How to calculate a zi wei dou shu chart

Draw a square of twelve boxes around an empty middle. Each box is one of the twelve earthly branches, and the branches never move: the Tiger sits at the lower left and the order runs clockwise from there, up the left side, across the top and down the right. Throughout this page, forward means clockwise, to the next branch in order (Rat, Ox, Tiger, Rabbit…), and backward means counterclockwise. When a rule says "count five from the Tiger", the Tiger itself is one.

Zi wei dou shu does not use the Western date at all. It wants the lunar month and lunar day, and the year's heavenly stem, all of which you can read off the Chinese calendar converter. Then turn the clock time into one of twelve two-hour branches. This calculator reads the clock hour you enter; some schools correct to local solar time first, which can move a birth near an hour boundary into the next branch. Two small traps: a birth between 11pm and midnight is in the Rat hour, and most modern charts, ours included, count it with the following lunar day. And if the converter says your month is a leap month, keep reading to the section on disagreements before you go on.

Start on the Tiger and call it the first month. Count forward to your birth month. From there, call that box the Rat hour and count backward to your birth hour: where you stop is the Life Palace. Go back to the birth-month box and count forward by the hour instead, and you land on the Body Palace. The Quanshu puts it in one sentence and then checks itself: born in the first month at the Rat hour, both palaces sit on the Tiger; at the Ox hour, the Life Palace moves back to the Ox and the Body Palace forward to the Rabbit. Or skip the counting and use the grid.

From the Life Palace, write the remaining names backward around the board, one per box, in a fixed order: Siblings, Spouse, Children, Wealth, Health, Travel, Friends, Career, Property, Fortune, Parents. The Quanshu's instruction is blunt about the direction, for men and women alike: backward, and never forward. The board doesn't move; the labels rotate with the Life Palace, which is why two people born two hours apart have their Spouse palace in different branches. What each palace covers is listed on the calculator page.

Each box also carries one of the ten heavenly stems, and the birth year decides them. The rule is the Five Tigers, which the Quanshu gives as a single five-part rule and which bazi readers use for month pillars too: the year stem tells you which stem goes on the Tiger, and the stems then run forward in order (Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui, and round again) to the Ox. Ten stems on twelve boxes means the Rat and Ox repeat the stems of the Tiger and Rabbit.

The Life Palace now has a stem and a branch, which together make one of the sixty pairs of the Chinese cycle. Every pair has a nayin, a "sound" element with a poetic name ("metal in the sea", "fire in the furnace"), and the element picks the bureau: Water 2, Wood 3, Metal 4, Earth 5 or Fire 6. The number is used twice more, to place the Emperor star and to start the decade limits.

The Quanshu's own example is the one to remember: someone born in a Jia year with the Life Palace on the Tiger gets Bing on that box, Bing-Tiger is "fire in the furnace", so the chart is a Fire 6. Because neighboring boxes always share a nayin, the whole thing fits in a five-by-six table.

This is the step people search for, and the only one with real arithmetic in it. Take the lunar birth day and the bureau number. Add the smallest number (zero or more) that makes the day divide evenly by the bureau, and remember what you added. Divide. Count the quotient from the Tiger, the Tiger being one. Then move again by the number you added: forward if it is even, backward if it is odd. That box holds Zi Wei, the Emperor, the pole star the system is named after.

The Quanshu's check: a Fire 6 chart born on the first day. Add 5 to make 6, divide to get 1, so you start on the Tiger itself, and 5 is odd, so step back five to the Rooster. The text says the Rooster, and adds the old proverb about a hair's error at the start becoming a thousand miles at the end. It is right to worry, because every major star hangs off this one. The table gives the answer for every day and bureau.

The Treasury star, Tian Fu, is the Emperor's reflection across the line that runs from the Tiger to the Monkey. If the Emperor is on the Tiger or the Monkey, the two share a box; otherwise, swap sides: Rabbit and Ox, Dragon and Rat, Snake and Pig, Horse and Dog, Goat and Rooster.

The remaining twelve major stars come in two families, and the Quanshu fixes both in a four-line verse. Five follow the Emperor backward, with gaps: the Strategist next door, skip one, then the Sun, the General and the Child together, skip two, the Enforcer, and an empty stretch of three before you would reach the Emperor again. Seven follow the Treasury forward in an unbroken run (the Moon, the Wolf, the Great Gate, the Minister, the Elder, the Seven Killings), then three empty boxes, then the Army-Breaker. Because the spacing never changes, the fourteen always sit in the same arrangement relative to each other; only the rotation differs from chart to chart.

Two literary stars go by the hour and two assistants by the month. They are four of the many minor stars a full chart carries, and our calculator places them because the next step needs them: five of the ten transformation rows name one of these four.

Nothing moves in this step. The birth year's stem picks four stars already on the board and gives each a second reading: prosperity, power, repute, affliction. The Quanshu's verse opens with the Jia row (Enforcer, Army-Breaker, General, Sun) and spells that row out as its worked example. Here is the full table our calculator uses.

The first decade begins in the Life Palace at the age the bureau names: a Water 2 chart at two, a Fire 6 chart at six. Each palace then governs ten years. A man born in a yang year (Jia, Bing, Wu, Geng, Ren) or a woman born in a yin year runs forward; the other two run backward. That is how Wang Tingzhi's lecture notes put it, and it is what our calculator does.

Most of the procedure is settled; every source we read gives the same Life Palace rule, the same bureau, the same Emperor arithmetic and the same star spacing. Three things are not, and a hand-cast chart that differs from an app's is usually differing on one of these.

Three rows of the transformation table. For seven year stems everyone agrees. For Wu, Geng and Ren years, the repute star depends on which book you open, and the difference is often one written character: the Quanshu's Ren line reads "fu", which is the Treasury, while the Quanji puts the Left Assistant, whose name is also pronounced fǔ. Our calculator follows the Quanshu for Wu and Geng and the Quanji for Ren. That is a choice, not a verdict, and nobody should pretend the question is closed.

In a Geng year the affliction moves with it: where the Treasury takes repute, as in Wang Tingzhi's notes, the Child takes affliction and the Moon gets nothing. Chinese Wikipedia's comparison table prints the Quanshu's Geng row with the Moon and the Child the other way round, which only shows that editions of the Quanshu differ too.

Leap months. The Quanshu is explicit: someone born in a leap first month sets up the chart in the second month, and every leap month follows that example. Our calculator instead counts a leap month as the month it is numbered, and when you were born in one, the result page shows what a split at the fifteenth day would do. That makes three rules in circulation, and the arithmetic says what each one does. Since the Life Palace is counted forward from the Tiger palace by the month and back by the hour, the Quanshu rule always moves it one palace forward, and the Body Palace, the Left and Right Assistants and possibly the bureau with it. The split at the fifteenth leaves a birth on days 1 to 15 exactly as our calculator has it and treats days 16 onward the way the Quanshu does.

Where the first decade starts. The Quanshu's line on decade limits names the Parents palace for a yang man or yin woman and the Siblings palace for the others. Those are the two neighbors of the Life Palace, so the line certainly fixes the direction; read literally, it could also mean the count begins one palace along. The modern teaching starts the first decade in the Life Palace itself.

A smaller one: a birth between 11pm and midnight. Chinese Wikipedia notes that rolling it into the next day is now the mainstream practice, and our calculator does that, but some schools keep it on the calendar day, which can move the Emperor star.