The sexagenary cycle: all sixty stem-branch years

Ten heavenly stems (天干) run against twelve earthly branches (地支). Both advance by one each year, so the pair returns to its starting point after sixty years rather than after 120 — the cycle that gives 還暦 its name, and that puts 甲子 on 1924, 1984 and 2044 alike.

The ten stems

The ten heavenly stems, in order. Each element takes two stems, one yang and one yin.
PositionStemRomanisedElementPolarityVietnamese
Stem 1甲JiaWood (木)YangGiáp
Stem 2乙YiWood (木)YinẤt
Stem 3丙BingFire (火)YangBính
Stem 4丁DingFire (火)YinĐinh
Stem 5戊WuEarth (土)YangMậu
Stem 6己JiEarth (土)YinKỷ
Stem 7庚GengMetal (金)YangCanh
Stem 8辛XinMetal (金)YinTân
Stem 9壬RenWater (水)YangNhâm
Stem 10癸GuiWater (水)YinQuý

The twelve branches

The twelve earthly branches, in order, with the Chinese zodiac animal each carries.
PositionBranchRomanisedAnimalVietnamese
Branch 1子ZiRat (鼠)Tý
Branch 2丑ChouOx (牛)Sửu
Branch 3寅YinTiger (虎)Dần
Branch 4卯MaoRabbit (兔)Mão
Branch 5辰ChenDragon (龙)Thìn
Branch 6巳SiSnake (蛇)Tỵ
Branch 7午WuHorse (马)Ngọ
Branch 8未WeiGoat (羊)Mùi
Branch 9申ShenMonkey (猴)Thân
Branch 10酉YouRooster (鸡)Dậu
Branch 11戌XuDog (狗)Tuất
Branch 12亥HaiPig (猪)Hợi

The sixty combinations

Because the two lists advance together, a stem in an odd position can only ever meet a branch in an odd position. Half the 120 conceivable pairings therefore never occur, and the sixty that do are these.

All sixty stem-branch years in order, with three of the Gregorian years each one names. The cycle turns at Lunar New Year, not on 1 January.
PositionStem-branchRomanisedElement and animalCan chiYears
Cycle year 1甲子Jia-ZiYang Wood RatGiáp Tý1924, 1984, 2044
Cycle year 2乙丑Yi-ChouYin Wood OxẤt Sửu1925, 1985, 2045
Cycle year 3丙寅Bing-YinYang Fire TigerBính Dần1926, 1986, 2046
Cycle year 4丁卯Ding-MaoYin Fire RabbitĐinh Mão1927, 1987, 2047
Cycle year 5戊辰Wu-ChenYang Earth DragonMậu Thìn1928, 1988, 2048
Cycle year 6己巳Ji-SiYin Earth SnakeKỷ Tỵ1929, 1989, 2049
Cycle year 7庚午Geng-WuYang Metal HorseCanh Ngọ1930, 1990, 2050
Cycle year 8辛未Xin-WeiYin Metal GoatTân Mùi1931, 1991, 2051
Cycle year 9壬申Ren-ShenYang Water MonkeyNhâm Thân1932, 1992, 2052
Cycle year 10癸酉Gui-YouYin Water RoosterQuý Dậu1933, 1993, 2053
Cycle year 11甲戌Jia-XuYang Wood DogGiáp Tuất1934, 1994, 2054
Cycle year 12乙亥Yi-HaiYin Wood PigẤt Hợi1935, 1995, 2055
Cycle year 13丙子Bing-ZiYang Fire RatBính Tý1936, 1996, 2056
Cycle year 14丁丑Ding-ChouYin Fire OxĐinh Sửu1937, 1997, 2057
Cycle year 15戊寅Wu-YinYang Earth TigerMậu Dần1938, 1998, 2058
Cycle year 16己卯Ji-MaoYin Earth RabbitKỷ Mão1939, 1999, 2059
Cycle year 17庚辰Geng-ChenYang Metal DragonCanh Thìn1940, 2000, 2060
Cycle year 18辛巳Xin-SiYin Metal SnakeTân Tỵ1941, 2001, 2061
Cycle year 19壬午Ren-WuYang Water HorseNhâm Ngọ1942, 2002, 2062
Cycle year 20癸未Gui-WeiYin Water GoatQuý Mùi1943, 2003, 2063
Cycle year 21甲申Jia-ShenYang Wood MonkeyGiáp Thân1944, 2004, 2064
Cycle year 22乙酉Yi-YouYin Wood RoosterẤt Dậu1945, 2005, 2065
Cycle year 23丙戌Bing-XuYang Fire DogBính Tuất1946, 2006, 2066
Cycle year 24丁亥Ding-HaiYin Fire PigĐinh Hợi1947, 2007, 2067
Cycle year 25戊子Wu-ZiYang Earth RatMậu Tý1948, 2008, 2068
Cycle year 26己丑Ji-ChouYin Earth OxKỷ Sửu1949, 2009, 2069
Cycle year 27庚寅Geng-YinYang Metal TigerCanh Dần1950, 2010, 2070
Cycle year 28辛卯Xin-MaoYin Metal RabbitTân Mão1951, 2011, 2071
Cycle year 29壬辰Ren-ChenYang Water DragonNhâm Thìn1952, 2012, 2072
Cycle year 30癸巳Gui-SiYin Water SnakeQuý Tỵ1953, 2013, 2073
Cycle year 31甲午Jia-WuYang Wood HorseGiáp Ngọ1954, 2014, 2074
Cycle year 32乙未Yi-WeiYin Wood GoatẤt Mùi1955, 2015, 2075
Cycle year 33丙申Bing-ShenYang Fire MonkeyBính Thân1956, 2016, 2076
Cycle year 34丁酉Ding-YouYin Fire RoosterĐinh Dậu1957, 2017, 2077
Cycle year 35戊戌Wu-XuYang Earth DogMậu Tuất1958, 2018, 2078
Cycle year 36己亥Ji-HaiYin Earth PigKỷ Hợi1959, 2019, 2079
Cycle year 37庚子Geng-ZiYang Metal RatCanh Tý1960, 2020, 2080
Cycle year 38辛丑Xin-ChouYin Metal OxTân Sửu1961, 2021, 2081
Cycle year 39壬寅Ren-YinYang Water TigerNhâm Dần1962, 2022, 2082
Cycle year 40癸卯Gui-MaoYin Water RabbitQuý Mão1963, 2023, 2083
Cycle year 41甲辰Jia-ChenYang Wood DragonGiáp Thìn1964, 2024, 2084
Cycle year 42乙巳Yi-SiYin Wood SnakeẤt Tỵ1965, 2025, 2085
Cycle year 43丙午Bing-WuYang Fire HorseBính Ngọ1966, 2026, 2086
Cycle year 44丁未Ding-WeiYin Fire GoatĐinh Mùi1967, 2027, 2087
Cycle year 45戊申Wu-ShenYang Earth MonkeyMậu Thân1968, 2028, 2088
Cycle year 46己酉Ji-YouYin Earth RoosterKỷ Dậu1969, 2029, 2089
Cycle year 47庚戌Geng-XuYang Metal DogCanh Tuất1970, 2030, 2090
Cycle year 48辛亥Xin-HaiYin Metal PigTân Hợi1971, 2031, 2091
Cycle year 49壬子Ren-ZiYang Water RatNhâm Tý1972, 2032, 2092
Cycle year 50癸丑Gui-ChouYin Water OxQuý Sửu1973, 2033, 2093
Cycle year 51甲寅Jia-YinYang Wood TigerGiáp Dần1974, 2034, 2094
Cycle year 52乙卯Yi-MaoYin Wood RabbitẤt Mão1975, 2035, 2095
Cycle year 53丙辰Bing-ChenYang Fire DragonBính Thìn1976, 2036, 2096
Cycle year 54丁巳Ding-SiYin Fire SnakeĐinh Tỵ1977, 2037, 2097
Cycle year 55戊午Wu-WuYang Earth HorseMậu Ngọ1978, 2038, 2098
Cycle year 56己未Ji-WeiYin Earth GoatKỷ Mùi1979, 2039, 2099
Cycle year 57庚申Geng-ShenYang Metal MonkeyCanh Thân1980, 2040, 2100
Cycle year 58辛酉Xin-YouYin Metal RoosterTân Dậu1981, 2041, 2101
Cycle year 59壬戌Ren-XuYang Water DogNhâm Tuất1982, 2042, 2102
Cycle year 60癸亥Gui-HaiYin Water PigQuý Hợi1983, 2043, 2103

How this table is produced, and how it was checked

The pairings are arithmetic, not a lookup: the stem is the year modulo ten and the branch is the year modulo twelve, both offset so that 1984 comes out as 甲子, the first year of the current cycle. This page and the calculator call the same function, so a table here and a number there cannot disagree.

The arithmetic is checked against years whose sexagenary names are part of the historical record rather than against the code's own output — if a function is wrong, its output is wrong consistently.

Years named for their place in the cycle.
YearComputed here asKnown as
1894甲午 (Jia-Wu)甲午戰爭 — the First Sino-Japanese War, named for the year
1911辛亥 (Xin-Hai)辛亥革命 — the Xinhai Revolution, named for the year
1898戊戌 (Wu-Xu)戊戌變法 — the Hundred Days’ Reform, named for the year

One thing deliberately left out. Vietnam's zodiac assigns a different animal to two of the branches — Mão is the cat rather than the rabbit — so the can chi column above gives the branch name only, and no Vietnamese animal is claimed anywhere on this site until it has been checked against a Vietnamese source.

Which year you belong to

The sexagenary year turns at Lunar New Year, which falls between 21 January and 21 February, so anyone born in January or the first days of February belongs to the previous year's pair — not the one matching their Gregorian birth year. The Lunar New Year table gives that boundary date for every year from 1901 to 2099.

The cycle is also applied to months, days and two-hour periods, and was historically used for all four at once. This site uses it for years only, which is the use that survives in ordinary speech.