Vector A
Vector B

​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 (°).


Formula of ​Angle Between two Vectors Calculator

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

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


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


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


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.