Calculation conventions

The year pillar advances at the exact instant of Li Chun, the first solar term. In 2024 that instant was 2024-02-04 16:27:07 China Standard Time. A birth one minute earlier belongs to the previous year pillar.

BaZi is a solar system. The twelve month pillars are defined by the twelve major solar terms (節), which are positions of the sun on the ecliptic, not lunar months. Chinese New Year is a lunisolar date and can fall weeks either side of Li Chun; using it would put the year pillar out of step with the month pillar it must agree with.

The year and month pillars are decided by taking the absolute instant of birth and comparing it to the solar-term instant. True solar time is NOT used for this comparison. The hour pillar, and the day pillar, are taken from true solar time at the birth longitude — the day pillar because the late-zi day boundary (see the late-zi rule, section 4) is itself a statement about true solar midnight, not civil midnight.

A solar term happens at one moment for the whole world. True solar time is a local sun position, not a timezone conversion, so comparing a true-solar clock reading against a solar-term table mixes two frames. Doing so produces the wrong YEAR pillar for births near a term. Worked example: a New York birth at 2024-02-04 03:30 EST is 16:30 China Standard Time and therefore after Li Chun (16:27:07), giving 甲辰. Its true solar time is 03:20, and a chain that fed that into the term comparison would return 癸卯 — wrong by a whole year. The day pillar is the opposite case: it is deliberately computed from true solar time, because whether a late-night birth belongs to the current day or the next is a question about the sun, not about the civil clock.

Clock time is corrected in four steps: the historical UTC offset in force on that date at that place (from the IANA time zone database, including historical daylight saving), then longitude at four minutes per degree from the zone’s reference meridian, then the equation of time for that instant. The result is true apparent solar time, and the hour branch is read from it.

The hour branch is a statement about where the sun actually was. Two corrections are needed and most calculators apply only the first. Longitude alone gives Local Mean Time — a fictional even-paced sun. The equation of time, which reaches ±14 to ±16 minutes, is the difference between that fiction and the real sun. Near a two-hour boundary those minutes decide the branch.

The zi hour (子時) spans 23:00–00:59 true solar time. This engine uses the convention that the late half (23:00–23:59) keeps the day pillar of the day it is still in, and only the hour pillar belongs to zi.

The day boundary is a genuine disagreement between schools, not a settled fact. This engine states which side it takes and lets you see the other.

If the birth time is not known, no hour pillar is produced and no true-solar-time correction is shown, because that correction cannot be computed without a real time to correct. The day pillar uses that same date directly, without the late-zi true-solar adjustment described in SOLAR_TERM_FRAME — an unknown hour means it is also unknown whether the birth fell in the late-zi window, so that correction cannot honestly be applied either way. The year and month pillars are produced only when the date alone settles them: the engine casts both ends of that local day and compares. On roughly twelve dates a year the day crosses a solar term, the two ends disagree, and the pillar is therefore a fact about the unknown hour rather than about the date — on those dates it is omitted and both candidates are named instead.

Defaulting an unknown hour to midnight, or to any other clock reading, would silently manufacture a zi-hour pillar sitting on the day boundary — the single most consequential position in the chart — and would let an internal reference time leak into the day-pillar correction as if it were a real fact about the birth. A missing pillar is honest; an invented one is not.

Births before 1970 are served but flagged. Ambiguous local times (the hour repeated when daylight saving ends) and non-existent local times (the hour skipped when it begins) are detected and reported rather than silently resolved.

IANA time zone data before 1970 is sparser and less reliable, and many places had no legal standard time at all. Rather than pretend to a precision the underlying data does not support, those charts carry a visible caveat.

When a gender is given, this engine derives a sequence of ten-year luck pillars starting from the month pillar and stepping through the sixty-pair cycle one step per decade, forward for a yang year stem with male gender or a yin year stem with female gender, and backward for the opposite pairing. The onset is the distance from birth to the solar term that BOUNDS the birth month - the twelve month-opening terms (節) only, not the twelve mid-month terms (中氣), so it is not always the nearest of the twenty-four - taking the previous boundary running backward and the next one running forward. That distance is counted in whole two-hour periods (時辰) and converted at three days to a year, one day to four months, and one two-hour period to ten days. Ages are nominal (虛歲): the calendar year of birth counts as age 1, and the anchor is the birth year on the birth certificate, not the year the birth instant falls in once converted to China Standard Time. Every quantity here - year polarity, the month pillar used as the base, and the boundary-term distance - is read from the same absolute-instant chart used for the year and month pillars (see the solar-term frame, section 2), never from true solar time. When the birth hour is unknown the sequence and its direction are still derived, because neither involves the hour, but no onset and no age or year bands are produced (see the unknown-hour rule, section 5).

Direction and onset are usually explained as month-pillar and gender-based, but both are ultimately anchored to the same solar-term structure that fixes the year and month pillars. Deriving them from true solar time instead - an easy mistake, since the rest of the report reads local sun position - would silently flip the direction and shift the onset age for anyone born within the same window that produces a wrong year pillar under that error (see SOLAR_TERM_FRAME's worked New York example): a birth minutes either side of a term can invert the whole sequence. The counting is stated in two-hour periods rather than clock hours because that is the resolution the traditional method actually works at: two births an hour apart inside the same 時辰 give the same onset, and the day component therefore only ever lands on 0, 10 or 20 days. Anyone re-deriving the onset by hand needs that, or their arithmetic will not reproduce ours.