The Chinese Sexagenary Cycle is a cyclic numeral system of 60 combination of the two basic cycles, the ten Celestial Stems cycle and the twelve Earthly Branches cycle.

The ten Celestial Stems (pinyin: Tian Gan), sometimes known as Heavenly Stems, are the elements of an ancient Chinese cyclic character numeral system: (1) Jia, (2) Yi, (3) Bing, (4) Ding , (5) Wu , (6) Ji , (7) Geng, (8) Xin, (9) Ren, (10) Gui. They were used for dates as early as the Shang Dynasty (approx: 1766BC), and are now used with the twelve Earthly Branches in the Sexagenary cycle. They are associated with the concepts of yin and yang and the Five Elements.

The Earthly Branches (pinyin: Shi Er Di Zhi); literally the “twelve branches”) : (a) Zi, (b) Chou, (c) Yin, (d) Mao, (e) Chen, (f) Si, (g) Wu, (h) Wei, (i) Shen, (j) You, (k) Xu, (l) Hai, provide one Chinese system for reckoning time.

This system was built from the observations of the orbit of Jupiter. Chinese astronomers divided the celestial circle into 12 sections to follow the orbit of the Suixing (Jupiter, the Year Star). Astronomers rounded the orbit of Suixing to 12 years (from 11.86).

The Earthly Branches are today used with the Heavenly Stems in the current version of the “traditional Chinese calendar”.

The Sexagenary calendar system is calculated by combining the Ten Heavenly Stems and the Twelve Earthly Branches. Combining the series form a greater cycle of 60 terms, as the least common multiple of 10 and 12 is 60. The first term is formed by adding the first stem to the first branch, then the second stem to the second branch, and so on. You start with (1) Jia (a) Zi (Wood Rat), and the 61st year would also be Jia (stem) Zi (Branch) (Wood Rat) year again. The 2nd cycle would be (2)(a) and the 3rd would be (3)(c) and so on.

Notes:

1. I have replace the Chinese text with the Pinyin (Phonic) equal because without proper rendering support, you may see question marks, boxes, or other symbols instead of Chinese characters.