Vector A
Vector B

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.

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).


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	 


|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|