Miter Angle Calculator
Enter your corner angle and choose a cut type to get the exact miter angle to set on your saw. Supports flat trim with equal or unequal board widths, crown molding compound cuts with any spring angle, and both inside and outside corners. Results include the saw scale reading you dial in and a show-your-work panel so you can follow the trigonometry step by step.
What is a miter angle?
A miter angle is the diagonal cut made across the face of a board so that two pieces join at a corner. Unlike a square butt joint, where boards simply meet end-to-end, a mitered joint hides the end grain and creates a cleaner finished look. Miters are used in picture frames, baseboards, door casings, crown molding, and anywhere two pieces of trim meet at an angle. The key number is how many degrees each board must be rotated from a 90-degree (straight) cut so the two angled faces add up exactly to the corner angle.
Equal vs. unequal board widths
When both boards have the same face width, the math is simple: each board gets cut at half the corner angle. For a 90-degree inside corner that means 45 degrees each, and most saw protractors read 45 directly. When the boards have different widths, such as a narrow door stop meeting a wide architrave, equal miter angles would leave a visible step at the joint face. The general formula uses the arctangent function to distribute the corner angle unequally so the joint line remains visually straight across both board faces regardless of the width difference.
Crown molding: why compound cuts are needed
Crown molding sits tilted between wall and ceiling at a fixed "spring angle" that is built into the profile, typically 38 or 45 degrees. Because the molding is not flat, a single miter rotation is not enough to close the joint correctly. The solution is a compound cut: a miter angle (horizontal blade rotation) combined with a bevel angle (blade tilt). The compound formula converts the spring angle and the corner angle into these two saw settings so the molding can be cut flat on the saw table rather than held at its spring angle against the fence. Crown molding is one of the trickier carpentry tasks, so always cut test pieces in cheap material before touching the finished molding.
Inside and outside corners
An inside corner is the concave angle you see where two walls of a room meet. An outside corner is the convex angle at a protruding column or bay window. For calculation purposes, an outside corner uses the supplement of the measured angle: if the wall forms a 90-degree outside corner, the effective angle for the formula is 180 - 90 = 90 degrees, giving the same 45-degree miter. However, the direction of the cuts is reversed on the board compared to an inside corner, which is why it helps to think through which board face is the "show" face before making cuts.
Common polygon miter angles
| Shape | Sides | Interior angle | Miter angle (each board) | Saw scale setting |
|---|---|---|---|---|
| Triangle | 3 | 60 deg | 30 deg | 60 deg |
| Square / frame | 4 | 90 deg | 45 deg | 45 deg |
| Pentagon | 5 | 108 deg | 54 deg | 36 deg |
| Hexagon | 6 | 120 deg | 60 deg | 30 deg |
| Octagon | 8 | 135 deg | 67.5 deg | 22.5 deg |
| Decagon | 10 | 144 deg | 72 deg | 18 deg |
| Dodecagon | 12 | 150 deg | 75 deg | 15 deg |
For regular polygon frames, each joint corner equals the interior angle shown. The saw scale setting is what you dial on most miter saws.
Frequently asked questions
What is the miter angle for a 90-degree corner?
For a standard 90-degree corner with equal-width boards, each board is cut at 45 degrees. Most miter saws read this directly on their protractor scale. If your boards have different widths, use this calculator to find the two unequal angles.
What is the difference between a miter angle and a bevel angle?
A miter angle is the horizontal rotation of the saw blade, cutting diagonally across the face of the board when viewed from above. A bevel angle is the tilt of the blade away from vertical, cutting diagonally across the thickness of the board. Flat trim needs only a miter angle. Crown molding installed flat on the saw table needs both a miter angle and a bevel angle at the same time, which is called a compound cut.
How do I read the angle on my miter saw?
Most miter saws measure from 0 degrees at the straight-ahead position rather than from 90 degrees as geometry does. That means the saw scale reading equals |90 - miter angle|. For example, a 45-degree miter reads 45 degrees on the saw scale, but a 60-degree miter (for a 30-degree saw-cut reading) shows 30 on the scale. This calculator reports both the geometric miter angle and the saw scale setting so you do not need to do the conversion.
What spring angle should I use for crown molding?
The spring angle is stamped or printed on the back of most crown molding, or you can measure it by holding the molding flat against a table and measuring the angle the back surface makes with the tabletop. Standard residential crown molding is most often 38 degrees or 45 degrees. If you are unsure, 38 degrees is the most common value for stock crown profiles.
Why does my miter joint have a gap?
Gaps usually come from one of three causes: the angle setting is off by a degree or two, the saw fence or the wall surface is not perfectly flat, or the board ends are not perfectly square before the miter cut. Adjust by halving the gap angle and correcting each piece equally rather than trying to fix the entire gap on one board. A sharp blade also makes a cleaner joint: a dull blade tends to push the cut slightly off angle.
Can I use this calculator for picture frames?
Yes. A standard picture frame has four 90-degree corners, so each board gets a 45-degree cut. If your frame has an unusual shape, enter the interior angle of the frame corner, select "Flat trim" and "Inside corner", and the calculator gives you the miter angle for each piece.