Matrix Addition Calculator
Add two equally sized matrices entry by entry and instantly see the resulting matrix and its dimensions.
How does this calculator work?
To add two matrices, they must be the same size. Add the numbers in matching positions: the entry in row i, column j of the result is A[i][j] + B[i][j]. Enter each matrix with one row per line and spaces between entries, and the result keeps the same dimensions.
Formula
How this is calculated
Enter Matrix A and Matrix B as text: put each row on its own line and separate the entries within a row using spaces or commas. The calculator parses each text block into an m×n grid of numbers, where m is the number of rows and n is the number of columns.
Matrix addition is only defined when both matrices have exactly the same shape. The tool checks that A and B share the same number of rows and columns; if they differ, it reports a dimension error. When the shapes match, it computes the sum element by element with C[i][j] = A[i][j] + B[i][j], producing a new matrix C of the same size.
Addition is commutative and associative, so A + B equals B + A. Entries may be integers or decimals, positive or negative. The result preserves the original layout, and the summary reports the dimensions, the total element count, and the sum of all entries as a quick sanity check.
Frequently asked questions
No. Matrix addition requires both matrices to have the same number of rows and the same number of columns. Otherwise it is undefined and the calculator shows a dimension error.
Type one row per line, and separate the numbers in each row with spaces or commas. For example, "1 2" on the first line and "3 4" on the second line is a 2×2 matrix.
No. Matrix addition is commutative, so A + B and B + A give the same result.
Also known as
TG we-Calculate Editorial Team. (2026). Matrix Addition Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/matrix-addition-calculator
TG we-Calculate Editorial Team. "Matrix Addition Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/matrix-addition-calculator.
TG we-Calculate Editorial Team, "Matrix Addition Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/matrix-addition-calculator
@misc{wecalculate_matrix_addition_calculator, title = {Matrix Addition Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/matrix-addition-calculator}}, year = {2026}, note = {TG we-Calculate} }
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