Magic Square Generator
This tool generates a magic square — a square grid of distinct numbers where the sums of each row, column, and both diagonals are equal. It’s ideal for students learning number patterns, teachers building puzzles, and math enthusiasts exploring recreational mathematics.
Generate an N×N Magic Square Online
Magic Constant Formula
$$\text{Magic Constant} = M = \frac{n(n^2 + 1)}{2}$$
Explanation:
In an $$n \times n$$ magic square, the magic constant $$M$$ is the sum of numbers in every row, column, or diagonal. The square contains all numbers from $$1$$ to $$n^2$$ exactly once.
Calculation Example
For n = 3:
Magic constant: (3 × (9 + 1)) / 2 = 15
Generated 3×3 magic square:
| 8 | 1 | 6 |
| 3 | 5 | 7 |
| 4 | 9 | 2 |
All rows, columns, and diagonals = 15
Magic squares have a rich history in mathematics, art, and culture. They’re used in logic puzzles, mathematical exploration, and pattern recognition. This generator supports odd-sized squares (3×3, 5×5, etc.), and can be used for teaching symmetry, combinatorics, or recreational math challenges.