BaZi (Four Pillars): the calendar calculation
Definition
BaZi (eight characters) represents a birth moment as four pillars, year, month, day and hour, each a pair of one heavenly stem (10) and one earthly branch (12). It uses the solar calendar, not planetary positions.
Year and month
The year changes at Lichun, when the Sun reaches 315° tropical longitude (about 4 February). Year stem = (year − 4) mod 10; year branch = (year − 4) mod 12. Months change at each jie solar term (Sun at 315°, 345°, 15° …). Month index m = floor(((Sun longitude − 315) mod 360) ÷ 30); month branch = (2 + m) mod 12; month stem = ((year stem mod 5) × 2 + 2 + m) mod 10.
Day and hour
Day pillar index = (Julian Day Number + 49) mod 60; stem = index mod 10, branch = index mod 12 (index 0 is Jia Zi). Check: 1 October 1949 gives Jia Zi; 1 January 2000 gives Wu Wu. Hour branch = floor((local solar hour + 1) ÷ 2) mod 12; hour stem = ((day stem mod 5) × 2 + hour branch) mod 10.
Day Master and elements
The day stem is called the Day Master. Each stem and branch is assigned one of the Five Elements; Jyotishya counts the eight characters by element. Jyotishya's Chinese day score compares each day's pillar with the Day Master and day branch using fixed element and branch rules, shown for every day.
In Jyotishya
Day and hour use local mean solar time, with the day starting at midnight (some schools use 23:00).