# Angle between two vectors calculator

Learning how to **find** the angle between **two** vectors is not always **simple** and easy. Being a mathematics **student**, you must have **faced** problems while **doing** so. It is because you have to **deal** with different **coordinates** and dimensions related to **vectors**. Do you want to **make** this learning **easy** and calculation fast?

You **should** use this **angle between two vectors calculator **that has been **designed** for this **purpose**. It is an online maths calculator** **that can **help** you in calculating the angle between **any** two vectors with any measurements within a **fraction** of a second. By using it, you **can** also learn the **way** to do this manually. Want to **learn** more? Keep **scrolling** to do so.

**Table of Contents**

## What is an angle?

**Angle** is one of the most **basic** concepts of **geometrical** mathematics that has **wide** usage in different **aspects**. An angle is a **region** between two lines when they **cross/intersect** each other. **For example**, when two lines **intersect**, the particular region is **surrounded** by them at the **point** of intersection.

That **region** represents the **angle** of those two **lines**. In **terms** of two **vectors**, it represents the **shortest** angle between the given **vectors** when they are **aligned** in a specific **plane**. To find the **angle**, we need to **align** the initial points of the vectors **properly**.

### What are vectors?

A vector is a **specific** term used in **mathematics** and physics that **represents** the measurements with **magnitude** and direction. In simple **terms**, it represents the **distance** between **two** specific **points** having particular **values** for their **coordinates**

The vectors **can** be **two-dimensional** as well as **three-dimensional** according to the **plane** in which they **exist**. Normally, a two-dimensional vector will have **x** and **y** coordinates while the **three-dimensional** vector will have **x**, **y**, and **z** all three **coordinates**.

A vector is **represented** using a **capital** alphabet with an **arrow** on its head. **Also**, sometimes, vectors are **represented** by writing the **capital** alphabet in **bold** format. **For example**, if you have a vector “**A**”, it can be written as “**A**” or “**A**”

### Angle between two vectors formula

Multiple **methods** can be **adopted** to find the **angle** between two vectors. But the **simplest** one is through the **dot product** of vectors. Here is the **formula** that has been **derived** from this type of product for the **sake** of angle calculation.

Cos𝜽 = A . B/|A| |B|

In the above formula,

- “A” and “B” in the numerator represent the vectors.
- “A” and “B” in the denominator represent the magnitude of the vectors.

### How to find the angle between two vectors?

Finding the angle between **two vectors** is **not** a difficult task if you are **following** these steps.

By following these steps, you can **easily** find the angle between two vectors. For the **sake** of your understanding, we have also solved an **example** here.

- Find the dot product of “A” and “B”.
- Find the magnitude of vector A.
- Find the magnitude of vector B.
- Divide the answer to the dot product by the multiplication of the magnitude of vectors
- Now, take the cos inverse of the final answer to find the angle

**Example 1:**

Find the angle between two vectors A (2, 5, 0) and B (3, 9, 0).

**Solution:**

First of all, let’s find the dot product of A and B.

A . B = 2 x 3 + 5 x 9 + 0 x 0

= 6 + 45 + 0

= 51

Now, we have to find the magnitude of A and B separately.

|A| = √(2)^{2}+ (5)^{2}

= √29

Similarly,

|B| = √90

= √310

Now, we need to put the values in the above formula.

Cos𝜽 = 51/√29 (3√10)

Cos𝜽 = 51/3√290

𝜽 = 0.99

### How to use the angle between two vectors calculator?

Using this **tool** by Calculator’s Bag is a simple **task**. Here are the steps that you need to adopt for using it.

The steps to use the angle between two vectors calculator are as follows:

**Step 1: **Enter the value of components of vector A in the first required input.

**Step 2: **Enter the value of components of vector B in the second required input.

**Step 3: **The calculator will automatically display an answer on the screen.

### FAQ | Angle between two vectors

**Does a vector have an angle?**

Yes, a vector makes an angle with the horizontal line.

**What is the angle made by the vector? **

The angle between two vectors is calculated by dividing the dot product of two vectors by the product of the magnitude of those vectors.

**How do you find the angle between two coordinates? **

To find the angle between two coordinates, we need to divide the y coordinates by the x coordinates.

**What is the angle between two 3D vectors? **

To find the angle between two 3D vectors, you have to follow this formula.

Cos𝜽 = A . B/|A| |B|