# Miter Angle Calculator

URL: https://speedycalculator.com/calculators/construction/miter-angle/
Last updated: 2026-10-25

> The miter angle calculator finds the miter cut angles for joining two boards of different widths at any angle, so the joint line meets both outside and inside corners, plus the saw settings for each board.

## Inputs

- Angle between boards (°, rad)
- Width of board 1 (in, cm, mm, ft, m)
- Width of board 2 (in, cm, mm, ft, m)

## Results

- Cut angle on board 1
- Cut angle on board 2
- Saw setting for board 1
- Saw setting for board 2
- Joint line length

## 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
```

## Explanation

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.

### Tips for an accurate estimate

- Measure angles with a digital angle finder or sliding bevel, not by eye.
- Make a test cut in scrap before cutting expensive stock.
- Small angle errors add up over many joints – check the first assembly before cutting the rest.
- Keep a written list of the dimensions and angles you set on the saw or machine.

### Common mistakes to avoid

- Reading the saw scale as the angle from the edge rather than from square.
- Rounding intermediate results too early.
- Mixing degrees and percent grade.

### Inputs explained

FieldWhat to enterAngle between boardsUnits: °, radWidth of board 1Units: in, cm, mm, ft, mWidth of board 2Units: 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 (°)4518.5567.527.49035.54112.542.2413545.58

## 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.

## FAQ

**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.

**What formula does the Miter Angle Calculator use?**
α = atan(n sin θ ÷ (m + n cos θ)), β = θ − α.