The miter saw angle is essential for perfect workpiece joints. Miter saw angle depends on the joint angle and workpiece width; due to the various angles and lengths it’s unable to calculate quickly. So let’s see how to calculate the miter saw angles in a few steps.

A miter saw angle depends on the joint angle and workpiece width. If you need to calculate the miter saw angle, you will need a bit of depth of knowledge about trigonometry functions. It is easy. So let’s see how to calculate the miter saw angle quickly.

## Mathematical Steps to Find Miter Saw Angle

So, let’s prove a common equation by using workpiece widths and angles to be cut.

**Eqn 01 ↦ α+β=θ**
X - Face Length
Using Sin Low
Sinα = A∕X Sinβ=B∕X
Hence,
**Eqn 02 ↦ A∕Sinα = B/Sinβ**
α+β=θ Can be written as below
α=θ-β
Hence,
**Eqn 03 ↦Sinα = Sin(θ-β)**
From **Eqn 02 , and Eqn 03;**
Sin(θ-β) = A*Sinβ/B
**Expanding Sin(θ-β)**
SinθCosβ-CosθSinβ = A*Sinβ/B
**Divide both sides from (÷Sinβ)**
SinθCotβ-Cosθ = A/B
Cotβ = (A/B + Cosθ ) /Sinθ
**Tanβ = Sinθ/ (A/B + Cosθ ) **
**β = Arctan(Sinθ/ (A/B + Cosθ ) )**
**α = θ-β**

After you get the angles for **α** and **β**, it will not be the miter angle. It is the angle you have to keep in your workpiece. So you need the angle to be removed.

**This can be calculated by reducing 90 degrees. **

So, let’s see how to do it.

**Trigonometric **Tables For Sin, Cos, Tan** Values

Read more about – **Miter saw Parts and Functions**

## Calculating Miter Angle for 120 Degrees for 8cm and 12cm Workpiece Joints

Calculate the miter angle for joining angle **θ = 120** and workpiece width **8cm and 12cm**.

**Eqn 01 ↦ α+β=120**
X - Face Length
Using Sin Low
Sinα = 8∕X Sinβ=12∕X
Hence,
**Eqn 02 ↦ 8∕Sinα = 12/Sinβ**
α+β=120 Can be written as below
α=120-β
Hence,
**Eqn 03 ↦Sinα = Sin(120-β)**
From **Eqn 02 , and Eqn 03;**
Sin(120-β) = 8*Sinβ/12
**Expanding Sin(θ-β)**
Sin120Cosβ-Cos120Sinβ = 8*Sinβ/12
**Divide both sides from (÷Sinβ)**
Sin120Cotβ-Cos120 = A/B
Cotβ = (8/12 + Cos120 ) /Sin120
**Tanβ = Sin120/ (8/12 + Cosθ120 ) **
**β = Arctan(Sin120/ (8/12 + Cos120 ) )**
**β** **=** **Arctan(0.866/(8/12 - 0.5)**
**β** **=** **Arctan(5.1)**
**β** **=** **78.90**
**α = θ-β**
**α = 120-78.90**
**α = 41.1**

**Hence Miter Angle for 8 cm workpiece = 90 – 41.1 = 48.9 Degree**

**Hence Miter Angle for 8 cm workpiece = 90 – 78.90= 11.1 Degree**