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A 12x12 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (870)

A Magic Square is a square of numbers in which every row, every column, and both diagonals add up to the same number. This number is often called the magic sum. The 12 by 12 magic square shown below has a magic sum equal to 870.
Though magic squares can be made with non-consecutive and non-regular sequences, they are usually seen made up of consecutive numbers, possibly because it is harder to be consecutive.

The method described below can be used to create all 4N+0 (multiple-of-four) magic squares. This is just one method for creating magic squares, there are many other methods, and many-many-many magic squares to be found.

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How to Create a 12x12 Magic Square
with a Magic Sum of 870

The method described on this page can be used to create 4x4, 8x8, 12x12, 16x16 and larger 4N+0 magic squares

Steps:

Draw a 12x12 blank grid and color in the two main diagonals.
Also, color in the two main diagonals of each 4x4 box within this 12x12 square.
Starting in the top left corner, moving left to right through the rows, count the squares, 1, 2, 3, 4, but only write down the numbers you say when you get to one of the colored in squares. If you do this properly, you will write 1 in the top left corner and write 144 in the bottom right corner.
Next, do the same thing, starting in the bottom right corner, moving right-to-left upward through the rows, again count from 1 to 144, but this time, only write down the numbers in the non-shaded squares.

Step One: Draw a 12x12 blank grid and
shade in the two main diagonals

You don't necessarily have to shade in the squares. You could simply draw a light line that passes through these squares. You only need to be able to tell the difference between squares that are on these 4x4 diagonals and those that are not.

Step Two: Shade in all the 4x4 diagonals

If you are making a square larger than 4x4, the entire square can be visualized as a collection of 4x4 squares. Shade in the main diagonals of each 4x4 square within the big square.

If you do this correctly, by the time you are done, you will have shaded in exactly half the squares in your overall grid. If you had simply drawn diagonal lines through those squares, you would see a series of X's.

Step Three: Count the squares
(writing only on the shaded squares)

This is fairly straightforward. Starting in the top left corner, and moving left-to-right through each row, count the squares, but only write down the numbers in the shaded squares, but remember to count all the blank squares. In the first four spaces, you would write down 1, count 2 and 3, and write down 4. Continue until you have written down the last number (144).

1			4	5			8	9			12
	14	15			18	19			22	23
	26	27			30	31			34	35
37			40	41			44	45			48
49			52	53			56	57			60
	62	63			66	67			70	71
	74	75			78	79			82	83
85			88	89			92	93			96
97			100	101			104	105			108
	110	111			114	115			118	119
	122	123			126	127			130	131
133			136	137			140	141			144

Step Four: Count the squares again, counting backward,
writing into the blank squares

This time, you can either

Start counting backward, starting with 144 (which you would not write down) and count downward, writing down the number whenever you come to a blank square. The last two numbers you write down would be 3 and 2 just before you get to the 144 which you wrote down in Step Three.
Or, if you prefer counting upward, start with 1 in the bottom right corner and move right-to-left through each row until you get to the top left corner. Working this way, you will skip 1 (because 144 is already written in that square), write down 2 and 3, then skip 4, etc.

1	143	142	4	5	139	138	8	9	135	134	12
132	14	15	129	128	18	19	125	124	22	23	121
120	26	27	117	116	30	31	113	112	34	35	109
37	107	106	40	41	103	102	44	45	99	98	48
49	95	94	52	53	91	90	56	57	87	86	60
84	62	63	81	80	66	67	77	76	70	71	73
72	74	75	69	68	78	79	65	64	82	83	61
85	59	58	88	89	55	54	92	93	51	50	96
97	47	46	100	101	43	42	104	105	39	38	108
36	110	111	33	32	114	115	29	28	118	119	25
24	122	123	21	20	126	127	17	16	130	131	13
133	11	10	136	137	7	6	140	141	3	2	144

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A 12-by-12 Magic Square

(Magic Sum = 870)

1	143	142	4	5	139	138	8	9	135	134	12
132	14	15	129	128	18	19	125	124	22	23	121
120	26	27	117	116	30	31	113	112	34	35	109
37	107	106	40	41	103	102	44	45	99	98	48
49	95	94	52	53	91	90	56	57	87	86	60
84	62	63	81	80	66	67	77	76	70	71	73
72	74	75	69	68	78	79	65	64	82	83	61
85	59	58	88	89	55	54	92	93	51	50	96
97	47	46	100	101	43	42	104	105	39	38	108
36	110	111	33	32	114	115	29	28	118	119	25
24	122	123	21	20	126	127	17	16	130	131	13
133	11	10	136	137	7	6	140	141	3	2	144

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A 12x12 Magic Square

Scroll down to see a magic square in which all rows, columns, and both diagonals add up to the same magic sum (870)

Read more about Magic Squares

How to Create a 12x12 Magic Square with a Magic Sum of 870

Step One: Draw a 12x12 blank grid and shade in the two main diagonals

Step Two: Shade in all the 4x4 diagonals

Step Three: Count the squares (writing only on the shaded squares)

Step Four: Count the squares again, counting backward, writing into the blank squares

A 12-by-12 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (870)

How to Create a 12x12 Magic Square
with a Magic Sum of 870

Step One: Draw a 12x12 blank grid and
shade in the two main diagonals

Step Three: Count the squares
(writing only on the shaded squares)

Step Four: Count the squares again, counting backward,
writing into the blank squares