Magic Square Generator
Generate magic square puzzles where rows, columns, and diagonals all sum to the same number. A classic math puzzle that builds addition skills and logical thinking.
What is a Magic Square?
A magic square is a grid of numbers where every row, column, and diagonal adds up to the same "magic sum". Use each number from 1 to 9 exactly once.
Select your options and click
"Generate Magic Square" to create a puzzle
About This Tool
The Magic Square Generator creates number grid puzzles where every row, column, and diagonal adds up to the same 'magic sum.' Use numbers 1 through n² exactly once to complete the grid. For a 3×3 square, use 1-9 and each line sums to 15. For 4×4, use 1-16 summing to 34. Magic squares have fascinated mathematicians for thousands of years and provide excellent practice combining addition skills with logical deduction.
Frequently Asked Questions
A magic square is a grid of numbers where every row, column, and diagonal adds up to the same total—called the magic sum. For a 3×3 grid using 1-9, the magic sum is 15. Each number is used exactly once. The challenge is placing numbers so all lines sum correctly.
The magic sum formula is n(n²+1)/2 where n is the grid size. For 3×3: 15. For 4×4: 34. For 5×5: 65. The generator shows the magic sum so students know their target as they solve.
Start by calculating what's missing in rows or columns with the most given numbers. The center cell in a 3×3 is always 5. Look for cells that appear in multiple lines (corners appear in row, column, and diagonal). Use subtraction: if a row needs 15 and has 3 and 8, the missing number is 15-3-8=4.
Magic squares have been studied for over 4,000 years and connect to number theory, algebra, and combinatorics. They appear in recreational math, art (Dürer's famous engraving), and even modern applications like error-correcting codes. They're a gateway to mathematical thinking!