What this calculator does
A miter cut angles calculator works out the angle to set a miter saw to when a closed shape is being built from several equal-length pieces, such as a hexagonal picture frame, an octagonal planter box or a multi-sided garden bed. For any regular shape with N equal sides, the miter angle on each piece is 180 degrees divided by N.
The common mistake is confusing the miter angle with the interior corner angle the shape actually forms. A regular hexagon has 120 degree interior corners, but each piece is cut at 30 degrees, not 120, because two 30 degree cuts join to form each 120 degree corner. Getting this backwards is the most frequent cause of a shape that will not close up cleanly.
The formula
Divide 180 degrees by the number of equal sides the finished shape has. That gives the miter angle each piece is cut at. The interior angle the shape forms at each joint, shown alongside it, is (N minus 2) times 180 degrees divided by N.
| Term | Meaning |
|---|---|
| Miter angle | The angle each piece of material is actually cut at on the saw. |
| Interior angle | The angle the shape forms at each joint once assembled, equal to (N minus 2) times 180 degrees divided by N. |
| Regular shape | A closed shape made of equal-length sides meeting at equal angles, such as a square, hexagon or octagon. |
The inputs explained
| Field | What to enter |
|---|---|
| Number of sides in the shape | The number of equal sides in the finished shape, such as 4 for a square frame or 6 for a hexagonal one. |
When to use it
Building a hexagonal or octagonal frame
A picture frame, mirror surround or garden planter built from more than four sides needs a shallower miter angle than the familiar 45 degrees, worked out directly from the side count.
Building a multi-sided garden bed or table
A regular hexagonal or octagonal structure needs each piece cut at the angle matching its number of sides, so the pieces close up into a true regular shape without gaps.
Checking a design before cutting
Working out the miter angle and the resulting interior angle before cutting confirms the pieces will actually close into the intended shape, rather than discovering a gap after assembly.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What is the miter angle for regular shapes with different numbers of sides?
The miter cut angle needed as the number of equal sides in the shape increases.
| Number of sides | Miter cut angle | Interior corner angle |
|---|---|---|
| 3 | 60.00° | 60.00° |
| 4 | 45.00° | 90.00° |
| 5 | 36.00° | 108.00° |
| 6 | 30.00° | 120.00° |
| 8 | 22.50° | 135.00° |
| 12 | 15.00° | 150.00° |
Questions
Why is a square picture frame cut at 45 degrees, not 90?
The 90 degree figure is the interior corner the frame forms, not the cut angle. Each of the two pieces meeting at that corner is cut at half of it, 45 degrees, so that the two 45 degree cuts join to form the full 90 degree corner.
What is the miter angle for a hexagonal frame?
A regular hexagon has six equal sides, so the miter angle is 180 divided by 6, which is 30 degrees per cut.
What if I am cutting a single corner rather than a full regular shape?
For a one-off corner joint at a chosen angle rather than a full regular shape, use the mitre cut calculator instead, which halves a given corner angle directly.
Does the material thickness affect the miter angle?
No, the miter angle is a matter of geometry and depends only on the number of sides in the shape. Material thickness affects the length each piece needs to be cut to, not the angle of the cut itself.
For a single corner joint at a chosen angle rather than a full regular shape, see the mitre cut calculator. For frame material quantities, see the board feet calculator.