Zi Wei Dou Shu calculation conventions
The same birth data can produce different charts in different tools. The difference almost always comes from a handful of conventions: how true solar time is computed, which day starts the new year, how leap months are assigned, which day the late Zi hour belongs to, and which school's star placement is used. Here is every one of them as implemented on 9zi.ai — and which can be switched in the calculator.
Calendar
Gregorian ↔ lunar conversion uses lunar-javascript for 1900–2099. The Chinese calculator also accepts lunar dates with a leap-month flag.
Year boundary: Lunar New Year (switchable to Li Chun)
The stem of the birth year decides the birth-year transformations, the stems of the twelve palaces and the Five Elements Bureau, so the boundary between years changes the whole chart. 9zi.ai defaults to the standard Zi Wei Dou Shu convention: the year changes on the first day of the first lunar month. You can switch to Start of Spring (Li Chun, about 4 February) under “Calculation settings”. It only affects births between Lunar New Year and Li Chun. Example: someone born on 30 January 1990 — after Lunar New Year (27 Jan), before Li Chun (4 Feb) — is a Geng-Wu (Horse) year chart by default, and a Ji-Si (Snake) year chart with Li Chun. Change note: before 2026-10-01 the site had no explicit setting and silently inherited the engine's default (iztro 2.5.3), which is Li Chun. We consider that non-standard and changed the default; charts for births in that window made earlier are worth recalculating. Decade and annual cycles change year on the same boundary.
True solar time: time zone + longitude + equation of time, including historical DST
Birth time is converted to local true solar time before choosing the hour. Step 1: convert the clock time to UTC using the birthplace's IANA time zone (the database includes historical daylight saving and zone changes). Step 2: add the longitude correction, 4 minutes per degree. Step 3: add the equation of time (Spencer's formula, error under one minute). If the result crosses midnight, the chart date moves by a day. Daylight saving is the usual trap. Mainland China observed it each summer from 1986 to 1991; Hong Kong did until 1979, and Taiwan in 1974–75 and 1979. Example: Beijing, 15 May 1990, clock 07:30 — daylight saving was in force (UTC+9), so true solar time is about 06:20, the Mao hour; ignoring it gives the Chen hour. Change note: before 2026-10-01 the Chinese form applied only a longitude correction, assuming UTC+8, with no daylight saving and no date change, while the methodology page claimed automatic DST handling. That was inaccurate and is fixed; charts for births in 1986–1991 summers made earlier may be one hour-branch off.
The late Zi hour
The twelve double-hours are defined on true solar time; 23:00–00:59 is Zi. Whether 23:00–23:59 belongs to the same day or the next differs by school. 9zi.ai counts it as the same day by default and lets you choose the next day.
Leap months
The first half of a leap month (days 1–15) belongs to that month; the second half (day 16 on) to the next, following the Quan Shu convention.
Star-placement school
The default is the standard Zi Wei Dou Shu Quan Shu method; the Zhongzhou school is selectable. Other schools' four-transformation variants are not available yet.
Transformations, decades, annual cycles
Birth-year transformations come from the year stem (with the boundary above); palace-stem flying transformations come from each palace's stem. Decades start from the Bureau number and run clockwise or counter-clockwise by yin–yang and gender. Annual cycles change on the year boundary above — for 2027, Lunar New Year is 6 February and Li Chun is 4 February.
Comparing with another tool, in this order
1) Year boundary. 2) Clock time → did the tool apply true solar time, which time zone, and daylight saving? 3) Late Zi hour and leap months. 4) School. If the first three agree, the Life Palace, Body Palace, Five Elements Bureau and Zi Wei position should match exactly. See “Why charts differ”.
Q: Does 9zi.ai use Lunar New Year or Li Chun as the year boundary?
Lunar New Year by default (the standard convention), switchable to Li Chun under Calculation settings.
Q: Does daylight saving affect a Zi Wei Dou Shu chart?
Yes. A clock one hour ahead of standard time can move the birth into the neighbouring double-hour. The calculator applies historical daylight saving from the birthplace's time zone.