How to Calculate a Zi Wei Dou Shu Chart by Hand: 8 Steps and Lookup Tables

Before you start: which ruleset this is

This page follows the standard Complete Book of Zi Wei Dou Shu method, which is also what this site's engine uses. The input is the lunar birth date and the birth double-hour (Zi hour is 23:00–01:00); the clock time is first corrected to true solar time for the birthplace. Schools differ on three points — where the year changes, leap months and the late Zi hour — covered in the calculation-conventions guide. The example below uses this site's defaults: the year changes at lunar New Year, the first half of a leap month counts in the current month and the second half in the next, and the late Zi hour counts as the same day.

The twelve branches run Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai. On the chart the twelve palaces sit in fixed branch positions, and every 'count forward' or 'count backward' below is counting along these twelve branches.

Step 1: the Life Palace

Rule: start at Yin and call it month 1; count forward to the lunar birth month. From that position call the Zi hour 0 and count backward to the birth hour. The branch you land on is the Life Palace.

Lookup table (rows are lunar months; each cell is the birth hour and the Life Palace branch):

Life Palace lookup table

Month 1: Zi hour → Yin · Chou hour → Chou · Yin hour → Zi · Mao hour → Hai · Chen hour → Xu · Si hour → You · Wu hour → Shen · Wei hour → Wei · Shen hour → Wu · You hour → Si · Xu hour → Chen · Hai hour → Mao

Month 2: Zi hour → Mao · Chou hour → Yin · Yin hour → Chou · Mao hour → Zi · Chen hour → Hai · Si hour → Xu · Wu hour → You · Wei hour → Shen · Shen hour → Wei · You hour → Wu · Xu hour → Si · Hai hour → Chen

Month 3: Zi hour → Chen · Chou hour → Mao · Yin hour → Yin · Mao hour → Chou · Chen hour → Zi · Si hour → Hai · Wu hour → Xu · Wei hour → You · Shen hour → Shen · You hour → Wei · Xu hour → Wu · Hai hour → Si

Month 4: Zi hour → Si · Chou hour → Chen · Yin hour → Mao · Mao hour → Yin · Chen hour → Chou · Si hour → Zi · Wu hour → Hai · Wei hour → Xu · Shen hour → You · You hour → Shen · Xu hour → Wei · Hai hour → Wu

Month 5: Zi hour → Wu · Chou hour → Si · Yin hour → Chen · Mao hour → Mao · Chen hour → Yin · Si hour → Chou · Wu hour → Zi · Wei hour → Hai · Shen hour → Xu · You hour → You · Xu hour → Shen · Hai hour → Wei

Month 6: Zi hour → Wei · Chou hour → Wu · Yin hour → Si · Mao hour → Chen · Chen hour → Mao · Si hour → Yin · Wu hour → Chou · Wei hour → Zi · Shen hour → Hai · You hour → Xu · Xu hour → You · Hai hour → Shen

Month 7: Zi hour → Shen · Chou hour → Wei · Yin hour → Wu · Mao hour → Si · Chen hour → Chen · Si hour → Mao · Wu hour → Yin · Wei hour → Chou · Shen hour → Zi · You hour → Hai · Xu hour → Xu · Hai hour → You

Month 8: Zi hour → You · Chou hour → Shen · Yin hour → Wei · Mao hour → Wu · Chen hour → Si · Si hour → Chen · Wu hour → Mao · Wei hour → Yin · Shen hour → Chou · You hour → Zi · Xu hour → Hai · Hai hour → Xu

Month 9: Zi hour → Xu · Chou hour → You · Yin hour → Shen · Mao hour → Wei · Chen hour → Wu · Si hour → Si · Wu hour → Chen · Wei hour → Mao · Shen hour → Yin · You hour → Chou · Xu hour → Zi · Hai hour → Hai

Month 10: Zi hour → Hai · Chou hour → Xu · Yin hour → You · Mao hour → Shen · Chen hour → Wei · Si hour → Wu · Wu hour → Si · Wei hour → Chen · Shen hour → Mao · You hour → Yin · Xu hour → Chou · Hai hour → Zi

Month 11: Zi hour → Zi · Chou hour → Hai · Yin hour → Xu · Mao hour → You · Chen hour → Shen · Si hour → Wei · Wu hour → Wu · Wei hour → Si · Shen hour → Chen · You hour → Mao · Xu hour → Yin · Hai hour → Chou

Month 12: Zi hour → Chou · Chou hour → Zi · Yin hour → Hai · Mao hour → Xu · Chen hour → You · Si hour → Shen · Wu hour → Wei · Wei hour → Wu · Shen hour → Si · You hour → Chen · Xu hour → Mao · Hai hour → Yin

Step 2: the Body Palace

Rule: the same start — Yin is month 1, count forward to the birth month. From there call the Zi hour 0, but this time count forward to the birth hour. The branch you land on is the Body Palace. It can only land in six palaces — Life, Spouse, Wealth, Travel, Career or Spirit — and marks the focus of mid-to-late life.

Lookup table:

Body Palace lookup table

Month 1: Zi hour → Yin · Chou hour → Mao · Yin hour → Chen · Mao hour → Si · Chen hour → Wu · Si hour → Wei · Wu hour → Shen · Wei hour → You · Shen hour → Xu · You hour → Hai · Xu hour → Zi · Hai hour → Chou

Month 2: Zi hour → Mao · Chou hour → Chen · Yin hour → Si · Mao hour → Wu · Chen hour → Wei · Si hour → Shen · Wu hour → You · Wei hour → Xu · Shen hour → Hai · You hour → Zi · Xu hour → Chou · Hai hour → Yin

Month 3: Zi hour → Chen · Chou hour → Si · Yin hour → Wu · Mao hour → Wei · Chen hour → Shen · Si hour → You · Wu hour → Xu · Wei hour → Hai · Shen hour → Zi · You hour → Chou · Xu hour → Yin · Hai hour → Mao

Month 4: Zi hour → Si · Chou hour → Wu · Yin hour → Wei · Mao hour → Shen · Chen hour → You · Si hour → Xu · Wu hour → Hai · Wei hour → Zi · Shen hour → Chou · You hour → Yin · Xu hour → Mao · Hai hour → Chen

Month 5: Zi hour → Wu · Chou hour → Wei · Yin hour → Shen · Mao hour → You · Chen hour → Xu · Si hour → Hai · Wu hour → Zi · Wei hour → Chou · Shen hour → Yin · You hour → Mao · Xu hour → Chen · Hai hour → Si

Month 6: Zi hour → Wei · Chou hour → Shen · Yin hour → You · Mao hour → Xu · Chen hour → Hai · Si hour → Zi · Wu hour → Chou · Wei hour → Yin · Shen hour → Mao · You hour → Chen · Xu hour → Si · Hai hour → Wu

Month 7: Zi hour → Shen · Chou hour → You · Yin hour → Xu · Mao hour → Hai · Chen hour → Zi · Si hour → Chou · Wu hour → Yin · Wei hour → Mao · Shen hour → Chen · You hour → Si · Xu hour → Wu · Hai hour → Wei

Month 8: Zi hour → You · Chou hour → Xu · Yin hour → Hai · Mao hour → Zi · Chen hour → Chou · Si hour → Yin · Wu hour → Mao · Wei hour → Chen · Shen hour → Si · You hour → Wu · Xu hour → Wei · Hai hour → Shen

Month 9: Zi hour → Xu · Chou hour → Hai · Yin hour → Zi · Mao hour → Chou · Chen hour → Yin · Si hour → Mao · Wu hour → Chen · Wei hour → Si · Shen hour → Wu · You hour → Wei · Xu hour → Shen · Hai hour → You

Month 10: Zi hour → Hai · Chou hour → Zi · Yin hour → Chou · Mao hour → Yin · Chen hour → Mao · Si hour → Chen · Wu hour → Si · Wei hour → Wu · Shen hour → Wei · You hour → Shen · Xu hour → You · Hai hour → Xu

Month 11: Zi hour → Zi · Chou hour → Chou · Yin hour → Yin · Mao hour → Mao · Chen hour → Chen · Si hour → Si · Wu hour → Wu · Wei hour → Wei · Shen hour → Shen · You hour → You · Xu hour → Xu · Hai hour → Hai

Month 12: Zi hour → Chou · Chou hour → Yin · Yin hour → Mao · Mao hour → Chen · Chen hour → Si · Si hour → Wu · Wu hour → Wei · Wei hour → Shen · Shen hour → You · You hour → Xu · Xu hour → Hai · Hai hour → Zi

Step 3: the stem of each palace (the Five Tigers rule)

Rule: the birth-year stem sets the stem of the Yin palace — Jia or Ji years start at Bing Yin, Yi or Geng at Wu Yin, Bing or Xin at Geng Yin, Ding or Ren at Ren Yin, Wu or Gui at Jia Yin. Then continue in order, one stem per branch (after Gui comes Jia again).

The stem of every palace for each year-stem group:

Five Tigers table

Jia or Ji year: Yin Bing, Mao Ding, Chen Wu, Si Ji, Wu Geng, Wei Xin, Shen Ren, You Gui, Xu Jia, Hai Yi, Zi Bing, Chou Ding

Yi or Geng year: Yin Wu, Mao Ji, Chen Geng, Si Xin, Wu Ren, Wei Gui, Shen Jia, You Yi, Xu Bing, Hai Ding, Zi Wu, Chou Ji

Bing or Xin year: Yin Geng, Mao Xin, Chen Ren, Si Gui, Wu Jia, Wei Yi, Shen Bing, You Ding, Xu Wu, Hai Ji, Zi Geng, Chou Xin

Ding or Ren year: Yin Ren, Mao Gui, Chen Jia, Si Yi, Wu Bing, Wei Ding, Shen Wu, You Ji, Xu Geng, Hai Xin, Zi Ren, Chou Gui

Wu or Gui year: Yin Jia, Mao Yi, Chen Bing, Si Ding, Wu Wu, Wei Ji, Shen Geng, You Xin, Xu Ren, Hai Gui, Zi Jia, Chou Yi

Step 4: the five-element bureau

The stem and branch of the Life Palace decide the bureau. Stem numbers: Jia and Yi 1, Bing and Ding 2, Wu and Ji 3, Geng and Xin 4, Ren and Gui 5. Branch numbers: Zi, Chou, Wu, Wei 1; Yin, Mao, Shen, You 2; Chen, Si, Xu, Hai 3. Add the two; if the sum is over 5, subtract 5 (repeat if needed). 1 is Wood 3, 2 is Metal 4, 3 is Water 2, 4 is Fire 6 and 5 is Earth 5. The number (2 to 6) is the age at which the first decade starts, and it is used to place Zi Wei.

Lookup table (by the stem and branch of the Life Palace):

Bureau lookup table

Life Palace stem Jia: Zi → Metal 4, Yin → Water 2, Chen → Fire 6, Wu → Metal 4, Shen → Water 2, Xu → Fire 6

Life Palace stem Yi: Chou → Metal 4, Mao → Water 2, Si → Fire 6, Wei → Metal 4, You → Water 2, Hai → Fire 6

Life Palace stem Bing: Zi → Water 2, Yin → Fire 6, Chen → Earth 5, Wu → Water 2, Shen → Fire 6, Xu → Earth 5

Life Palace stem Ding: Chou → Water 2, Mao → Fire 6, Si → Earth 5, Wei → Water 2, You → Fire 6, Hai → Earth 5

Life Palace stem Wu: Zi → Fire 6, Yin → Earth 5, Chen → Wood 3, Wu → Fire 6, Shen → Earth 5, Xu → Wood 3

Life Palace stem Ji: Chou → Fire 6, Mao → Earth 5, Si → Wood 3, Wei → Fire 6, You → Earth 5, Hai → Wood 3

Life Palace stem Geng: Zi → Earth 5, Yin → Wood 3, Chen → Metal 4, Wu → Earth 5, Shen → Wood 3, Xu → Metal 4

Life Palace stem Xin: Chou → Earth 5, Mao → Wood 3, Si → Metal 4, Wei → Earth 5, You → Wood 3, Hai → Metal 4

Life Palace stem Ren: Zi → Wood 3, Yin → Metal 4, Chen → Water 2, Wu → Wood 3, Shen → Metal 4, Xu → Water 2

Life Palace stem Gui: Chou → Wood 3, Mao → Metal 4, Si → Water 2, Wei → Wood 3, You → Metal 4, Hai → Water 2

Step 5: placing Zi Wei

Take the lunar birth day and the bureau number. Add the smallest number x to the day that makes the sum an exact multiple of the bureau number; the quotient is how many palaces to count from Yin (Yin is 1). Then use x: if x is even, move forward x branches from there; if x is odd, move backward x branches. The branch you land on is Zi Wei.

Example: Earth 5, lunar day 21. Add 4 to reach 25; the quotient is 5, so count five palaces from Yin to reach Wu. x = 4 is even, so move forward four branches to Xu: Zi Wei sits at Xu.

Lookup table (Zi Wei branch by bureau and lunar day):

Zi Wei position table

Water 2: day 1 Chou · day 2 Yin · day 3 Yin · day 4 Mao · day 5 Mao · day 6 Chen · day 7 Chen · day 8 Si · day 9 Si · day 10 Wu · day 11 Wu · day 12 Wei · day 13 Wei · day 14 Shen · day 15 Shen · day 16 You · day 17 You · day 18 Xu · day 19 Xu · day 20 Hai · day 21 Hai · day 22 Zi · day 23 Zi · day 24 Chou · day 25 Chou · day 26 Yin · day 27 Yin · day 28 Mao · day 29 Mao · day 30 Chen

Wood 3: day 1 Chen · day 2 Chou · day 3 Yin · day 4 Si · day 5 Yin · day 6 Mao · day 7 Wu · day 8 Mao · day 9 Chen · day 10 Wei · day 11 Chen · day 12 Si · day 13 Shen · day 14 Si · day 15 Wu · day 16 You · day 17 Wu · day 18 Wei · day 19 Xu · day 20 Wei · day 21 Shen · day 22 Hai · day 23 Shen · day 24 You · day 25 Zi · day 26 You · day 27 Xu · day 28 Chou · day 29 Xu · day 30 Hai

Metal 4: day 1 Hai · day 2 Chen · day 3 Chou · day 4 Yin · day 5 Zi · day 6 Si · day 7 Yin · day 8 Mao · day 9 Chou · day 10 Wu · day 11 Mao · day 12 Chen · day 13 Yin · day 14 Wei · day 15 Chen · day 16 Si · day 17 Mao · day 18 Shen · day 19 Si · day 20 Wu · day 21 Chen · day 22 You · day 23 Wu · day 24 Wei · day 25 Si · day 26 Xu · day 27 Wei · day 28 Shen · day 29 Wu · day 30 Hai

Earth 5: day 1 Wu · day 2 Hai · day 3 Chen · day 4 Chou · day 5 Yin · day 6 Wei · day 7 Zi · day 8 Si · day 9 Yin · day 10 Mao · day 11 Shen · day 12 Chou · day 13 Wu · day 14 Mao · day 15 Chen · day 16 You · day 17 Yin · day 18 Wei · day 19 Chen · day 20 Si · day 21 Xu · day 22 Mao · day 23 Shen · day 24 Si · day 25 Wu · day 26 Hai · day 27 Chen · day 28 You · day 29 Wu · day 30 Wei

Fire 6: day 1 You · day 2 Wu · day 3 Hai · day 4 Chen · day 5 Chou · day 6 Yin · day 7 Xu · day 8 Wei · day 9 Zi · day 10 Si · day 11 Yin · day 12 Mao · day 13 Hai · day 14 Shen · day 15 Chou · day 16 Wu · day 17 Mao · day 18 Chen · day 19 Zi · day 20 You · day 21 Yin · day 22 Wei · day 23 Chen · day 24 Si · day 25 Chou · day 26 Xu · day 27 Mao · day 28 Shen · day 29 Si · day 30 Wu

Step 6: placing the other thirteen major stars

Once Zi Wei is fixed, the rest follow at fixed spacing. The Zi Wei group runs backward (against the branch order) from Zi Wei: Tian Ji is 1 branch back, Tai Yang 3, Wu Qu 4, Tian Tong 5 and Lian Zhen 8. The Tian Fu group is placed from Tian Fu: Tian Fu mirrors Zi Wei across the Yin–Shen axis (the two positions' branch numbers, counting Zi as 0, add up to 4 modulo 12). From Tian Fu go forward: Tai Yin 1, Tan Lang 2, Ju Men 3, Tian Xiang 4, Tian Liang 5, Qi Sha 6, and Po Jun 10.

The resulting co-locations are fixed: for example Zi Wei and Tian Fu can only share a palace at Yin or Shen. Each star's overview page lists where it sits alone and with which partner.

Step 7: the four transformations

The birth-year stem selects one star each for Hua Lu, Hua Quan, Hua Ke and Hua Ji, and the palaces those four stars fall in show which life areas are activated. The ten-stem table is in the four-transformations guide. Palace stems also send out transformations of their own — the flying-star method.

Step 8: the masters and the decades

The Life master comes from the Life Palace's branch: Zi → Tan Lang, Chou → Ju Men, Yin → Lu Cun, Mao → Wen Qu, Chen → Lian Zhen, Si → Wu Qu, Wu → Po Jun, Wei → Wu Qu, Shen → Lian Zhen, You → Wen Qu, Xu → Lu Cun, Hai → Ju Men. The Body master comes from the birth-year branch: Zi year → Huo Xing, Chou year → Tian Xiang, Yin year → Tian Liang, Mao year → Tian Tong, Chen year → Wen Chang, Si year → Tian Ji, Wu year → Huo Xing, Wei year → Tian Xiang, Shen year → Tian Liang, You year → Tian Tong, Xu year → Wen Chang, Hai year → Tian Ji.

Decades start at the age given by the bureau number (Water 2 at age 2, Wood 3 at 3, Metal 4 at 4, Earth 5 at 5, Fire 6 at 6) and last ten years each, beginning at the Life Palace. For a yang-stem male or a yin-stem female, the decades move forward along the branches; for a yin-stem male or a yang-stem female, they move backward.

A complete example: 15 May 1990, 07:30, Beijing, female

The clock reads 07:30; Beijing was on daylight saving time that year, so true solar time is 06:20, the Mao hour (05:00–07:00). The lunar date is the 21st day of the 4th month of the Geng-Wu year.

1) Life Palace: start at Yin as month 1 and count forward to month 4, reaching Si. From Si, call Zi hour 0 and count backward to the Mao hour (Si, Chen, Mao, Yin — three steps back): the Life Palace is at Yin. The table agrees: month 4, Mao hour gives Yin.

2) Body Palace: from Si count forward to the Mao hour (Si, Wu, Wei, Shen): Shen.

3) Palace stems: a Geng year starts at Wu Yin, so the Life Palace is Wu Yin.

4) Bureau: Wu is 3 and Yin is 2; the sum is 5, which is Earth: Earth 5.

5) Zi Wei: Earth 5, day 21: add 4 to reach 25, quotient 5, x is even so move forward four: Zi Wei is at Xu.

6) The other stars: Zi Wei at Xu, Tian Ji at You, Tai Yang at Wei, Wu Qu at Wu, Tian Tong at Si, Lian Zhen at Yin, Tian Fu at Wu, Tai Yin at Wei, Tan Lang at Shen, Ju Men at You, Tian Xiang at Xu, Tian Liang at Hai, Qi Sha at Zi, Po Jun at Chen.

7) Transformations: for a Geng year, Tai Yang takes Hua Lu, Wu Qu Hua Quan, Tai Yin Hua Ke and Tian Tong Hua Ji.

8) Life master Lu Cun, Body master Huo Xing. Earth 5 starts at age 5, and a female with a yang stem (Geng) moves backward, so the decades run: Life Palace ages 5–14, then Siblings 15–24, then Spouse 25–34, and so on.

Every step matches the chart engine's output for the same birth data.

Why still use software

Doing it by hand shows where each placement comes from and helps you pin down a mismatch when two tools disagree. Software is more reliable at three things: true solar time and historical daylight saving (easy to miss by hand), lunar and leap-month conversion, and bulk labelling of transformations and flying stars. When you compare, check the year boundary first, then the time, then the late Zi hour and leap months.

Next steps

Cast your chart and check it against these eight steps. Then read how to read a chart in five steps. For rule differences between sites, see the calculation-conventions and why-charts-differ guides.

Q: What is the first step in calculating a Zi Wei Dou Shu chart?

Find the Life Palace: count forward from Yin to the lunar birth month, then from that palace count backward from the Zi hour to the birth hour.

Q: How is the five-element bureau calculated?

Add the stem number and the branch number of the Life Palace (stems: Jia/Yi 1, Bing/Ding 2, Wu/Ji 3, Geng/Xin 4, Ren/Gui 5; branches: Zi/Chou/Wu/Wei 1, Yin/Mao/Shen/You 2, Chen/Si/Xu/Hai 3), subtract 5 if over 5: 1 Wood 3, 2 Metal 4, 3 Water 2, 4 Fire 6, 5 Earth 5.

Q: How is Zi Wei placed?

Add the smallest number to the lunar day to make a multiple of the bureau number; the quotient is the palace count from Yin, and an even or odd remainder number moves forward or backward.

• Zi Wei Dou Shu calculation conventions
• Why Zi Wei Dou Shu charts differ between websites
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• Zi Wei Dou Shu chart API
• How to read a Zi Wei Dou Shu chart: a beginner's five steps
• Zi Wei Dou Shu vs BaZi: what's the difference?
• The four transformations (Si Hua) explained
• Free chart calculator