Angle Between Two Vectors Calculator

Vectors are of great use in our day to day lives. Vectors are used in almost each and every field with the major use of vectors in the field of Physics. We often encounter vectors and major calculations, and these are dependent on the angles between those vectors.

Angle Between Two Vectors Calculator
Vector A
Vector B
Angle Between Two Vectors Calculator Results
Angle Between Two Vectors

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Angle Between Two Vectors Calculator. This image shows the Angle Between Two Vectors with associated calculations used by the Angle Between Two Vectors Calculator

A Good Calculator for Calculations of angle between two 3D vectors

You can use this online interface by iCalculator to find out the angle between two vectors in 3 dimensions.

The concept of all those physical quantities that have a direction and magnitude associated with them is described by using the angle between two vectors. To calculate the angle between two vectors, we consider the endpoint of the first vector to the endpoint of the second vector. The endpoint is determined with the help of the vector direction in which the vector was measured.

For calculating the angle between two 2D vectors, you can use our 2D vector angle calculator that can calculate the angle between two 2D vectors in no time. Let us understand some of the aspects related to the 3D vector angle calculator now.

Different properties of vector

The following are some of the important properties of vectors:

  • Two vectors (say 'a' and 'b') are said to be equal if and only if each of them has their respective components (i.e., ai and bi) equal for every component of the vector 'i'. For example, the vector (2,5,6) is equal to another vector (2,5,6) because the i, j, and k component (i.e., the component on 'x', 'y', and 'z' axis respectively) of both the vectors are equal.
  • Vectors have a commutative property i.e. if you add two vectors in a particular order and after that, you change the order, the sum in both the cases will be the same. For example, a + b = b + a, where a and b are two different angles.
  • Vectors also follow the law of associativity i.e, a + (b + c) = (a + b) + c, where a, b, and c are three different vectors.

How to calculate the angles between two 3D vectors

Vectors are quantities that have both magnitude and direction. The distance of the vector is represented by its magnitude while the direction in which the vector is covering the distance is represented by its direction.

In the case, when a common vertex is shared between two vectors, the angle formed is known as the angle between those two vectors. You can easily use this online calculator to find out the angle between two 3D vectors. Here are the steps that are performed in order to find the angle:

Let us suppose that the given vectors are in the form:

A = a1i + b1j + c1k
B = a2i + b2j + c2k

Where a1, b1, c1, a2, b2, and c2 are the components of the above vectors in 'x', 'y' and 'z' axis.

After that, we have to find out the magnitude of the above vectors i.e., |A| and |B|.

The magnitude can be calculated by adding and finding out the square root of the summation of the components of both the vectors.

|A| = (a12 + b12 + c12)½
|B| = (a22 + b22 + c22)½

The final step will be to calculate the angle between both the vectors by using the cosine formula. The formula can be defined as:

Cos (θ) = a1a2 + b1b2 + c1c2/|A||B|

You can find out the angle θ by finding the inverse of the cosine.


We have provided you with such a great online calculator calculates the angle between two 3D vectors, which is a very complicated and time consuming task. You can easily use this calculator by entering the components of two vectors in the required fields is all you have to do. You will get the result as soon as you add inputs to the calculator.

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