# Reference Angle Calculator

**Measurement **of angle is not **difficult **unless you are asked to **find **it with a **reference **point. It will be difficult to find the reference **angle **because you may be **confused **about the reference **axis**. The reason is you may not be **able **to understand whether to **pick **the previous axes or the upcoming **axes **as the reference.

If you are making **mistakes **in this **calculation**, you should **use **this **reference angle calculator**. This online maths calculator has been **programmed **well to find this **angle **only. Whenever you will insert the **angle **measurement, it will set a **reference **automatically and **show **you the reference angle. Learn in **detail **here about this **angle **and the **use **of the calculator.

**Table of Contents**

## What is Reference Angle?

It is the **smallest **angle formed between the** x-axis **and the **terminal **line. Normally, we find the **measure **of an angle from the **positive **x-axis to the **terminal **arm/line. But the **reference **angle is a **part **of this angle that is **considered **the shortest one between the x-axis and the **terminal **arm.

In **general **mathematics, this type of angle is not **important**. But it has great **significance **when it comes to **solving **problems **related **to Trigonometry. The **reference **angle helps in finding the **values **of Sine and Cosine with the **identification **of their quadrant.

### How to find the reference angle?

Finding the **reference **angle is **not **a **difficult **task if you follow these simple **steps**.

- Choose the closest x-axis line to the terminal angle arm.
- Set its values as a reference point.
- If the terminal arm is beyond the reference axis, subtract its angle from the terminal angle.
- If the terminal arm is behind the reference axis, subtract the terminal angle from the axis angle.

To let you **understand **these steps, we have also solved an **example **here. Just have a look at this example to **memorize **the solution.

**Example 1:**

Find the terminal angle of 145 degrees.

**Solution:**

When 145 degrees is drawn on the x-y coordinate system, the closest angle on the x-axis is 180 degrees. To find the reference angle, we have to subtract the given angle from 180 degrees.

So,

Reference angle = 180 - 145

= 35 degrees

### How to use Reference Angle Calculator?

You can use this online tool of Calculator’s Bag in a single step. Here is the step you have to follow:

- Insert the given angle in the text insertion box
- This calculator will automatically work and show you the value for the reference angle.

### What is Reference Angle for...?

For quick answers, we have enlisted some angles here with their reference angles too:

Angle Measurement |
Reference Angle |

1 | 1 |

2 | 2 |

5 | 5 |

30 | 30 |

60 | 60 |

120 | 60 |

150 | 30 |

220 | 40 |

250 | 70 |

### FAQ | Reference Angle Calculator

**What is the reference angle of 45 degrees?**

The reference angle of 45 degrees is 45 because the closest angle on the x-axis is 0 degrees.

**What is the reference angle of 120?**

The reference angle of 120 degrees is 60 because the closest x-axis angle is 180 degrees.

**What is the reference angle of 30? **

The reference angle of 30 is also 30 degrees.

**What is the reference angle of 2pi? **

The reference angle of 2pi is 0 because it is on the positive x-axis terminal.