The Chinese sexagenary, or Gan-Zhi, cycle names years by pairing ten heavenly stems with twelve earthly branches. Both lists advance one place at a time; their first simultaneous return is after 60 steps, when the pair sequence starts again at Jia-Zi. This is a year-labeling pattern, not a complete method for calculating Chinese calendar dates.
How the 60-year sequence is calculated
Number the ten stems from 0 to 9 and the twelve branches from 0 to 11. At step n, pair stem n mod 10 with branch n mod 12. Starting with zero makes the first pair Jia-Zi.
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Because each step advances both lists, a pair repeats only when the step count is divisible by both 10 and 12. Their least common multiple is 60, so there are 60 ordered pairs—not 120—before the sequence returns to its start. The Hong Kong Observatory and NASA describe this ordered cycle and its length (Hong Kong Observatory: Heavenly Stems and Earthly Branches; NASA: Calendars and their History).
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1Repair Windows errors before they cause bigger problems2Scan for outdated or missing drivers - takes under a minute3Clear out junk files and repair common Windows errors- List the stems: Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui.
- List the branches: Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai.
- Advance both lists together: after Jia-Zi comes Yi-Chou, then Bing-Yin, continuing in order.
- After 60 pairs, restart: the 60th listed pair is Gui-Hai; the next is Jia-Zi again.
In pseudocode, the rule is:
stems = [Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui]
branches = [Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai]
for n in 0..59:
print(stems[n mod 10], branches[n mod 12])What the cycle does—and does not—tell you
A Gan-Zhi year name identifies a position in a repeating sequence. On its own, it cannot identify one unique year in the Gregorian calendar: the cycle has no unique initial epoch, as NASA notes in its calendar history reference. To map a name to an absolute year, you need an external year count or a chosen epoch.
Nor does the 60-step pattern calculate Chinese New Year or the lengths of Chinese calendar months. The Chinese calendar is lunisolar and includes intercalary months. The Hong Kong Observatory describes Lunar New Year’s Day as the first day of the second new moon after the winter solstice, excluding a leap month from that count; it also notes a pattern of seven leap months in 19 years (Hong Kong Observatory: What year is it today?).
When does the Gan-Zhi year change?
The boundary depends on the convention being used, so the calendar year name should not be treated as though it changes on one universally agreed date. The Hong Kong Observatory changes the Gan-Zhi year on Lunar New Year’s Day, the first day of the first Chinese calendar month. Some discussions instead use “Spring Commences,” a solar term that can fall earlier. These are distinct boundary conventions, not interchangeable dates; consult the relevant calendar or practice for a particular year (Hong Kong Observatory: What year is it today?).
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Formal calendar calculation is also addressed by national standards. The Standardization Administration of China lists GB/T 33661-2017, “Calculation and promulgation of the Chinese calendar,” as current, with publication on 2017-05-12 and implementation on 2017-09-01 (standard listing). The listing establishes the standard’s title and status; it is not the full standard text.
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