Chinese sexagenary cycle

Sexagenary cycle
Chinese 六十干支
Chinese 干支

The sexagenary cycle, also known as the Stems-and-Branches or ganzhi, is a cycle of sixty terms used for reckoning time in China and the East Asian cultural sphere.[1] It appears as a means of recording days in the first Chinese written texts, the Shang oracle bones of the late second millennium BC. Its use to record years began around the middle of the 3rd century BC.[2] The cycle and its variations have been an important part of the traditional calendrical systems in Chinese-influenced Asian states and territories, particularly those of Japan, Korea, and Vietnam, with the old Chinese system still in use in Taiwan.

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 is still used in names of many historical events, such as the Chinese Xinhai Revolution, the Japanese Boshin War, and the Korean Imjin War. It also continues to have a role in contemporary Chinese astrology and fortune telling.


Statues of Tai Sui deities responsible for individual years of the sexagenary cycle

Each term in the sexagenary cycle consists of two Chinese characters, the first being one of the ten Heavenly Stems of the Shang-era week and the second being one of the twelve Earthly Branches representing the years of Jupiter's duodecennial orbital cycle. The first term jiǎzǐ (甲子) combines the first heavenly stem with the first earthly branch. The second term yǐchǒu (乙丑) combines the second stem with the second branch. This pattern continues until both cycles conclude simultaneously with guǐhài (癸亥), after which it begins again at jiǎzǐ. This termination at ten and twelve's least common multiple leaves half of the combinations—such as jiǎchǒu (甲丑)—unused; this is traditionally explained by reference to pairing the stems and branches according to their yin and yang properties.

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 regnal 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 discovered documents showing this usage are among the silk manuscripts recovered from Mawangdui tomb 3, sealed in 168 BC. In one of these documents, a sexagenary grid diagram is annotated in three places to mark notable events. For example, the first year of the reign of Qin Shi Huang (秦始皇), 246 BC, is noted on the diagram next to the position of the 60-cycle term yǐ-mǎo (乙卯, 52 of 60), 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 1, but rather the lunar new year of the traditional Chinese calendar. For example, the ji-chou 己丑 year (coinciding roughly with 2009) began on January 26, 2009. (However, for astrology, the year begins with the first solar term "Lìchūn" (立春), which occurs near February 4.)

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) (literally 'return of calendar') 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 Rabbit (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 yuet3 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 mo6 bo () tsuchinoe (土の兄) mu mậu yang earth
6 gei2 ki () 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 yam4 jin (じん) mizunoe (水の兄) im nhâm yang water
10 guǐ gwai3 ki () mizunoto (水の弟) gye quý yin

Twelve Earthly Branches[]

No. Earthly
Onyomi Kunyomi Romanized Hangul
1 ji2 shi ne ja Rat (chuột;𤝞) Rat () 11 p.m. to 1 a.m.
2 chǒu chau2 chū ushi chuk sửu Water buffalo (trâu;𤛠) Ox () 1 to 3 a.m.
3 yín yan4 in tora in dần Tiger (hổ/cọp;虎/𧲫) Tiger () 3 to 5 a.m.
4 mǎo maau5 u myo mão/mẹo Cat (mèo;猫) Rabbit () 5 to 7 a.m.
5 chén san4 shin tatsu jin thìn Dragon (rồng;龍) Dragon () 7 to 9 a.m.
6 ji6 shi mi sa tỵ Snake (rắn;𧋻) Snake () 9 to 11 a.m.
7 ng5 go uma o ngọ Horse (ngựa;馭) Horse () 11 a.m. to 1 p.m.
8 wèi mei6 mi or bi hitsuji mi mùi Goat (dê;羝) Goat () 1 to 3 p.m.
9 shēn san1 shin saru shin thân Monkey (khỉ;𤠳) Monkey () 3 to 5 p.m.
10 yǒu jau5 tori yu dậu Rooster (gà;𪂮) Rooster () 5 to 7 p.m.
11 sut1 jutsu inu sul tuất Dog (chó;㹥) Dog () 7 to 9 p.m.
12 hài hoi6 gai i hae hợi Pig (lợn/heo;𤞼/㺧) Pig () 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 years[]

Sexagenary days[]

Date Year mod 40 Century N Century Year mod 16 Date
01 11 21 31 Feb Jun Jul 04 06 25 27 01 14 Jul 01 13 25
02 12 22 Aug 08 10 29 31 17 24 02 02 06 10 14 18 05 02 14 26
03 13 23 Sep Oct 12 14 33 35 01 03 05 07 09 11 13 15 22 03 21 03 12 Sep 03 15 27
04 14 24 Nov Dec 16 18 37 39 04 24 10 Nov 04 16 28
05 15 25 01 03 20 22 20 05 01 05 09 13 01 05 17 29
06 16 26 05 07 24 26 18 06 17 08 15 Apri Feb 06 18 30
07 17 27 09 11 28 30 23 07 20 23 06 Feb Jun 07 19 31
08 18 28 13 15 32 34 00 02 04 06 08 10 12 14 16 08 00 04 08 12 13 Aug 08 20

09 19 29 Mar Jan 17 19 36 38 21 09 04 11 Oct 09 21
10 20 30 Jan Apr May Feb 02 21 23 00 19 10 16 19 02 Dec 10 22
Jan and Feb for leap years
Stems on the left and branches on the right
11 03 07 11 15 22 09 Mar Jan 11 23
12 07 00 Jan May 12 24

For the stem-branch (SB) of October 1, 1949

Conversion between cyclic years and Western years[]

Relationship between sexagenary cycle and recent Common Era years

As mentioned above, the cycle first started to be used for indicating years during the Han dynasty, but it also 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] 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 59, 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. Show one of the Sexagenary Cycle tables (the following section), look for 44 in the first column (No) and obtain Fire Goat (丁未; dīng-wèi).

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. Show one of the Sexagenary Cycle table (the following section), look for 52 in the first column (No) and obtain Wood Rabbit (乙卯; yǐ-mǎo).

A shorter equivalent method[]

Start from the AD year, take directly the remainder mod 60, and look into column AD:

For a BC year: discard the minus sign, take the remainder of the year mod 60 and look into column BC:

When doing these conversions, year 246 BC cannot be treated as -246 AD due to the lack of a year 0 in the Gregorian AD/BC system.

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




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—jiànchǒuyuè, 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 jiànchǒuyuè ((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. [12] 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 term before 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.[13]

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) LichunJingzhe 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)

JingzheQingming 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) QingmingLixia 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) LixiaMangzhong 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) MangzhongXiaoshu 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) XiaoshuLiqiu 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) LiqiuBailu 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) BailuHanlu 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) HanluLidong 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) LidongDaxue 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) DaxueXiaohan 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) XiaohanLichun 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. ^ Nussbaum, 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), fig. 3 and p. 145; Smith (2011), p. 29.
  6. ^ Smith (2011), p. 28.
  7. ^ National Diet Library, "Calendar History; the Source" Archived January 6, 2013, at the Wayback Machine.; 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. ^ 新唐書•本紀六 肅宗、代宗(上元)二年……,九月壬寅,大赦,去“乾元大圣光天文武孝感”号,去“上元”号,称元年,以十一月为岁首,月以斗所建辰为名。赐文武官阶、勋、爵,版授侍老官,先授者叙进之。停四京号。
  13. ^ Entry "三正” in the standard dictionary 広辞苑, 東京:岩波.