Magic Square

Order 3 magic square with
magic number 15.

A magic square is a square grid in which each small square contains a distinct number and the sum of the numbers in a column, row and diagonal is the same.

Each small square in the square grid is a cell, and a square grid with number of cells n on each side is a magic square of order n.

Standard magic square is magic square of order 3 because magic square of order 1 is said to be trivial and magic square of order 2 is impossible. A magic constant can't be derived from a magic square of order 2.

A magic constant (also magic sum) is the same numerical value obtained from the sum of numbers in a diagonal, column and row of a magic square.

The magic constant of the magic square of order 3 above is 15.


  1. Numbers in the right column are 6, 1 and 8. Magic sum = 6+1+8 = 15
  2. Numbers in the top row are 2, 7 and 6. Magic sum = 2 + 7 + 6 = 15
  3. Numbers in the diagonal from top left to bottom right are 2, 5 and 8. Magic sum = 2 + 5 + 8 = 15
Examples of magic squares are:
  1. Lo Shu Square
  2. Chautisa Yantra
Lo Shu Square is a 3 by 3 magic square with magic constant 15. Chautisa Yantra is a 4 by 4 magic square with magic sum 34.

The holy city is a magic cube and the magic square is a two-dimensional structure of the cube.