A Magic Square is a series of numbers arranged in a square so that (at least) the values in each row, each column and both diagonals add up to the same total (T).
Although repeat values are sometimes permitted, the most elegant magic squares have different values in each cell.
Basic Magic Squares use the series of whole numbers from 1 to n, where n = the number of cells in the square.
Magic Squares of different sizes can be created, for example:
8  1  6 
3  5  7 
4  9  2 
1  15  14  4 
12  6  7  9 
8  10  11  5 
13  3  2  16 
17  24  1  8  15 
23  5  7  14  16 
4  6  13  20  22 
10  12  19  21  3 
11  18  25  2  9 
1  35  34  3  32  6 
30  8  28  27  11  7 
24  23  15  16  14  19 
13  17  21  22  20  18 
12  26  9  10  29  25 
31  2  4  33  5  36 
While, minimally, every row, column, and both diagonals must add up to the same total (T), some magic squares permit the total to be achieved in many more ways.
Our Magic Square Generator produces 'most perfect' 4 x 4 magic squares where T (if an even number) can be found in 52 different ways!
The mathematics, symmetry and symbolism of magic squares have fascinated people for thousands of years. In many cultures they are believed to be imbued with ‘magical’ qualities, and are sometimes worn as amulets to bring fortune.
TEDx Talk on Magic Squares by Michael Daniels
The Lo Shu square is an ancient 3x3 magic square which features in Chinese divination. Some people claim that it may date from around 2800 BCE.
All other basic 3x3 magic squares are rotations and/or reflections of the Lo Shu square.
4  9  2 
3  5  7 
8  1  6 
The Lo Shu Square
This famous square is believed to date from the 11th Century CE.
The Jaina Square (so named because it is also found in a 12th or 13th Century Jaina/Jain inscription at Khajuraho, Northern India) is an example of what has been termed a ‘diabolic’ or ‘mostperfect’ magic square because the total (T) can be produced in many (52) different ways.
7  12  1  14 
2  13  8  11 
16  3  10  5 
9  6  15  4 
The Jaina Square
This 4x4 magic square is featured in Albrecht Dürer’s (14711528) famous engraving “Melencolia I” (1514).
Note the date 1514 in the bottom row.
16  3  2  13 
5  10  11  8 
9  6  7  12 
4  15  14  1 
The Dürer Square
Heinrich Cornelius Agrippa (14861535) was an occultist, astrologer and alchemist who attributed specific magic squares to the seven ‘planets’ known at the time.
4  9  2 
3  5  7 
8  1  6 
T = 15
4  14  15  1 
9  7  6  12 
5  11  10  8 
16  2  3  13 
T = 34
11  24  7  20  3 
4  12  25  8  16 
17  5  13  21  9 
10  18  1  14  22 
23  6  19  2  15 
T = 65
6  32  3  34  35  1 
7  11  27  28  8  30 
19  14  16  15  23  24 
18  20  22  21  17  13 
25  29  10  9  26  12 
36  5  33  4  2  31 
T = 111
22  47  16  41  10  35  4 
5  23  48  17  42  11  29 
30  6  24  49  18  36  12 
13  31  7  25  43  19  37 
38  14  32  1  26  44  20 
21  39  8  33  2  27  45 
46  15  40  9  34  3  28 
T = 175
8  58  59  5  4  62  63  1 
49  15  14  52  53  11  10  56 
41  23  22  44  45  19  18  48 
32  34  35  29  28  38  39  25 
40  26  27  37  36  30  31  33 
17  47  46  20  21  43  42  24 
9  55  54  12  13  51  50  16 
64  2  3  61  60  6  7  57 
T = 260
37  78  29  70  21  62  13  54  5 
6  38  79  30  71  22  63  14  46 
47  7  39  80  31  72  23  55  15 
16  48  8  40  81  32  64  24  56 
57  17  49  9  41  73  33  65  25 
26  58  18  50  1  42  74  34  66 
67  27  59  10  51  2  43  75  35 
36  68  19  60  11  52  3  44  76 
77  28  69  20  61  12  53  4  45 
T = 369
You can make a Magic Squares for your Birth Year, Lucky Number, Name Numerology, House Number, etc.
Total =  
Enter Magic Square Total in box above, then click Make Square  

EVEN totals have 52 summation patterns
ODD totals have 36 summation patterns
Note: These squares may contain repeated, zero, or negative values.


MMDD Format
DDMM Format



All totals have 36 summation patterns
Click green buttons to show squares giving this total 