Magic Square

A magic square is a square made up of rows of letters or Numbers, used in making TalismanS and Charms. There are different types of magical squares.


Magical squares have been in use since ancient times. It is not known exactly when or where they originated. The earliest known record of magic squares is in the Chinese Lo Shu, a scroll in manuscripts of the I CHING dating to the Chou Dynasty (951–1126 C.E.). According to the Lo Shu, a magic square showing the unity of all things was revealed to the Emperor Yu in about 2200 B.C.E. when he observed a divine tortoise crawl out of the River Lo with the pattern upon its shell.

Magic squares have been in use in India and elsewhere in the East; they are inscribed on Amulets. Magic squares came into prominence in Western occultism in about the 14th century.

Squares Composed of Letters

The simplest magical square is composed of rows of letters which spell out the same words of power or names of power horizontally and vertically. Some squares are entirely filled with letters, while others have letters and voids or portions of the square left deliberately vacant. Squares are inscribed on magical Tools or talismanic objects or paper. One of the best-known letter magical squares is the SATOR square that was used in ancient Rome for protection. It may have also been inscribed on sacred vessels. It was in use during early Christian times.

The book of ABRA-MELIN THE MAGE, said to be divine wisdom given from God to Moses and handed down through the patriarchs, contains many magical letter squares. Among them are squares to know the future, find hidden treasure, acquire magical abilities, raise the dead, divine by NECROMANCY, walk on water and operate under water, command spirits and have visions. One square is sort of alchemical in nature, for the instant manifestation of all the GOLD and SILVER one may desire for necessities and “to live in opulence.”

Squares Composed of Numbers

Squares composed of rows of consecutive numbers are mathematically complex. The numbers are arranged on the cells in a square according to various formulae, for example, starting the number 1 in a certain cell, skipping to another line and position for number 2, and so on. When finished, the sum of any row of the square—vertical, horizontal, or diagonal—equals the same number. Squares are known by their “order,” that is, the number of cells in a row. A three-cell grid, which has nine cells total, is an “order 3” magic square. The higher the order, the more permutations are possible. A permutation is the creation of another square by inverting, reflecting, or tipping the original square. There are no order 2 squares, only one order 3 square, but there are 880 order 4 squares with 7,040 possible permutations. There are 275,305,224 order 5 squares.

The construction of a square depends on its class:

• odd squares, which have an odd-numbered order

• doubly even squares, which have four squares of an even order when they are divided into four equal parts by a cross

• singly even squares, which have four squares of an odd order when they are divided into four equal parts by a cross.

In addition, there are pandiagonal squares, in which broken diagonals are the sum of the order of the square.

Henry Cornelius Agrippa gave instructions for constructing the magical squares of the planets. Saturn has the lowest order of 3, and the Moon has the highest order of 9. None of Agrippa’s squares are pandiagonal.

Magic squares are used in Rituals to invoke the powers and spirits associated with specific planets. In addition, the magic squares of planets are used to create the SEALS of the PLANETS by connecting numbers in lines and circles according to mathematical formulae. Magic squares have within them magic circles, drawn according to numbers arranged magically in rays radially about a center point, and magic stars, created by the equal sums of numbers on the interstices or rays. Planetary Sigils are created by tracing the name of a planet according to the number that is equivalent to the appropriate Hebrew letters spelling the name of the planet.

Magic squares are made with nonconsecutive numbers and primary numbers as well. A doubly magic square is magic for both its numbers and the squares of the numbers, and a trebly magic square is magic for its numbers, their squares, and their cubes. Furthermore, a magic cube is composed of layers of magic squares so that all columns and diagonals add up to the same number.


  • Mathers, S. L. MacGregor. The Book of the Sacred Magic of Abra-Melin the Mage. Wellingborough, England: The Aquarian Press, 1976.
  • Three Books of Occult Philosophy Written by Henry Cornelius Agrippa of Nettesheim. James Freake, trans. Ed. and annot. by Donald Tyson. St. Paul, Minn.: Llewellyn Publications, 1995.

The Encyclopedia of Magic and Alchemy Written by Rosemary Ellen Guiley Copyright © 2006 by Visionary Living, Inc.