Magic Square Calculator
Generate Perfect Magic Squares
Generate magic squares where all rows, columns, and diagonals sum to the same magic constant.
Generate Magic Square
Enter between 3 and 15 (size 2 does not exist)
What is a Magic Square?
A magic square is an n×n grid filled with distinct numbers such that all rows, columns, and diagonals sum to the same value.
• Contains numbers 1 to n²
• All rows sum to M
• All columns sum to M
• Both diagonals sum to M
M = n(n² + 1) / 2
Features
- Generate 3×3 to 15×15 squares
- Odd order algorithm (Siamese)
- Doubly even algorithm
- Singly even algorithm
- Automatic verification
- Sum calculations
- Copy to clipboard
- Download as text file
Types
n = 3, 5, 7, 9, 11, 13, 15...
Uses Siamese method
n = 4, 8, 12...
Divisible by 4
n = 6, 10, 14...
Even but not divisible by 4
History
Lo Shu square (3×3) from 650 BC
Used in astrology and architecture
Advanced mathematical studies
Dürer's Melencolia I (1514)
Applications
- Mathematical puzzles and games
- Recreational mathematics
- Number theory research
- Cryptography and coding theory
- Statistical design of experiments
- Art and architecture
- Educational tools
- Cultural and historical studies
Famous Magic Squares
Notable Examples:
Oldest known magic square, M = 15
Featured in Melencolia I, M = 34
Benjamin Franklin's creation, M = 260
Contains his birth date
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