When two boards of the same width meet, the miter splits the corner angle in half. When the widths differ (a wide casing meeting a narrow apron, or a thick and thin moulding), each board needs a different angle so the joint line runs from the outside corner to the inside corner.
How to use the Miter Angle Calculator
- Angle between boards
- Width of board 1
- Width of board 2
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the angle between the two boards and the width of each.
Inputs explained
| Field | What to enter |
|---|---|
| Angle between boards | Units: °, rad |
| Width of board 1 | Units: in, cm, mm, ft, m |
| Width of board 2 | Units: in, cm, mm, ft, m |
What each result means
- Cut angle on board 1 = deg(atan([Width of board 2]×sin(rad([Angle between boards]))÷([Width of board 1] + [Width of board 2]×cos(rad([Angle between boards])))))
- Cut angle on board 2 = [Angle between boards] – [Cut angle on board 1]
- Saw setting for board 1 = 90 – [Cut angle on board 1]
- Saw setting for board 2 = 90 – [Cut angle on board 2]
- Joint line length = [Width of board 2]÷sin(rad([Cut angle on board 1]))
Example values
How the main result changes when Angle between boards changes and everything else stays at the example values above:
| Angle between boards (°) | Cut angle on board 1 (°) |
|---|---|
| 45 | 18.55 |
| 67.5 | 27.4 |
| 90 | 35.54 |
| 112.5 | 42.24 |
| 135 | 45.58 |
Formula
α = atan(n sin θ ÷ (m + n cos θ)), β = θ − α
with θ the angle between the boards, m and n their widths
Saw setting = 90° − cut angle
Worked example
Inputs: Angle between boards: 90 °; Width of board 1: 3.5 in; Width of board 2: 2.5 in.
Results: Cut angle on board 1 = 35.54 °; Cut angle on board 2 = 54.46 °; Saw setting for board 1 = 54.46 °; Saw setting for board 2 = 35.54 °; Joint line length = 4.301 in.
Frequently asked questions
What miter angle for equal boards at 90°?
45° each.
Why do boards of different widths need different angles?
So the joint line connects the outer and inner corners; equal angles would leave a step.
How do I cut a miter on a miter saw?
Set the saw to 90° minus the cut angle measured from the board's edge.