Heavenly Stems and Earthly Branches: the sixty-year cycle

Ten stems and twelve branches

The stems are Jia 甲, Yi 乙, Bing 丙, Ding 丁, Wu 戊, Ji 己, Geng 庚, Xin 辛, Ren 壬 and Gui 癸. They alternate yang and yin, with two stems for each phase: Wood, Fire, Earth, Metal and Water.

The branches are Zi 子, Chou 丑, Yin 寅, Mao 卯, Chen 辰, Si 巳, Wu 午, Wei 未, Shen 申, You 酉, Xu 戌 and Hai 亥. They also alternate polarity and correspond to the Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Goat, Monkey, Rooster, Dog and Pig.

The romanized Wu of a stem and Wu of the Horse branch refer to different characters. Retaining the character alongside the pronunciation prevents that ambiguity.

Why the cycle has sixty pairs

Advance one stem and one branch at a time, beginning with Jia-Zi. The next pair is Yi-Chou, then Bing-Yin. Because the two sequences advance together, yang stems pair with yang branches and yin with yin. You do not get every possible combination.

The sequences meet again after sixty steps. Jia-Zi is therefore followed by another Jia-Zi sixty years later. A stem-and-branch label without a date or cycle context is not a unique Gregorian year.

Converting a Gregorian year

Using 1984 as a Jia-Zi reference, count the offset modulo sixty. Equivalently, the stem follows (year − 4) modulo 10 and the branch follows (year − 4) modulo 12 when the result is normalized to a nonnegative index.

For example, 2027 gives Ding-Wei: Ding is yin Fire and Wei is the Goat branch. The calendar-year lookup identifies the cycle label, but a birth chart still needs the year-boundary rule described below.

Taiwan’s ROC year notation

For years in the Republic of China calendar, add 1911 to obtain the Gregorian year: ROC 116 corresponds to 2027. The reverse subtracts 1911. This is a numbering convention, not a different astronomical year.

International readers should not interpret an unlabeled “116” as a Gregorian date. The lookup and reference tables explicitly distinguish the two systems.

Li Chun is not Lunar New Year

BaZi here changes the year pillar at the instant of Li Chun, the Start of Spring solar term. Popular zodiac customs often change the animal year on the first day of the lunar year. These can be different dates, so a birth between them can receive different year labels under the two conventions.

For 2027, the civil dates in Taiwan are February 4 for Li Chun and February 6 for Lunar New Year. The chart must compare the actual instant of Li Chun, including location and time-zone conversion; the whole day is not automatically the new year.

If the birth time is unknown on a date containing the boundary, the form requests it rather than assuming the transition has already occurred.

Year tables and the lookup

The reference year rows cover 1924–2043, two complete sixty-year cycles. The interactive lookup also follows its stated input range and shows the distinction between a year label and the precise birth boundary.

The tables below retain Chinese characters as technical identifiers while explaining their pronunciation and elements in English. Use the Five Phases guide for generation and control, and the ten-year-cycle guide for how consecutive pairs form a personal time sequence.

A year label does not describe the entire chart. Month, day and hour pairs come from their own calendar rules, not by copying the animal or element of the birth year.