# Angle Between two Vectors

The angle between two vectors is referred to as the shortest angle, having a single starting point and the vectors are directed in different coordinates. These vectors are co-directional to each other. The exact definition of the **angle between two vectors** is equal to the **dot product of the vectors divided by the product of the** **intensity **or magnitude of the vector.

**Unit of angle:**

The unit of the angle is the degree (°).

**Table of Contents**

## Formula of Angle Between two Vectors Calculator

The angle between two vectors can be calculated by the formula:

\[\cos \theta = \frac{{A.B}}{{|A||B|}}\]

**Where,**

θ = angle between the vectors

A = 1st vector

B = 2nd vector

|A| = magnitude of 1st angle

|B| = magnitude of 2nd angle

"." = dot product of the vectors

**Note:**

To gain knowledge about reference angles, click the Reference Angle Calculator.

### Example

To get an idea of how to calculate the angle between the vectors, we have illustrated a detailed example in the following lines.

Vector A has a magnitude of 4,3 and that of vector B is 3,5, calculate the angle between these two vectors. We will find the angle using the above-mentioned formula.

\[\cos \theta = \frac{{A.B}}{{|A||B|}}\]

Firstly, we will find the magnitude of the vectors by using the following method:

|A| = √(4)^{2}+ (3)^{2}

|A| = √25

|A| = 5

For that of vector b, using the same method we will get a magnitude is **√34**.

Secondly, we will find the dot product of the vectors

A.B = 12 + 15

A.B = 27

A.B = 4.3 + 3.5

Putting the values in the formula, we get:

\[\cos \theta = \frac{{A.B}}{{|A||B|}}\] \[\cos \theta = \frac{{27}}{{5\sqrt {34} }}\]

θ = 22.17°

### How to use Angle Between two Vectors Calculator?

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.

### Calculator use

This calculator can be helpful in getting the results in a few seconds. You simply have to put the values against the boxes and the result will be printed in the output field.