Quaternion Calculator


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Introduction to Quaternion Calculator

The quaternions calculator is an online tool that can calculate the sum, difference, product, magnitude, and conjugate of two quaternions by representing them in three-dimensional space. It also forms the matrix representation of quaternions by taking the input values from you.

In algebra, the quaternion calculation is used to generalise two-dimensional complex numbers to three dimensions. It is difficult for many students to find the quaternion and represent a two-dimensional complex number into a three-dimension because this concept is confusing. Therefore, here we introduce a tool that allows you to define complex numbers in the form of quaternions.

Formula used in Quaternion Rotation Calculator

The quaternion is a set of four dimensions to represent complex numbers in 3D representation or rotation. Here, there is 1 real dimension and 3 are imaginary dimensions. The quaternion can be represented as:

$$ Q_1 \;=\; a \;+\; bi \;+\; cj \;+\; dk $$


$$ Q2 \;=\; e \;+\; fi \;+\; gj \;+\; hk $$

This quaternion calculator uses the above representations of complex numbers and finds the sum, difference, product, magnitude, conjugate and matrix representations of two quaternions. These formulas to calculate quaternion are:

  1. Sum:
  2. $$ Q_1 \;+\; Q_2 \;=\; (a+e) \;+\; (bi+fi) \;+\; (cj+gj) \;+\; (dk+hk) $$
  3. Difference:
  4. $$ Q_1 \;-\; Q_2 \;=\; (a-e) \;+\; (bi-fi) \;+\; (cj-gj) \;+\; (dk-hk) $$
  5. Product:
  6. $$ Q_1 \;×\; Q_2 \;=\; (a+bi+cj+dk) \;×\; (e+fi+gj+hk) $$
  7. Magnitude:
  8. $$ Q_1 \;=\; \sqrt{a^2 \;+\; b^2 \;+\; c^2 \;+\; d^2} $$
  9. Conjugate:
  10. $$ Q_1 \;=\; -(a+bi+cj+dk) $$
  11. Matrix Representation:
  12. $$ Q_1 \;=\; a+bi+cj+dk $$

    In 2×2 order matrix,

    $$ [a+bic+di-c+dia-bi] $$

Note that the "i" of the complex numbers is distinct from the "i" of the quaternions.

How to use the Quaternion Formula Calculator?

Using this maths tool makes it easy to apply different operations to quaternions. Because it provides you with easy steps to use it. These steps are:

  • Search for calculators from your browser and select the quaternion calculator.
  • On the calculator page, enter the operation you want to apply to the quaternions.
  • Enter the coefficients of quaternions.
  • Or try the load examples option to select random values to find the quaternion.
  • Click on the calculate quaternion button.

By following the above given steps, you will get the solution within a few seconds.

Why use the Quaternion Multiplication Calculator?

In algebra, the concept of quaternions is used to represent two-dimensional complex numbers into three dimensions. It is beneficial to analyse the problems where the three dimensions are involved. It linearizes the issues to make them easy to solve. You can use our tool to apply different operations of quaternions to find their solutions.

It is challenging to implement a 2D problem into 3D by hand because of rotational orientations. But the quaternion calculator helps solve such problems by using only input values. Therefore, it is suggested to use this tool that is entirely reliable for you.

Benefits of using the Quaternion Addition Calculator

Using an online tool to solve mathematical problems is promoted by us so that you may be able to use the technology for learning purposes. Our agency has a lot of benefits. These are:

  1. Quaternion formula calculator can solve any complex problem of quaternion calculation by using different operations quickly.
  2. The quaternion multiplication calculator provides accurate and quick results that make it more reliable for you to find the quaternion.
  3. It is easy to calculate the quaternion, because it is user-friendly.
  4. Quaternions calculator allows you to solve many different problems to make the concept clear to you.


How to find a quaternion rotation calculator?

You can find it easily by searching calculatores from your browser. There will be a list of many maths tools available on this website. You can choose your desired tool from the list.

Alan Walker

Alan Walker

Last Updated June 02, 2022

Studies mathematics sciences, and Technology. Tech geek and a content writer. Wikipedia addict who wants to know everything. Loves traveling, nature, reading. Math and Technology have done their part, and now it's the time for us to get benefits.