Reference Tables: The Lo Shu Square, the 24 Mountains and the Kua Directions
This page is the lookup shelf of the knowledge base. Nothing here teaches a method; everything here is data a reading needs, collected so that the articles can refer to it instead of repeating it. The tables are drawn from the classical sources and are the same ones the Baguame calculators use — if a number below and a number in a calculator disagree, the calculator is the one to check first.
The Lo Shu square
The Lo Shu (洛書) is the nine-palace grid that underlies every compass school, the Flying Stars above all. Its arrangement of the numbers 1 to 9 is fixed: whichever number sits in the centre, the others take their places around it in the same sequence. The grid below shows the numbers in the Later Heaven arrangement, with the palace, its direction and its trigram.
| Lo Shu cell | Number | Palace | Direction | Trigram |
|---|---|---|---|---|
| Top left | 4 | Xun | South-East | Xun |
| Top centre | 9 | Li | South | Li |
| Top right | 2 | Kun | South-West | Kun |
| Middle left | 3 | Zhen | East | Zhen |
| Centre | 5 | — | Centre | — |
| Middle right | 7 | Dui | West | Dui |
| Bottom left | 8 | Gen | North-East | Gen |
| Bottom centre | 1 | Kan | North | Kan |
| Bottom right | 6 | Qian | North-West | Qian |
Two facts follow from the grid and are worth knowing by heart. Every row, column and diagonal adds up to 15. And the flight order used in annual and period charts never changes: Centre → North-West → West → North-East → South → North → South-West → East → South-East. The same grid is explained as a map of life in the Later Heaven Bagua.
The He Tu pairs
The He Tu (河圖) is older than the Lo Shu and pairs the numbers instead of arranging them in a magic square. Each pair is a generating relationship between the same element in its yang and yin forms — Fire is 7 (yang) with 2 (yin), Water is 1 with 6, and so on.
| Pair | Element | Direction |
|---|---|---|
| 1 and 6 | Water | North |
| 2 and 7 | Fire | South |
| 3 and 8 | Wood | East |
| 4 and 9 | Metal | West |
| 5 and 10 | Earth | Centre |
The full treatment is in The He Tu.
The 24 Mountains
Each of the eight directions is divided into three sectors of 15°, and each sector carries a name taken from the Heavenly Stems and Earthly Branches. This is the ring of 24 Mountains on the luopan, and it is the resolution at which a facing direction is recorded and a chart is built.
| Mountain | Character | Direction group | Degrees |
|---|---|---|---|
| Ren | 壬 | North | 337.5° – 352.5° |
| Zi | 子 | North | 352.5° – 7.5° |
| Gui | 癸 | North | 7.5° – 22.5° |
| Chou | 丑 | North-East | 22.5° – 37.5° |
| Gen | 艮 | North-East | 37.5° – 52.5° |
| Yin | 寅 | North-East | 52.5° – 67.5° |
| Jia | 甲 | East | 67.5° – 82.5° |
| Mao | 卯 | East | 82.5° – 97.5° |
| Yi | 乙 | East | 97.5° – 112.5° |
| Chen | 辰 | South-East | 112.5° – 127.5° |
| Xun | 巽 | South-East | 127.5° – 142.5° |
| Si | 巳 | South-East | 142.5° – 157.5° |
| Bing | 丙 | South | 157.5° – 172.5° |
| Wu | 午 | South | 172.5° – 187.5° |
| Ding | 丁 | South | 187.5° – 202.5° |
| Wei | 未 | South-West | 202.5° – 217.5° |
| Kun | 坤 | South-West | 217.5° – 232.5° |
| Shen | 申 | South-West | 232.5° – 247.5° |
| Geng | 庚 | West | 247.5° – 262.5° |
| You | 酉 | West | 262.5° – 277.5° |
| Xin | 辛 | West | 277.5° – 292.5° |
| Xu | 戌 | North-West | 292.5° – 307.5° |
| Qian | 乾 | North-West | 307.5° – 322.5° |
| Hai | 亥 | North-West | 322.5° – 337.5° |
Reading a facing direction to the nearest mountain rather than to the nearest of the eight directions is what separates a usable Flying Stars chart from a rough one. The 24 Mountains calculator does the conversion.
The Kua directions
The Ba Zhai (Eight Mansions) system sorts each person into one of eight Kua numbers, derived from the year of birth and gender, and each number has four favourable and four unfavourable directions. The energies are identical for everyone; only the directions they occupy differ. The table below is the verified one used across the Ba Zhai articles.
The four favourable directions
| Gua | Palace | Sheng Qi 生气 | Tian Yi 天医 | Yan Nian 延年 | Fu Wei 伏位 |
|---|---|---|---|---|---|
| 1 | Kan | South-East | East | South | North |
| 3 | Zhen | South | North | South-East | East |
| 4 | Xun | North | South | East | South-East |
| 9 | Li | East | South-East | North | South |
| 2 | Kun | North-East | West | North-West | South-West |
| 6 | Qian | West | North-East | South-West | North-West |
| 7 | Dui | North-West | South-West | North-East | West |
| 8 | Gen | South-West | North-West | West | North-East |
The four unfavourable directions
| Gua | Palace | Huo Hai 祸害 | Wu Gui 五鬼 | Liu Sha 六煞 | Jue Ming 绝命 |
|---|---|---|---|---|---|
| 1 | Kan | West | North-East | North-West | South-West |
| 3 | Zhen | South-West | North-West | North-East | West |
| 4 | Xun | North-West | South-West | West | North-East |
| 9 | Li | North-East | West | South-West | North-West |
| 2 | Kun | East | South-East | South | North |
| 6 | Qian | South-East | East | North | South |
| 7 | Dui | North | South | South-East | East |
| 8 | Gen | South | North | East | South-East |
Each energy also carries a star and an element, which is what decides its remedy: Sheng Qi is Tan Lang (贪狼), Wood; Tian Yi is Ju Men (巨门), Earth; Yan Nian is Wu Qu (武曲), Metal; Fu Wei is Zuo Fu (左辅), Wood; Huo Hai is Lu Cun (禄存), Earth; Wu Gui is Lian Zhen (廉贞), Fire; Liu Sha is Wen Qu (文曲), Water; Jue Ming is Po Jun (破军), Metal. There is no Kua 5 — the middle number is assigned to 2 for men and 8 for women. Find your own number with the Kua number calculator, and read the directions in the Ba Zhai guide.
The Five Elements at a glance
| Element | Direction | Season | Colour | Climate |
|---|---|---|---|---|
| Wood | East | Spring | Green | Wind |
| Fire | South | Summer | Red | Heat |
| Earth | Centre | Late summer | Yellow | Damp |
| Metal | West | Autumn | White | Dryness |
| Water | North | Winter | Black | Cold |
These five lines carry more weight than they look. Most practical feng shui advice — support a star with its generating element, drain a malignant one with the element that weakens it — is applied from this table. Each element has its own article for the full treatment: Wood, Fire, Earth, Metal, Water.
Frequently Asked Questions
Do the numbers in the Lo Shu square change?
The grid itself never changes: the numbers 1 to 9 always sit in the same arrangement of palaces. What changes is which number takes the centre — in a period chart according to the period, in an annual chart according to the year — because every other star then shifts one place along the fixed flight order.
Why record a direction to 15 degrees rather than to the nearest of eight?
Because a whole palace is 45° wide, and the three mountains inside it behave differently in several systems, the Flying Stars chart above all. Two homes that both "face south" can be up to 45° apart, which is often the difference between two different charts.
Do I have a Kua number if I was born in a leap year or before Chinese New Year?
The Kua number follows the Chinese solar year, which begins at Li Chun in early February, not on January 1st. If you were born in January or early February, the year to use is the previous one. The Kua number calculator applies the boundary for you.
Which table should I use with a Feng Shui chart?
Different parts of a reading need different tables. The Lo Shu grid and the flight order are what a Flying Stars chart is built from; the 24 Mountains are what a facing direction is recorded to; the Kua table belongs to the Ba Zhai system and applies to people rather than to buildings. The Feng Shui tools cover the calculators, and the Bagua map places any of the results on your own floor plan.
