Rodika Tchi

Lo Shu Square: The Ancient Mathematical Root of Feng Shui

Rodika Tchi

June 21, 2025

The Lo Shu Square is an ancient mathematical grid at the root of the feng shui bagua, Flying Stars, 9 Star Ki and the I Ching. Its nine numbers form a precise pattern in which every row, column and diagonal adds up to 15. Many of oldest feng shui formulas and calculations are based on the wisdom of the Lo Shu Square.

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The magic Lo Shu Square is an ancient tool that was used for divination by ancient daoists and feng shui masters. It is not something one directly applies when working with the feng shui of a home but rather a conceptual layer that can help see feng shui in its depth a bit more clearly. The bagua, as we know it, evolved from the Lo Shu Square, so it is good to understand its roots and wisdom.

The Lo (Luo) Shu Square, often called the Magic Square, is also at the root of ancient feng shui astrology (9 Star Ki), the Flying Stars school (Xuan Kong), as well as the I-Ching, of course.

As the story goes, an ancient Chinese master derived the wisdom of the magic square from the patterns on the back of the turtle. By reading and deeply contemplating those patterns, he realized the pattern of Universal rhythms as expressed in the Lo Shu Square. There are several slightly different stories about different masters, the more popular one is about the Emperor Yu walking along the river Lo (thus Lo Shu Square is translated as the Scroll of River Lo).

This legend dates to 650 BC, the times of great floods in China. The turtle that emerged from the river had an unusual 3 x 3 pattern on its shell which later became the basis of the Lo Shu Square, a mathematical grid where the sum of numbers from each row, column or diagonal is the same. No matter which direction you add the numbers — horizontal, vertical or diagonal — they always add up to 15. This is considered a powerful number because it corresponds to the number of days in each of the 24 cycles of Chinese Year. Meaning, it is the number of days in the cycle from the New Moon to Full Moon.

In the Lo Shu Square, number 5 is in the centre, with the odd and even numbers alternating on its periphery. The four even numbers (2, 4, 6, 8) are at the four corners of the square, with the five odd ones (1, 3, 5, 7, 9) forming a cross in the centre (you can see this in the Lo Shu Square image above).

If you are familiar with feng shui bagua, you can also clearly see how the bagua evolved from the Lo Shu Square, especially when you know that in ancient China South direction was always placed at the top of the maps.

Number 9 is the number for the South bagua area (on top) and number 1 is of the North bagua sector (bottom of the square). The odd numbers are of Yang polarity, and the even numbers are of Yin. In the Lo Shu Square the Yin & Yang numbers alternate around its centre: number 5.

All numbers in the Lo Shu Square are considered to have specific properties, and be expressions of specific energies. For example, number 9 carries the strong energy of the Fire feng shui element, while number 1 is an expression of the Water element. In the Flying Stars feng shui school (Xuan Kong) they are called stars, following a specific pattern in their movement, which can be charted to define the location of positive and negative energies. Based on this movement, annual and monthly suggestions are given for a more peaceful and balanced home.

However, the mystery of Lo Shu Square extends way beyond its feng shui applications. There are stories of using the magic square movements in specific rituals in ancient temples, rituals that were used at specific times of the year in order to evoke specific results. There is also the knowing that Lo Shu square numbers initially connected to the movement of specific celestial bodies.

As with most ancient texts, there are layers of mystery and alchemical complexity in the deeper levels of Lo Shu Square. It is called the magic square for a reason, so it might keep many of its mysteries intact. At least part of its mystery, though, is expressed in the bagua, which you can apply in your home to create good energy.

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Rodika Tchi works with private clients worldwide to create homes that support health, relationships and daily life. She is the author of two published books and has been interviewed by Psychology Today, Business Insider and Elle Décor.

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