Matrix Addition Calculator
Adding Matrices, Cell by Cell
Matrix addition is the most literal of the matrix operations: line up two matrices of the same size and add each pair of matching entries. No cross-multiplication, no determinants — just position-by-position addition, which is why it only works when both matrices share identical dimensions.
The Formula
C = A + B (element-wise addition)
Cij = Aij + Bij
Cij = Aij + Bij
Worked Example
For A = [1, 2; 3, 4] and B = [5, 6; 7, 8]:
| Position | Calculation | Result |
|---|---|---|
| Row 1 | 1+5, 2+6 | 6, 8 |
| Row 2 | 3+7, 4+8 | 10, 12 |
Result matrix: [6, 8; 10, 12].
Where This Matters
- Combining datasets — summing matrices of sales, sensor readings, or grades across two periods to get combined totals.
- Image processing — blending or adjusting images represented as pixel-value matrices uses element-wise addition.
- Superposition in physics — adding transformation or state matrices to combine multiple simultaneous effects.
How to Use This Calculator
- Choose the matrix size: 2 x 2 Matrices or 3 x 3 Matrices.
- Enter each cell of Matrix A (A row1 col1, A row1 col2, and so on).
- Enter each cell of Matrix B in the same layout.
- Select Calculate to get the sum matrix.
Related Calculations
Need to subtract instead? Use the Matrix Subtraction Calculator, or combine matrices by multiplication with the Matrix Multiplication Calculator.