Magic Square Calculator: Ancient Math Meets Modern Precision
Used by mathematicians and puzzle enthusiasts worldwide, our magic square calculator generates perfect squares from 3×3 to 15×15 — from China’s Lo Shu to European Renaissance art.
"Ordo ab chao" — Order from chaos.
How the Magic Square Calculator Works
Magic constant formula:
M(n) = n(n² + 1)/2
For n=3: M = 15, n=4: M = 34, n=5: M = 65
For n=3: M = 15, n=4: M = 34, n=5: M = 65
Magic Square Calculator: Four Generation Modes
Order 3 Mode
The only 3×3 magic square (up to rotation) in our magic square calculator.
Order 4 Mode
Dürer, Siamese, and Strachey methods.
Order 5 Mode
Standard and panmagic (all diagonals equal).
Custom Order Mode
Any n from 3 to 15 with multiple types.
Magic Square Calculator: Global Magic Constants
| Order | Magic Constant | Total Squares |
|---|---|---|
| 3×3 | 15 | 8 (rotations) |
| 4×4 | 34 | 880 |
| 5×5 | 65 | 275,305,224 |
| 6×6 | 111 | ~10¹⁹ |
Magic Square Calculator: Special Properties
- Normal: Uses 1 to n²
- Panmagic: All broken diagonals equal
- Associative: a(i,j) + a(n+1-i,n+1-j) = n²+1
- Most Perfect: 2×2 subsquares sum to 2M/n
Pro Tips for Using the Magic Square Calculator
- Order 3 center must be 5 for standard
- Even orders use different methods than odd
- Panmagic only exists for n≥4 and n≠ multiple of 4
- Rotate/reflect to create variants
- Add constant to all cells for scaled versions
Unlock Mathematical Magic
From ancient China to modern cryptography, our magic square calculator reveals perfect symmetry.
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