Matrix Addition Calculator

Add matrices step by step

The calculator will find the sum of two matrices (if possible), with steps shown. It adds matrices of any size up to 10x10 (2x2, 3x3, 4x4, etc.).


If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

The Matrix Addition Calculator is a resource for quick and precise matrix addition calculations. Our digital tool is created to ease matrix addition, delivering correct results every time.

How to Use the Matrix Addition Calculator?

  • Input

    First, you'll need to input the matrices you want to add. Enter the elements of each matrix row by row and column by column. Make sure that the matrices have the same dimensions. In order for matrix addition to be possible, the two matrices must have the same number of rows and columns.

  • Calculation

    Once you've inputted and verified your matrices, click the "Calculate" button.

  • Result

    The Matrix Addition Calculator will instantly process the information and provide you with the resultant matrix. This matrix is the sum of the two matrices you've entered.

What Is Matrix Addition?

Matrix addition, a key operation in linear algebra, involves adding corresponding elements of two matrices that have identical dimensions. If you have two matrices $$$A$$$ and $$$B$$$, the sum, denoted as $$$A+B$$$, is computed by adding the corresponding elements of $$$A$$$ and $$$B$$$.

In the form of a formula, if $$$A=\left[a_{ij}\right]$$$ and $$$B=\left[b_{ij}\right]$$$ are matrices of the same size $$$m\times n$$$, then the sum $$$C=A+B$$$ is also a matrix of the size $$$m\times n$$$ with $$$c_{ij}=a_{ij}+b_{ij}$$$ for each $$$i$$$ and $$$j$$$.

For instance, suppose we have the following two matrices:


The sum of $$$A$$$ and $$$B$$$ is computed as follows:


which simplifies to


This example illustrates how matrix addition is performed element-wise.

What Is the Use of Matrix Addition?

Matrix addition plays a crucial role in many areas. It's used in computer graphics for 3D transformations, in quantum physics for state computations, and in economics for resource distribution models. Additionally, it's applied in engineering to solve systems of equations, in data science for dataset management, and in network theory to analyze graph structures. The key requirement is that the matrices must have identical dimensions.

Why Choose Our Matrix Addition Calculator?

  • Simplicity

    With an intuitive interface, adding matrices becomes a straightforward task.

  • Accuracy

    Our calculator guarantees precise results, reducing the chances of errors in your calculations.

  • Step-by-Step Solution

    In addition to the final answer, our calculator provides a detailed, step-by-step solution, enhancing your understanding of the process.

  • Accessibility

    Our calculator is web-based, making it accessible from any device, anywhere, anytime.


How do I use the Matrix Addition Calculator?

Simply input the two matrices you wish to add into the calculator and click the "Calculate" button. The calculator will output the matrix sum.

Does the Matrix Addition Calculator provide step-by-step solutions?

Yes, our calculator provides step-by-step solutions, which can enhance your understanding of matrix addition.

Can the Matrix Addition Calculator handle large matrices?

Yes, our calculator is designed to handle matrices of different sizes. However, for the best performance, we recommend using it for matrices of a manageable size.

How many times can I use the Matrix Addition Calculator?

There's no limit on the number of times you can use the Matrix Addition Calculator. You can use it as often as you need.