What is a magic square?

A magic square is a square grid filled with distinct positive integers so that the numbers in each row, each column, and both main diagonals all add up to the same total, called the magic constant. For example, a 3×3 magic square contains numbers 1-9 and every line sums to 15.

What is the magic constant?

The magic constant is the sum that every row, column, and main diagonal of a magic square must equal. It is calculated with the formula n(n²+1)/2, where n is the size of the square. For a 3×3 square the magic constant is 15, for 5×5 it is 65, and for 7×7 it is 175.

Why are only odd-sized squares supported?

This generator uses the Siamese (De la Loubère) method, which is a simple and elegant algorithm that works exclusively for odd-order magic squares. Even-order magic squares require different, more complex algorithms. Odd-order squares are the most commonly studied and used in education.

What is the Siamese method?

The Siamese method (also called De la Loubère method) is a classic algorithm for constructing odd-order magic squares. Start by placing 1 in the center of the top row, then move diagonally up and to the right for each successive number. If the move goes off the grid, wrap around; if the target cell is already occupied, move down one row instead.

Are the generated magic squares correct?

Yes, the Siamese method is a mathematically proven algorithm that always produces a valid magic square for any odd order. Every row, column, and main diagonal in the generated square will sum to exactly the magic constant n(n²+1)/2.

Can I use this tool for teaching?

Absolutely! Magic squares are excellent for teaching number patterns, arithmetic, algebra, and algorithmic thinking. Students can verify the magic constant by summing rows, columns, and diagonals, making this tool ideal for classroom demonstrations and homework exercises.

Is this tool free to use?

Yes, the magic square generator is completely free with no registration required. You can generate as many magic squares as you like, and all features including copy to clipboard and download are available at no cost.

What is the history of magic squares?

Magic squares date back over 4,000 years. The earliest known example is the Lo Shu square from ancient China (circa 2200 BCE). They appear in Indian, Arabic, and European mathematical traditions and have been studied by mathematicians including Benjamin Franklin and Leonhard Euler.

Magic Square Generator

Generate magic squares of odd orders where every row, column, and diagonal sums to the same magic constant. Perfect for mathematical puzzles, number theory exploration, and educational demonstrations of the Siamese method algorithm.

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Choose a magic square size to get started

Square Options

Select the size of your magic square

Square Size

3×3Magic Constant: 155×5Magic Constant: 657×7Magic Constant: 1759×9Magic Constant: 369

Odd-order sizes only — generated using the Siamese (De la Loubère) method

How it works: A magic square is a grid of distinct positive integers where every row, column, and main diagonal sums to the same value — the magic constant. For an n×n square the magic constant is n(n²+1)/2. This generator uses the classic Siamese method: place 1 in the middle of the top row, then move diagonally up-right for each successive number, wrapping around edges and dropping down when a cell is occupied.

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