measures the angle from the edge. A 22.5° saw setting produces a cut line at 67.5° to the board’s edge; the two always add up to 90°.
How do I calculate the length of each piece in a frame?+
Decide the outside (long-point) length of each side. The inside (short-point) length is that minus twice the stock width times the tangent of the miter angle. For a square frame with 45° miters and 2-inch stock, the short side is 4 inches shorter than the long side.