Magic Square Calculator - Multi-Tools

Magic Square Calculator

Result

About Magic Squares

A magic square is a grid of numbers where the sums of numbers in each row, column, and diagonal are equal. This sum is called the "magic constant" or "magic sum".

Properties:

  • For a 3x3 magic square, the magic constant is 15
  • For a 4x4 magic square, the magic constant is 34
  • For a 5x5 magic square, the magic constant is 65
  • Each number from 1 to n² (where n is the size) appears exactly once

Example (3x3):

Magic SquareProperties
8 1 6
3 5 7
4 9 2
  • Magic Constant: 15
  • All rows sum to 15
  • All columns sum to 15
  • Both diagonals sum to 15

Tips:

  • Start with the middle cell in the top row
  • Move diagonally up and right for the next number
  • If a cell is occupied, move down one cell instead
  • Use this calculator to verify your manual calculations

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