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.
Position	Stem	Romanised	Element	Polarity	Vietnamese
Stem 1	甲	Jia	Wood (木)	Yang	Giáp
Stem 2	乙	Yi	Wood (木)	Yin	Ất
Stem 3	丙	Bing	Fire (火)	Yang	Bính
Stem 4	丁	Ding	Fire (火)	Yin	Đinh
Stem 5	戊	Wu	Earth (土)	Yang	Mậu
Stem 6	己	Ji	Earth (土)	Yin	Kỷ
Stem 7	庚	Geng	Metal (金)	Yang	Canh
Stem 8	辛	Xin	Metal (金)	Yin	Tân
Stem 9	壬	Ren	Water (水)	Yang	Nhâm
Stem 10	癸	Gui	Water (水)	Yin	Quý

The twelve branches

The twelve earthly branches, in order, with the Chinese zodiac animal each carries.
Position	Branch	Romanised	Animal	Vietnamese
Branch 1	子	Zi	Rat (鼠)	Tý
Branch 2	丑	Chou	Ox (牛)	Sửu
Branch 3	寅	Yin	Tiger (虎)	Dần
Branch 4	卯	Mao	Rabbit (兔)	Mão
Branch 5	辰	Chen	Dragon (龙)	Thìn
Branch 6	巳	Si	Snake (蛇)	Tỵ
Branch 7	午	Wu	Horse (马)	Ngọ
Branch 8	未	Wei	Goat (羊)	Mùi
Branch 9	申	Shen	Monkey (猴)	Thân
Branch 10	酉	You	Rooster (鸡)	Dậu
Branch 11	戌	Xu	Dog (狗)	Tuất
Branch 12	亥	Hai	Pig (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.
Position	Stem-branch	Romanised	Element and animal	Can chi	Years
Cycle year 1	甲子	Jia-Zi	Yang Wood Rat	Giáp Tý	1924, 1984, 2044
Cycle year 2	乙丑	Yi-Chou	Yin Wood Ox	Ất Sửu	1925, 1985, 2045
Cycle year 3	丙寅	Bing-Yin	Yang Fire Tiger	Bính Dần	1926, 1986, 2046
Cycle year 4	丁卯	Ding-Mao	Yin Fire Rabbit	Đinh Mão	1927, 1987, 2047
Cycle year 5	戊辰	Wu-Chen	Yang Earth Dragon	Mậu Thìn	1928, 1988, 2048
Cycle year 6	己巳	Ji-Si	Yin Earth Snake	Kỷ Tỵ	1929, 1989, 2049
Cycle year 7	庚午	Geng-Wu	Yang Metal Horse	Canh Ngọ	1930, 1990, 2050
Cycle year 8	辛未	Xin-Wei	Yin Metal Goat	Tân Mùi	1931, 1991, 2051
Cycle year 9	壬申	Ren-Shen	Yang Water Monkey	Nhâm Thân	1932, 1992, 2052
Cycle year 10	癸酉	Gui-You	Yin Water Rooster	Quý Dậu	1933, 1993, 2053
Cycle year 11	甲戌	Jia-Xu	Yang Wood Dog	Giáp Tuất	1934, 1994, 2054
Cycle year 12	乙亥	Yi-Hai	Yin Wood Pig	Ất Hợi	1935, 1995, 2055
Cycle year 13	丙子	Bing-Zi	Yang Fire Rat	Bính Tý	1936, 1996, 2056
Cycle year 14	丁丑	Ding-Chou	Yin Fire Ox	Đinh Sửu	1937, 1997, 2057
Cycle year 15	戊寅	Wu-Yin	Yang Earth Tiger	Mậu Dần	1938, 1998, 2058
Cycle year 16	己卯	Ji-Mao	Yin Earth Rabbit	Kỷ Mão	1939, 1999, 2059
Cycle year 17	庚辰	Geng-Chen	Yang Metal Dragon	Canh Thìn	1940, 2000, 2060
Cycle year 18	辛巳	Xin-Si	Yin Metal Snake	Tân Tỵ	1941, 2001, 2061
Cycle year 19	壬午	Ren-Wu	Yang Water Horse	Nhâm Ngọ	1942, 2002, 2062
Cycle year 20	癸未	Gui-Wei	Yin Water Goat	Quý Mùi	1943, 2003, 2063
Cycle year 21	甲申	Jia-Shen	Yang Wood Monkey	Giáp Thân	1944, 2004, 2064
Cycle year 22	乙酉	Yi-You	Yin Wood Rooster	Ất Dậu	1945, 2005, 2065
Cycle year 23	丙戌	Bing-Xu	Yang Fire Dog	Bính Tuất	1946, 2006, 2066
Cycle year 24	丁亥	Ding-Hai	Yin Fire Pig	Đinh Hợi	1947, 2007, 2067
Cycle year 25	戊子	Wu-Zi	Yang Earth Rat	Mậu Tý	1948, 2008, 2068
Cycle year 26	己丑	Ji-Chou	Yin Earth Ox	Kỷ Sửu	1949, 2009, 2069
Cycle year 27	庚寅	Geng-Yin	Yang Metal Tiger	Canh Dần	1950, 2010, 2070
Cycle year 28	辛卯	Xin-Mao	Yin Metal Rabbit	Tân Mão	1951, 2011, 2071
Cycle year 29	壬辰	Ren-Chen	Yang Water Dragon	Nhâm Thìn	1952, 2012, 2072
Cycle year 30	癸巳	Gui-Si	Yin Water Snake	Quý Tỵ	1953, 2013, 2073
Cycle year 31	甲午	Jia-Wu	Yang Wood Horse	Giáp Ngọ	1954, 2014, 2074
Cycle year 32	乙未	Yi-Wei	Yin Wood Goat	Ất Mùi	1955, 2015, 2075
Cycle year 33	丙申	Bing-Shen	Yang Fire Monkey	Bính Thân	1956, 2016, 2076
Cycle year 34	丁酉	Ding-You	Yin Fire Rooster	Đinh Dậu	1957, 2017, 2077
Cycle year 35	戊戌	Wu-Xu	Yang Earth Dog	Mậu Tuất	1958, 2018, 2078
Cycle year 36	己亥	Ji-Hai	Yin Earth Pig	Kỷ Hợi	1959, 2019, 2079
Cycle year 37	庚子	Geng-Zi	Yang Metal Rat	Canh Tý	1960, 2020, 2080
Cycle year 38	辛丑	Xin-Chou	Yin Metal Ox	Tân Sửu	1961, 2021, 2081
Cycle year 39	壬寅	Ren-Yin	Yang Water Tiger	Nhâm Dần	1962, 2022, 2082
Cycle year 40	癸卯	Gui-Mao	Yin Water Rabbit	Quý Mão	1963, 2023, 2083
Cycle year 41	甲辰	Jia-Chen	Yang Wood Dragon	Giáp Thìn	1964, 2024, 2084
Cycle year 42	乙巳	Yi-Si	Yin Wood Snake	Ất Tỵ	1965, 2025, 2085
Cycle year 43	丙午	Bing-Wu	Yang Fire Horse	Bính Ngọ	1966, 2026, 2086
Cycle year 44	丁未	Ding-Wei	Yin Fire Goat	Đinh Mùi	1967, 2027, 2087
Cycle year 45	戊申	Wu-Shen	Yang Earth Monkey	Mậu Thân	1968, 2028, 2088
Cycle year 46	己酉	Ji-You	Yin Earth Rooster	Kỷ Dậu	1969, 2029, 2089
Cycle year 47	庚戌	Geng-Xu	Yang Metal Dog	Canh Tuất	1970, 2030, 2090
Cycle year 48	辛亥	Xin-Hai	Yin Metal Pig	Tân Hợi	1971, 2031, 2091
Cycle year 49	壬子	Ren-Zi	Yang Water Rat	Nhâm Tý	1972, 2032, 2092
Cycle year 50	癸丑	Gui-Chou	Yin Water Ox	Quý Sửu	1973, 2033, 2093
Cycle year 51	甲寅	Jia-Yin	Yang Wood Tiger	Giáp Dần	1974, 2034, 2094
Cycle year 52	乙卯	Yi-Mao	Yin Wood Rabbit	Ất Mão	1975, 2035, 2095
Cycle year 53	丙辰	Bing-Chen	Yang Fire Dragon	Bính Thìn	1976, 2036, 2096
Cycle year 54	丁巳	Ding-Si	Yin Fire Snake	Đinh Tỵ	1977, 2037, 2097
Cycle year 55	戊午	Wu-Wu	Yang Earth Horse	Mậu Ngọ	1978, 2038, 2098
Cycle year 56	己未	Ji-Wei	Yin Earth Goat	Kỷ Mùi	1979, 2039, 2099
Cycle year 57	庚申	Geng-Shen	Yang Metal Monkey	Canh Thân	1980, 2040, 2100
Cycle year 58	辛酉	Xin-You	Yin Metal Rooster	Tân Dậu	1981, 2041, 2101
Cycle year 59	壬戌	Ren-Xu	Yang Water Dog	Nhâm Tuất	1982, 2042, 2102
Cycle year 60	癸亥	Gui-Hai	Yin Water Pig	Quý Hợi	1983, 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.
Year	Computed here as	Known 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.