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The Chinese sexagenary cycle Chinese: 六十花甲; pinyin: liùshí huājiǎ), also known as the Stems-and-Branches (Chinese: 干支; pinyin: gānzhī), is a cycle of sixty terms used for recording days or years.[1] It appears, as a means of recording days, in the first Chinese written texts, the Shang dynasty oracle bones from the late second millennium BC. Its use to record years began around the middle of the 3rd century B.C.[2] The cycle, and variations on it, have been an important part of historical calendrical systems in other, Chinese-influenced Asian states, notably those of Japan, Korea and Vietnam. This traditional method of numbering days and years no longer has any significant role in modern Chinese time keeping or the official calendar. However, the sexagenary cycle continues to have a role in contemporary Chinese astrology and fortune telling.


Statues of Tai Sui deities responsible for individual years of the sexagenary cycleEach term in the sexagenary cycle consists of two Chinese characters, the first representing a term from a cycle of ten known as the Heavenly Stems (天干; tiāngān) and the second from a cycle of twelve known as the Earthly Branches (地支; dìzhī). The first term (甲子jiǎ-zǐ) combines the first heavenly stem (甲; jiǎ) with the first earthly branch (子; ). The second (乙丑; yǐ-chǒu) combines the second stem with the second branch. This continues, generating a total of 60 different terms (the least common multiple of ten and twelve), after which the cycle repeats itself. This combination of two sub-cycles to generate a larger cycle and its use to record time have parallels in other calendrical systems, notably the Akan calendar.[3]


The sexagenary cycle is attested as a method of recording days from the earliest written records in China, records of divination on oracle bones, beginning ca. 1250 BC. Almost every oracle bone inscription includes a date in this format. This use of the cycle for days is attested throughout the Zhou dynasty and remained common into the Han period for all documentary purposes that required dates specified to the day.

Almost all the dates in the Spring and Autumn Annals, a chronological list of events from 722 to 481 BC, use this system in combination with reign years and months (lunations) to record dates. Eclipses recorded in the Annals demonstrate that continuity in the sexagenary day-count was unbroken from that period onwards. It is likely that this unbroken continuity went back still further to the first appearance of the sexagenary cycle during the Shang period.[4]

The use of the sexagenary cycle for recording years is much more recent. The earliest document showing this usage is a diagram among the silk manuscripts from Mawangdui tomb 3, sealed in 168 BC. An annotation marking the first year of the reign of Qin Shi Huang (秦始皇), 246 BC, is applied to the diagram next to the position of the 60-cycle term (52 of 60, 乙卯—yǐ-mǎo) corresponding to that year.[5] Use of the cycle to record years became widespread for administrative time-keeping during the Western Han Dynasty (202 BC - 8 AD). The count of years has continued uninterrupted ever since:[6] the year 1984 began the present cycle (a 甲子—jiǎ-zǐ year), and 2044 will begin another. Note that in China the new year, when the sexagenary count increments, is not January 1st, but rather the lunar new year of the traditional Chinese calendar. For example, the yi-chou 己丑 year (coinciding roughly with 2009) began on January 26, 2009.

In Japan, according to Nihon shoki, the calendar was transmitted to Japan in 553. But it was not until the Suiko era that the calendar was used for politics. The year 604, when the Japanese officially adopted the Chinese calendar, was the first year of the cycle.[7]

The Japanese tradition of celebrating the 60th birthday (還暦 kanreki?) reflects the influence of the sexagenary cycle as a count of years.[8]

The Tibetan calendar also counts years using a 60-year cycle based on 12 animals and 5 elements, but while the first year of the Chinese cycle is always the year of the Wood Rat, the first year of the Tibetan cycle is the year of the Fire Hare (丁卯—dīng-mǎo, year 4 on the Chinese cycle).[9]

Ten Heavenly Stems[]

No. Heavenly










Yin yang Wu xing




Onyomi Kunyomi with

corresponding kanji

Romanized Hangul
1 jiǎ gaap3 kō (こう) kinoe (木の兄) gap giáp yang wood
2 jyut3 otsu (おつ) kinoto (木の弟) eul ất yin
3 bǐng bing2 hei (へい) hinoe (火の兄) byeong bính yang fire
4 dīng ding1 tei (てい) hinoto (火の弟) jeong đinh yin
5 mou6 bo (ぼ) tsuchinoe (土の兄) mu mậu yang earth
6 gei2 ki (き) tsuchinoto (土の弟) gi kỷ yin
7 gēng gang1 kō (こう) kanoe (金の兄) gyeong canh yang metal
8 xīn san1 shin (しん) kanoto (金の弟) shin tân yin
9 rén jam4 jin (じん) mizunoe (水の兄) im nhâm yang water
10 guǐ gwai3 ki (き) mizunoto (水の弟) gye quý yin

Twelve Earthly Branches[]

No. Earthly




















Onyomi Kunyomi Romanized Hangul
1 zi2 shi ne ja Rat (chuột) Rat (鼠) 11 p.m. to 1 a.m.
2 chǒu cau2 chū ushi chuk sửu Ox (trâu) Ox (牛) 1 to 3 a.m.
3 yín jan4 in tora in dần Tiger (hổ/cọp) Tiger (虎) 3 to 5 a.m.
4 mǎo maau5 u myo mẹo/mão Rabbit (mèo) Rabbit* (兔) 5 to 7 a.m.
5 chén san4 shin tatsu jin thìn Dragon (rồng) Dragon (龍) 7 to 9 a.m.
6 zi6 shi mi sa tỵ Snake (rắn) Snake (蛇) 9 to 11 a.m.
7 ng5 go uma o ngọ Horse (ngựa) Horse (馬) 11 a.m. to 1 p.m.
8 wèi mei6 mi or bi hitsuji mi mùi Goat (dê) Goat (羊) 1 to 3 p.m.
9 shēn san1 shin saru shin thân Monkey (khỉ) Monkey (猴) 3 to 5 p.m.
10 yǒu jau5 tori yu dậu Rooster (gà) Rooster (雞) 5 to 7 p.m.
11 seot1 jutsu inu sul tuất Dog (chó) Dog (狗) 7 to 9 p.m.
12 hài hoi6 gai i hae hợi Pig (lợn) Pig (豬) 9 to 11 p.m.
  • The names of several animals can be translated into English in several different ways. The Vietnamese Earthly Branches use Cat instead of Rabbit.

Sexagenary Cycle[]

Cyclic years and Western years[]

As mentioned above, the cycle first started to be used for indicating years during the Han Dynasty, but of course it can be used to indicate earlier years retroactively. Since it repeats, by itself it cannot specify a year without some other information, but it is frequently used with the Chinese era name (年号; "niánhào") to specify a year.[10] Of course, the year starts with the new year of whoever is using the calendar. In China, the cyclic year normally changes on the Chinese Lunar New Year. In Japan until recently it was the Japanese lunar new year, which was sometimes different from the Chinese; now it is January 1. So when calculating the cyclic year of a date in the Gregorian year, you have to consider what your "new year" is. Hence, the following calculation deals with the Chinese dates after the Lunar New Year in that Gregorian year; to find the corresponding sexagenary year in the dates before the Lunar New Year would require the Gregorian year to be decreased by 1.

As for example, the year 2697 BC (or -2696, using the astronomical year count), traditionally the first year of the reign of the legendary Yellow Emperor, was the first year (甲子; jiǎ-zǐ) of a cycle. 2700 years later in 4 AD, the duration equivalent to 45 60-year cycles, was also the starting year of a 60-year cycle. Similarly 1980 years later, 1984 was the start of a new cycle.

Thus, to find out the Gregorian year's equivalent in the sexagenary cycle use the appropriate method below.

  1. For any year number greater than 4 AD, the equivalent sexagenary year can be found by subtracting 3 from the Gregorian year, dividing by 60 and taking the remainder. See example below.
  2. For any year before 1 AD, the equivalent sexagenary year can be found by adding 2 to the Gregorian year number (in BC), dividing it by 60, and subtracting the remainder from 60. See example below.
  3. 1 AD, 2 AD and 3 AD correspond respectively to the 58th, 59th and 60th years of the sexagenary cycle.

The result will produce a number between 0 and 60, corresponding to the year order in the cycle; if the remainder is 0, it corresponds to the 60th year of a cycle. Thus, using the first method, the equivalent sexagenary year for 2012 AD is the 29th year (壬辰; rén-chén), as (2012-3) mod 60 = 29 (i.e., the remainder of (2012-3 divided by 60 is 29). Using the second, the equivalent sexagenary year for 221 BC is the 17th year (庚辰; gēng-chén), as 60- [(221+2) mod 60] = 17 (i.e., 60 minus the remainder of (221+2) divided by 60 is 17).


Step-by-step example to determine the sign for 1967:

  1. 1967 - 3 = 1964 ("subtracting 3 from the Gregorian year")
  2. 1964 ÷ 60 = 32 ("divide by 60 and discard any fraction")
  3. 1964 - (60 × 32) = 44 ("taking the remainder")
  4. 44 = Fire Sheep (丁未; dīng-wèi), see table.

Step-by-step example to determine the cyclic year of first year of the reign of Qin Shi Huang (246 BC):

  1. 246 + 2 = 248 ("adding 2 to the Gregorian year number (in BC)")
  2. 248 ÷ 60 = 4 ("divide by 60 and discard any fraction")
  3. 248 - (60 × 4) = 8 ("taking the remainder")
  4. 60 - 8 = 52 ("subtract the remainder from 60")
  5. 52 = Wood Rabbit (乙卯; yǐ-mǎo), see table.

The following tables show recent years (in the Gregorian calendar) and their corresponding years in the cycles:



Months in Sexagenary Cycle[]

The branches are used marginally to indicate months. Despite there being twelve branches and twelve months in a year, the earliest use of branches to indicate a twelve-fold division of a year was in the 2nd century BC. They were coordinated with the orientations of the Great Dipper, (建子月—jiànzǐyuè, 建丑月—jiànzǐyuè, etc.).[11] There are two systems of placing these months, the lunar one and the solar one.

One system follows the ordinary Chinese lunar calendar and connects the names of the months directly to the central solar term (中氣; zhōngqì). The jiànzǐyuè ((建)子月) is the month containing the winter solstice (i.e. the 冬至— Dōngzhì) zhōngqì. The jiànzǐyuè ((建)丑月) is the month of the following zhōngqì, which is Dàhán (大寒), while the jiànyínyuè((建)寅月) is that of the Yǔshuǐ (雨水) zhōngqì, etc. Intercalary months have the same branch as the preceding month.

In the other system (節月; jiéyuè) the "month" lasts for the period of two solar terms (two 氣策—qìcì). The zǐyuè (子月) is the period starting with Dàxuě (大雪), i.e. the solar termbefore the winter solstice. The chǒuyuè (丑月) starts with Xiǎohán (小寒), the term before Dàhán (大寒), while the yínyuè (寅月) starts with Lìchūn (立春), the term before Yǔshuǐ (雨水), etc. Thus in the solar system a month starts anywhere from about 15 days before to 15 days after its lunar counterpart.

The branch names are not usual month names; the main use of the branches for months is astrological. However, the names are sometimes used to indicate historically which (lunar) month was the first month of the year in ancient times. For example, since the Han Dynasty, the first month has been jiànyínyuè, but earlier the first month was jiànzǐyuè(during the Zhou Dynasty) or jiànchǒuyuè (traditionally during the Shang Dynasty) as well.[12]

For astrological purposes stems are also necessary, and the months are named using the sexegenary cycle following a five-year cycle starting in a jiǎ (甲; 1st) or  (己; 6th) year. The first month of the jiǎ or  year is a bǐng-yín (丙寅; 3rd) month, the next one is a dīng-mǎo (丁卯; 4th) month, etc., and the last month of the year is a dīng-chǒu (丁丑, 14th) month. The next year will start with a wù-yín (戊寅; 15th) month, etc. following the cycle. The 5th year will end with a yǐ-chǒu (乙丑; 2nd) month. The following month, the start of a or jiǎ year, will hence again be a bǐng-yín (3rd) month again. The beginning and end of the (solar) months in the table below are the approximate dates of current solar terms; they vary slightly from year to year depending on the leap days of the Gregorian calendar.

Earthly Branches of the certain months Solar term Zhongqi (the Middle solar term) Starts at Ends at Names in year of Jia or Ji(甲/己年) Names in year of Yi or Geng (乙/庚年) Names in year of Bing or Xin (丙/辛年) Names in year of Ding or Ren (丁/壬年) Names in year of Wu or Gui (戊/癸年)
Month of Yin (寅月) Lichun - Jingzhe Yushui February 4 March 6 Bingyin / 丙寅月 Wuyin / 戊寅月 Gengyin / 庚寅月 Renyin / 壬寅月 Jiayin / 甲寅月

Month of Mao (卯月)

Jingzhe - Qingming Chunfen March 6 April 5 Dingmao / 丁卯月 Jimao / 己卯月 Xinmao / 辛卯月 Guimao / 癸卯月 Yimao / 乙卯月
Month of Chen (辰月) Qingming - Lixia Guyu April 5 May 6 Wuchen / 戊辰月 Gengchen / 庚辰月 Renchen / 壬辰月 Jiachen / 甲辰月 Bingchen / 丙辰月
Month of Si (巳月) Lixia - Mangzhong Xiaoman May 6 June 6 Jisi / 己巳月 Xinsi / 辛巳月 Guisi / 癸巳月 Yisi / 乙巳月 Dingsi / 丁巳月
Month of Wu (午月) Mangzhong - Xiaoshu Xiazhi June 6 July 7 Gengwu / 庚午月 Renwu / 壬午月 Jiawu / 甲午月 Bingwu / 丙午月 Wuwu / 戊午月
Month of Wei (未月) Xiaoshu - Liqiu Dashu July 7 August 8 Xinwei / 辛未月 Guiwei / 癸未月 Yiwei / 乙未月 Dingwei / 丁未月 Jiwei / 己未月
Month of Shen (申月) Liqiu - Bailu Chushu August 8 September 8 Renshen / 壬申月 Jiashen / 甲申月 Bingshen / 丙申月 Wushen / 戊申月 Gengshen / 庚申月
Month of You (酉月) Bailu - Hanlu Qiufen September 8 October 8 Guiyou / 癸酉月 Yiyou / 乙酉月 Dingyou / 丁酉月 Jiyou / 己酉月 Xinyou / 辛酉月
Month of Xu (戌月) Hanlu - Lidong Shuangjiang October 8 November 7 Jiaxu / 甲戌月 Bingxu / 丙戌月 Wuxu / 戊戌月 Gengxu / 庚戌月 Renxu / 壬戌月
Month of Hai (亥月) Lidong - Daxue Xiaoxue November 7 December 7 Yihai / 乙亥月 Dinghai / 丁亥月 Jihai / 己亥月 Xinhai / 辛亥月 Guihai / 癸亥月
Month of Zi (子月) Daxue - Xiaohan Dongzhi December 7 January 6 Bingzi / 丙子月 Wuzi / 戊子月 Gengzi / 庚子月 Renzi / 壬子月 Jiazi / 甲子月
Month of Chou (丑月) Xiaohan - Lichun Dahan January 6 February 4 Dingchou / 丁丑月 Jichou / 己丑月 Xinchou / 辛丑月 Guichou / 癸丑月 Yichou / 乙丑月

See also[]


  1. ^ Louis-Frédéric. (2005). "Jikkan-jūnishi" in Japan Encyclopedia, p. 420.
  2. ^ Smith (2011), pp. 1, 28.
  3. ^ For the Akan calendar, see Bartle (1978).
  4. ^ Smith (2011), p. 24,26-27.
  5. ^ Kalinowski (1998), pp. 135–148, and fig. 3; Smith (2011), p. 29.
  6. ^ Smith (2011), p. 28.
  7. ^ National Diet Library, "Calendar History; the Source"; retrieved 2013-1-1.
  8. ^ Encyclopedia of Shinto, "Kanreki"; retrieved 2013-1-1.
  9. ^ Chattopadhyaya, Alaka. (1999). Atisa and Tibet: Life and Works of Dipamkara Srijnana in relation to the history and religion of Tibet, pp. 566-568.
  10. ^ The Mathematics of the Chinese Calendar
  11. ^ Smith (2011), p. 28, p. 29 fn2, ; Entry "建す” in the standard dictionary 広辞苑, 東京:岩波.
  12. ^ Entry "三正” in the standard dictionary 広辞苑, 東京:岩波.


Bartle, P. F. W. (1978). "Forty days: the Akan calendar". Africa: Journal of the International African Institute 48 (1): 80–84. doi: 10.2307/1158712.

Kalinowski, Marc (2007). "Time, space and orientation: figurative representations of the sexagenary cycle in ancient and medieval China". In Francesca Bray (ed.). Graphics and text in the production of technical knowledge in China : the warp and the weft. Leiden: Brill. pp. 137–168. ISBN 978-90-04-16063-7.

Smith, Adam (2011). "The Chinese sexagenary cycle and the ritual origins of the calendar". In John Steele (ed.). Calendars and years II : astronomy and time in the ancient and medieval world. Oxford: Oxbow. pp. 1–37. ISBN 978-1-84217-987-1.