Zi Wei Dou Shu Star Placement Formulas: How the 14 Main Stars Are Positioned

Once a Zi Wei Dou Shu (紫微斗数) chart has a Life Palace (命宫) and a Five Element Bureau (五行局), the rest of the chart is arithmetic. Fourteen main stars are placed by a small set of rules, and every one of those rules takes its inputs from things that were already fixed: the bureau, the lunar day, the lunar month, the birth hour, and the birth-year stem and branch.

This page sets out those rules as rules — not as a list of star meanings. If you want the meaning of a star, that is a different page. If you want to know why a star is in that box, this is the page. Each section also flags where published tables differ, because this is the layer of chart building where two tools are most likely to diverge without either being wrong.

What a placement formula needs

Every landing position in the chart is computed from a small number of inputs. Nothing is randomized, and nothing is interpreted:

Two things follow from this table. First, the placement layer is fully determined by five values — you can reproduce it by hand. Second, if any one of those five values is different, stars move. Most disagreements between charts for "the same" birth data are disagreements about these inputs, not about the rules.

Formula 1 — locating Zi Wei (紫微)

Zi Wei is the anchor of the whole chart. It is located from exactly two inputs: the Five Element Bureau number and the lunar day of birth.

The classical procedure is a division. Take the number of the bureau (2 to 6). Take the lunar day. If the day is not divisible by the bureau number, borrow forward — add 1, then 2, then 3, and so on — until the total is divisible. Divide, and you have a quotient. That quotient is counted out as palaces, and then the borrow you added is applied as a correction: counted forward if the borrow was an even number, counted backward if it was odd.

Written out like that it sounds fiddly. Tabulated, it is not — which is why most published versions of this rule appear as a ready-made table of "bureau × lunar day → palace". The table and the procedure are the same information in two shapes.

The worked example

Bureau: Fire Six (火六局) · Lunar day: 16

1. 16 ÷ 6 does not divide evenly (remainder 4). Borrow 1: 17, still not divisible. Borrow 2: 18 ÷ 6 = 3.
2. Quotient = 3. Count 3 palaces from the Yin (寅) palace: Yin, Mao, Chen — the third is Chen (辰).
3. The borrow was 2, an even number, so move forward 2 palaces from Chen: Si, Wu (午).
4. Zi Wei sits in Wu (午).

Where the Zi Wei tables differ

This is the single most consequential place where published material drifts. Because the procedure can be written in more than one way, and because many texts print only the finished table without the borrow rule that generated it, a table copied from one lineage can carry an entry that a table from another lineage does not have — particularly for the later days of the lunar month and for the higher bureau numbers.

The practical consequence is worth stating plainly: one palace of difference here moves most of the chart. Zi Wei anchors the largest group of main stars, so an entry that differs by one shifts a whole side of the chart. If you are comparing two tools, check this position first — it is the cheapest single check and it explains a large share of disagreements.

None of this means one edition is fraudulent and another is honest. It means a table is a transcript of a rule, and transcripts vary. Our own position is simply that the rule we use is stated, so the position can be checked rather than trusted.

Formula 2 — locating Tian Fu (天府)

Tian Fu is not looked up. It is derived from Zi Wei by a mirror relationship.

The mirror runs about the Yin–Shen (寅–申) axis. Two consequences make the rule easy to remember and easy to verify:

• When Zi Wei is in Yin (寅) or in Shen (申), Tian Fu is in the same palace as Zi Wei.
• As Zi Wei moves one palace in one direction, Tian Fu moves one palace in the other direction.

The worked example

Zi Wei is in Wu (午). Counting from the mirror axis, Tian Fu lands in Xu (戌) — which sits opposite Wu around the same axis. That single position then anchors the second group of main stars.

Formula 3 — the two star groups

The fourteen main stars are placed as two sequences, one anchored on Zi Wei and one anchored on Tian Fu. That is why people talk about "the Zi Wei group" and "the Tian Fu group". The two sequences run in opposite directions, which is the reason two nearby anchors can produce stars that look scattered across the chart.

The Zi Wei group — counted in reverse

The gaps in that list are not typos. The sequence is defined by fixed positions, not by consecutive ones — which is exactly why the offsets are 1, 3, 4, 5 and 8 rather than 1 through 6.

The Tian Fu group — counted forward

The worked example, resolved

With Zi Wei in Wu and Tian Fu in Xu, applying both sequences gives the complete main-star layer of the example chart:

Two palaces hold no main star. That is normal: fourteen stars cannot fill twelve palaces without some doubling up somewhere else. An empty palace is read through its opposite palace and the surrounding triangle, not treated as a blank.

Formula 4 — the main auxiliary stars

After the fourteen main stars, the auxiliary (辅星) layer is added. These rules are simpler individually, but there are more of them, and this is the layer where tools differ most freely — some include a star, some do not.

Three observations about this layer are worth carrying forward:

• The hour travels. Several rules take a fixed anchor and then advance by the birth double-hour. That means an error or a convention difference in Step 1 — the input stage — propagates into a handful of stars at once, not just one.
• Inclusion is a choice. The fourteen main stars are the stable core of the tradition. The auxiliary family around it is larger, and different systems draw the line in different places. A chart that looks sparse may be filtered rather than wrong.
• The lunar month matters twice. It sets the Life Palace and it anchors the month-based stars, so a leap-month convention difference moves both.

What changes a placement

Bringing the formulas together, a placed star moves for one of a small number of reasons:

• True solar time. If the birth clock time is corrected to the sun, a birth near a double-hour boundary can cross into a neighbouring hour — which changes the Life Palace, the bureau, the Zi Wei position, and every hour-based auxiliary star at once.
• Lunar day. The lunar day feeds Zi Wei directly. A one-day difference in conversion is not cosmetic.
• Lunar month and leap months. Month-based rules inherit whichever convention the converter used.
• Table edition. As above, for Zi Wei placement in particular.
• Which stars are shown. A display choice, not a calculation difference — but it looks like one when two charts are put side by side.

Notice the shape of that list: it is about inputs and editions, not about interpretation. The stars are placed before any reading begins, and they are placed by rules that can be written down and checked.

How to check a placement by hand

1. Start from the bureau. If you cannot reproduce the Life Palace and the bureau, stop — everything downstream inherits them.
2. Compute Zi Wei, then confirm it two ways. Do the division once and look at the table once. If the two disagree, you have found a table variant, which is itself useful information.
3. Mirror for Tian Fu. Confirm the mirror before you use Tian Fu to place anything.
4. Place one star from each group and check the directions. If both groups appear to run the same way, the sequence has been applied in the wrong direction.
5. Only then look at the auxiliary layer. It is the largest layer and the least standardised; it is a poor place to start a dispute.

Where this fits

Star placement is the third and fourth of the five steps that build a chart. The steps before it — converting the birth data and locating the Life Palace — decide the inputs, and the step after it is the reading itself. If you want the full sequence in one place, start with how a chart is calculated, step by step.

For the anchoring step in detail, see the Life Palace calculation. For what a chart calculator does with all of this — and why two calculators can return different charts — see what a calculator actually does. For the input stage, true solar time is the one correction most likely to move a chart.

For reference only.

FAQ

How are the 14 main stars placed? By a small set of fixed rules once the Life Palace (命宫) and Five Element Bureau (五行局) are set. Each rule takes its inputs from the bureau, the lunar date, the birth hour, and the birth-year stem.

What inputs does a placement formula need? The bureau, the lunar day, the lunar month, the birth hour, and the birth-year stem or branch — all of which are fixed before any star is moved.

Is any placement random? No. Every landing position is computed from those inputs, so the same birth data always produces the same chart.

How can I check a placement by hand? Work from the bureau and the 紫微 position first, then apply the star-group rules in order. If your result differs from a tool, compare your inputs before your arithmetic.