View source for Physics:Sexagenary cycle

{{short description|Historical method for reckoning time in China}}
{{chinese
|p=liùshí gānzhī
|mi={{IPAc-cmn|l|iu|4|.|sh|i|2|-|g|an|1|.|zh|i|1}}
|altname=Stems-and-Branches
|p2=gānzhī
|mi2={{IPAc-cmn|g|an|1|.|zh|i|1}}
}}

The '''sexagenary cycle''', also known as the '''Stems-and-Branches''' or '''ganzhi''' ({{lang-zh|干支|gānzhī}}), is a cycle of sixty terms, each corresponding to one year, thus a total of sixty years for one cycle, historically used for recording time in China and the rest of the [[Place:East Asian cultural sphere|East Asian cultural sphere]].<ref>{{cite encyclopedia |first=Louis-Frédéric |last=Nussbaum |translator-first=Käthe |translator-last=Roth |date=2005 |url=https://books.google.com/books?id=p2QnPijAEmEC&pg=PA420 |title=Jikkan-jūnishi |encyclopedia=Japan Encyclopedia |page=420|isbn=9780674017535 }}</ref> 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.{{sfn|Smith|2011|pages=1, 28}} 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, and to a lesser extent, in Mainland China.<ref>For example, the annual Lunar New Year's Eve ''Chunwan'' gala has continued to announce the sexagenary term of the upcoming year (庚子, ''gengzi'' for 2020).</ref>

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 used in the names of many historical events, such as the Chinese Xinhai Revolution, the Japanese Boshin War, the Korean Imjin War and the Vietnamese Famine of Ất Dậu, Tết Mậu Thân. It also continues to have a role in contemporary [[Philosophy:Chinese astrology|Chinese astrology]] and fortune telling. There are some parallels in this with the current 60-year cycle of the  [[Physics:Samvatsara|Hindu calendar]].

==Overview==
[[File:Changchun-Temple-Jiazi-Dian-a-row-of-Tai-Sui-0340.jpg|thumb|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 [[Unsolved:Earthly Branches|Earthly Branches]] representing the years of [[Astronomy:Jupiter|Jupiter]]'s duodecennial orbital cycle. The first term ''jiǎzǐ'' ({{lang|zh|{{linktext|甲子}}}}) combines the first heavenly stem with the first earthly branch. The second term ''yǐchǒu'' ({{lang|zh|{{linktext|乙丑}}}}) combines the second stem with the second branch. This pattern continues until both cycles conclude simultaneously with ''guǐhài'' ({{lang|zh|{{linktext|癸亥}}}}), after which it begins again at ''jiǎzǐ''. This termination at ten and twelve's [[Least common multiple|least common multiple]] leaves half of the combinations—such as ''jiǎchǒu'' ({{lang|zh|甲丑}})—unused; this is traditionally explained by reference to pairing the stems and branches according to their [[Yin and yang|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.<ref>For the Akan calendar, see {{harv|Bartle|1978|}}.</ref>

==History==
[[File:Heji 37986 Ganzhi table.jpg|thumb|right|upright|Bone inscribed with a table of the sexagenary cycle, dated to the early 11th century BC]]
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 {{Circa|1100 BC}}.<ref>{{Cite book|last=Selin|first=Helaine|url=https://books.google.com/books?id=DbsqBgAAQBAJ&pg=PA390|title=Mathematics Across Cultures: The History of Non-Western Mathematics|date=2012-12-06|publisher=Springer Science & Business Media|isbn=978-94-011-4301-1|pages=390|language=en}}</ref> 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.{{sfn|Smith|2011|pages=24, 26–27}}

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 ({{lang|und-Hani|秦始皇}}), 246 BC, is noted on the diagram next to the position of the 60-cycle term ''yǐ-mǎo'' ({{lang|und-Hani|乙卯}}, 52 of 60), corresponding to that year.{{sfn|Kalinowski|2007|page=145, fig. 3}} {{sfn|Smith|2011|page=29}} 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:{{sfn|Smith|2011|page=28}} the year 1984 began the present cycle (a {{lang|und-Hani|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 {{lang|und-Hani|己丑}} year (coinciding roughly with 2009) began on January 26, 2009. (However, for astrology, the year begins with the first solar term "Lìchūn" ({{lang|und-Hani|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.<ref>{{cite web |publisher=National Diet Library |url=http://www.ndl.go.jp/koyomi/e/history/02_index1.html |title=Calendar History; the Source |archive-url=https://web.archive.org/web/20130106054946/http://www.ndl.go.jp/koyomi/e/history/02_index1.html |archive-date=January 6, 2013 |access-date=January 1, 2013}}</ref>

The Korean ({{lang|ko|환갑; 還甲}} hwangap) and Japanese tradition ({{lang|ja|還暦}} ''kanreki'') of celebrating the 60th birthday (literally 'return of calendar') reflects the influence of the sexagenary cycle as a count of years.<ref>{{cite encyclopedia |encyclopedia=Encyclopedia of Shinto |url=http://eos.kokugakuin.ac.jp/modules/xwords/entry.php?entryID=1040 |title=Kanreki |access-date=January 1, 2013}}</ref>

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 [[Unsolved:Rat (zodiac)|Rat]], the first year of the Tibetan cycle is the year of the Fire [[Unsolved:Rabbit (zodiac)|Rabbit]] ({{lang|und-Hani|丁卯}}—''dīng-mǎo'', year 4 on the Chinese cycle).<ref>{{cite book |last=Chattopadhyaya |first=Alaka |date=1999 |url=https://books.google.com/books?id=H8Ssa5r7MZkC&pg=PA566 |title=Atisa and Tibet: Life and Works of Dipamkara Srijnana in relation to the history and religion of Tibet |pages=566–568|publisher=Motilal Banarsidass Publ. |isbn=9788120809284 }}</ref>

==Ten Heavenly Stems==
{| class="wikitable"
!rowspan=2|No.
!rowspan=2|Heavenly<br>Stem
!colspan=4|Chinese<br>name
!colspan=2|Japanese<br>name
!colspan=2|Korean<br>name
!rowspan=2|Vietnamese<br>name
!rowspan=2|[[Yin and yang|Yin Yang]]
!rowspan=2|[[Philosophy:Wuxing (Chinese philosophy)|Wu Xing]]
|-
!Mandarin<br>([[Pinyin]])
![[Social:Cantonese|Cantonese]]<br>([[Social:Jyutping|Jyutping]])
!Middle Chinese<br>(Baxter)
![[Social:Old Chinese|Old Chinese]]<br>(Baxter–Sagart)
!Onyomi
!Kunyomi with<br>corresponding [[Social:Kanji|kanji]]
![[Revised Romanization of Korean|Romanized]]
!Hangul
|- align="center"
|1||{{lang|zh-Hant|甲}}||jiǎ||gaap<sup>3</sup>||''kæp''||*[k]ˤr[a]p||kō ({{lang|ja|こう}})||kinoe ({{lang|ja|木の兄}})||gap||{{lang|ko|갑}}||{{lang|vi|giáp|italic=no}}||yang
|rowspan=2 |wood
|- align="center"
|2||{{lang|zh-Hant|乙}}||yǐ||jyut<sup>3</sup>||''ʔit''||*qrət||otsu ({{lang|ja|おつ}})||kinoto ({{lang|ja|木の弟}})||eul||{{lang|ko|을}}||{{lang|vi|ất|italic=no}}||yin
|- align="center"
|3||{{lang|zh-Hant|丙}}||bǐng||bing<sup>2</sup>||''pjæng<sup>X</sup>''||*praŋʔ||hei ({{lang|ja|へい}})||hinoe ({{lang|ja|火の兄}})||byeong||{{lang|ko|병}}||{{lang|vi|bính|italic=no}}||yang
|rowspan=2 |[[Unsolved:Fire (classical element)|fire]]
|- align="center"
|4||{{lang|zh-Hant|丁}}||dīng||ding<sup>1</sup>||''teng''||*tˤeŋ||tei ({{lang|ja|てい}})||hinoto ({{lang|ja|火の弟}})||jeong||{{lang|ko|정}}||{{lang|vi|đinh|italic=no}}||yin
|- align="center"
|5||{{lang|zh-Hant|戊}}||wù||mou<sup>6</sup>||''muw<sup>H</sup>''||*m(r)uʔ-s (~ *m(r)uʔ)||bo ({{lang|ja|ぼ}})||tsuchinoe ({{lang|ja|土の兄}})||mu||{{lang|ko|무}}||{{lang|vi|mậu|italic=no}}||yang
|rowspan=2 |[[Unsolved:Earth (classical element)|earth]]
|- align="center"
|6||{{lang|zh-Hant|己}}||jǐ||gei<sup>2</sup>||''ki<sup>X</sup>''||*k(r)əʔ||ki ({{lang|ja|き}})||tsuchinoto ({{lang|ja|土の弟}})||gi||{{lang|ko|기}}||{{lang|vi|kỷ|italic=no}}||yin
|- align="center"
|7||{{lang|zh-Hant|庚}}||gēng||gang<sup>1</sup>||''kæng''||*kˤraŋ||kō ({{lang|ja|こう}})||kanoe ({{lang|ja|金の兄}})||gyeong||{{lang|ko|경}}||{{lang|vi|canh|italic=no}}||yang
| rowspan=2 |metal
|- align="center"
|8||{{lang|zh-Hant|辛}}||xīn||san<sup>1</sup>||''sin''||*si[n]||shin ({{lang|ja|しん}})||kanoto ({{lang|ja|金の弟}})||sin||{{lang|ko|신}}||{{lang|vi|tân|italic=no}}||yin
|- align="center"
|9||{{lang|zh-Hant|壬}}||rén||jam<sup>4</sup>||''nyim''||*n[ə]m||jin ({{lang|ja|じん}})||mizunoe ({{lang|ja|水の兄}})||im||{{lang|ko|임}}||{{lang|vi|nhâm|italic=no}}||yang
| rowspan=2 |[[Chemistry:Water (classical element)|water]]
|- align="center"
|10||{{lang|zh-Hant|癸}}||guǐ||gwai<sup>3</sup>||''kjwij<sup>X</sup>''||*kʷijʔ||ki ({{lang|ja|き}})||mizunoto ({{lang|ja|水の弟}})||gye||{{lang|ko|계}}||{{lang|vi|quý|italic=no}}||yin
|}

==Twelve Earthly Branches==
{| class="wikitable"
!rowspan=2|No.
!rowspan=2|Earthly<br>Branch
!colspan=4|Chinese<br>name
!colspan=2|Japanese<br>name
!colspan=2|Korean<br>name
!rowspan=2|Vietnamese<br>name
!rowspan=2|Vietnamese<br>zodiac
!rowspan=2|[[Unsolved:Chinese zodiac|Chinese<br>zodiac]]
!rowspan=2|Corresponding<br>hours
|-
!Mandarin<br>([[Pinyin]])
![[Social:Cantonese|Cantonese]]<br>([[Social:Jyutping|Jyutping]])
!Middle Chinese<br>(Baxter)
![[Social:Old Chinese|Old Chinese]]<br>(Baxter–Sagart)
!Onyomi
!Kunyomi
![[Revised Romanization of Korean|Romanized]]
!Hangul
|- align="center"
|1||{{lang|zh-Hant|子}}||zǐ||zi<sup>2</sup>||''tsi<sup>X</sup>''||*[ts]əʔ||shi ({{lang|ja|し}})||ne ({{lang|ja|ね)}}||ja||{{lang|ko|자}}||{{lang|vi|tý|italic=no}}||[[Unsolved:Rat (zodiac)|Rat]] ({{lang|vi|chuột|italic=no}} {{lang|vi-hani|𤝞}})
|[[Unsolved:Rat (zodiac)|Rat]] ({{lang|zh-Hant|鼠}})||11 p.m. to 1 a.m.
|- align="center"
|2||{{lang|zh-Hant|丑}}||chǒu||cau<sup>2</sup>||''trhjuw<sup>X</sup>''||*[n̥]ruʔ||chū ({{lang|ja|ちゅう}})||ushi ({{lang|ja|うし}})||chuk||{{lang|ko|축}}||{{lang|vi|sửu|italic=no}}||[[Unsolved:Water buffalo (zodiac)|Water buffalo]] ({{lang|vi|trâu|italic=no}} {{lang|vi-hani|𤛠}})
|[[Biology:Ox (zodiac)|Ox]] ({{lang|zh-Hant|牛}})||1 to 3 a.m.
|- align="center"
|3||{{lang|zh-Hant|寅}}||yín||jan<sup>4</sup>||''yij''||*[ɢ] (r)ər||in ({{lang|ja|いん}})||tora ({{lang|ja|とら}})||in||{{lang|ko|인}}||{{lang|vi|dần|italic=no}}||[[Unsolved:Tiger (zodiac)|Tiger]] ({{lang|vi|hổ|italic=no}} {{vi-nom|虎}}/{{lang|vi|cọp|italic=no}} {{lang|vi-hani|𧲫}})
|[[Unsolved:Tiger (zodiac)|Tiger]] ({{lang|zh-Hant|虎}})||3 to 5 a.m.
|- align="center"
|4||{{lang|zh-Hant|卯}}||mǎo||maau<sup>5</sup>||''mæw<sup>X</sup>''||*mˤruʔ||bō ({{lang|ja|ぼう}})||u ({{lang|ja|う}})||myo||{{lang|ko|묘}}||{{lang|vi|mão/mẹo|italic=no}}||[[Unsolved:Cat (zodiac)|Cat]] ({{lang|vi|mèo|italic=no}} {{lang|vi-hani|猫}})
|[[Unsolved:Rabbit (zodiac)|Rabbit]] ({{lang|zh-Hant|兔}})||5 to 7 a.m.
|- align="center"
|5||{{lang|zh-Hant|辰}}||chén||san<sup>4</sup>||''dzyin''||*[d]ər||shin ({{lang|ja|しん}})||tatsu ({{lang|ja|たつ}})||jin||{{lang|ko|진}}||{{lang|vi|thìn|italic=no}}||[[Unsolved:Dragon (zodiac)|Dragon]] ({{lang|vi|rồng|italic=no}} {{lang|vi-hani|龍}})
|[[Unsolved:Dragon (zodiac)|Dragon]] ({{lang|zh-Hant|龍}})||7 to 9 a.m.
|- align="center"
|6||{{lang|zh-Hant|巳}}||sì||zi<sup>6</sup>||''zi<sup>X</sup>''||*s-[ɢ]əʔ||shi ({{lang|ja|し}})||mi ({{lang|ja|み}})||sa||{{lang|ko|사}}||{{lang|vi|tỵ|italic=no}}||[[Unsolved:Snake (zodiac)|Snake]] ({{lang|vi|rắn|italic=no}} {{lang|vi-hani|𧋻}})
|[[Unsolved:Snake (zodiac)|Snake]] ({{lang|zh-Hant|蛇}})||9 to 11 a.m.
|- align="center"
|7||{{lang|zh-Hant|午}}||wǔ||ng<sup>5</sup>||''ngu<sup>X</sup>''||*[m].qʰˤaʔ||go ({{lang|ja|ご}})||uma ({{lang|ja|うま}})||o||{{lang|ko|오}}||{{lang|vi|ngọ|italic=no}}||[[Unsolved:Horse (zodiac)|Horse]] ({{lang|vi|ngựa|italic=no}} {{lang|vi-hani|馭}})
|[[Unsolved:Horse (zodiac)|Horse]] ({{lang|zh-Hant|馬}})||11 a.m. to 1 p.m.
|- align="center"
|8||{{lang|zh-Hant|未}}||wèi||mei<sup>6</sup>||''mjɨj<sup>H</sup>''||*m[ə]t-s||mi ({{lang|ja|み}}) ''or'' bi ({{lang|ja|び}})||hitsuji ({{lang|ja|ひつじ}})||mi||{{lang|ko|미}}||{{lang|vi|mùi|italic=no}}||[[Unsolved:Goat (zodiac)|Goat]] ({{lang|vi|dê|italic=no}} {{lang|vi-hani|羝}})
|[[Unsolved:Goat (zodiac)|Goat]] ({{lang|zh-Hant|羊}})||1 to 3 p.m.
|- align="center"
|9||{{lang|zh-Hant|申}}||shēn||san<sup>1</sup>||''syin''||*l̥i[n]||shin ({{lang|ja|しん}})||saru ({{lang|ja|さる}})||sin||{{lang|ko|신}}||{{lang|vi|thân|italic=no}}||[[Unsolved:Monkey (zodiac)|Monkey]] ({{lang|vi|khỉ|italic=no}} {{lang|vi-hani|𤠳}})
|[[Unsolved:Monkey (zodiac)|Monkey]] ({{lang|zh-Hant|猴}})||3 to 5 p.m.
|- align="center"
|10||{{lang|zh-Hant|酉}}||yǒu||jau<sup>5</sup>||''yuw<sup>X</sup>''||*N-ruʔ||yū ({{lang|ja|ゆう}})||tori ({{lang|ja|とり}})||yu||{{lang|ko|유}}||{{lang|vi|dậu|italic=no}}||[[Unsolved:Rooster (zodiac)|Rooster]] ({{lang|vi|gà|italic=no}} {{lang|vi-hani|𪂮}})
|[[Unsolved:Rooster (zodiac)|Rooster]] ({{lang|zh-Hant|雞}})||5 to 7 p.m.
|- align="center"
|11||{{lang|zh-Hant|戌}}||xū||seot<sup>1</sup>||''swit''||*s.mi[t]||jutsu ({{lang|ja|じゅつ}})||inu ({{lang|ja|いぬ}})||sul||{{lang|ko|술}}||{{lang|vi|tuất|italic=no}}||[[Unsolved:Dog (zodiac)|Dog]] ({{lang|vi|chó|italic=no}} {{lang|vi-hani|㹥}})
|[[Unsolved:Dog (zodiac)|Dog]] ({{lang|zh-Hant|狗}})||7 to 9 p.m.
|- align="center"
|12||{{lang|zh-Hant|亥}}||hài||hoi<sup>6</sup>||''hoj<sup>X</sup>''||*[g]ˤəʔ||gai ({{lang|ja|がい}})||i ({{lang|ja|い}})||hae||{{lang|ko|해}}||{{lang|vi|hợi|italic=no}}||[[Unsolved:Pig (zodiac)|Pig]] ({{lang|vi|lợn|italic=no}} {{lang|vi-hani|𤞼}}/{{lang|vi|heo|italic=no}} {{lang|vi-hani|㺧}})
|[[Unsolved:Pig (zodiac)|Pig]] ({{lang|zh-Hant|豬}})||9 to 11 p.m.
|}
<nowiki>*</nowiki>The names of several animals can be translated into English in several different ways. The Vietnamese [[Unsolved:Earthly Branches|Earthly Branches]] use cat instead of [[Unsolved:Rabbit (zodiac)|Rabbit]].

==Sexagenary years==
{|class="wikitable collapsible collapsed"
!No.||Stem-Branch||Mandarin Chinese [[Pinyin]]||Korean||Japanese||Vietnamese||Associations||AD||BC||Current Cycle
|- align="center"
|1||甲子||jiǎ-zǐ||gapja 갑자||{{unbulleted list|kōshi|kasshi|kinoe-ne}}||Giáp Tý||Yang Wood [[Unsolved:Rat (zodiac)|Rat]]||4||57||1984
|- align="center"
|2||乙丑||yǐ-chǒu||eulchuk 을축||{{unbulleted list|itchū|kinoto-ushi}}||Ất Sửu||Yin Wood [[Biology:Ox (zodiac)|Ox]]||5||56||1985
|- align="center"
|3||丙寅||bǐng-yín||byeongin 병인||{{unbulleted list|heiin|hinoe-tora}}||Bính Dần||Yang Fire [[Unsolved:Tiger (zodiac)|Tiger]]||6||55||1986
|- align="center"
|4||丁卯||dīng-mǎo||jeongmyo 정묘||{{unbulleted list|teibō|hinoto-u}}||Đinh Mão||Yin Fire [[Unsolved:Rabbit (zodiac)|Rabbit]]||7||54||1987
|- align="center"
|5||戊辰||wù-chén||mujin 무진||{{unbulleted list|boshin|tsuchinoe-tatsu}}||Mậu Thìn||Yang Earth [[Unsolved:Dragon (zodiac)|Dragon]]||8||53||1988
|- align="center"
|6||己巳||jǐ-sì||gisa 기사||{{unbulleted list|kishi|tsuchinoto-mi}}||Kỷ Tỵ||Yin Earth [[Unsolved:Snake (zodiac)|Snake]]||9||52||1989
|- align="center"
|7||庚午||gēng-wǔ||gyeongo 경오||{{unbulleted list|kōgo|kanoe-uma}}||Canh Ngọ||Yang Metal [[Unsolved:Horse (zodiac)|Horse]]||10||51||1990
|- align="center"
|8||辛未||xīn-wèi||sinmi 신미||{{unbulleted list|shinbi|kanoto-hitsuji}}||Tân Mùi||Yin Metal [[Unsolved:Goat (zodiac)|Goat]]||11||50||1991
|- align="center"
|9||壬申||rén-shēn||imsin 임신||{{unbulleted list|jinshin|mizunoe-saru}}||Nhâm Thân||Yang Water [[Unsolved:Monkey (zodiac)|Monkey]]||12||49||1992
|- align="center"
|10||癸酉||guǐ-yǒu||gyeyu 계유||{{unbulleted list|kiyū|mizunoto-tori}}||Quý Dậu||Yin Water [[Unsolved:Rooster (zodiac)|Rooster]]||13||48||1993
|- align="center"
|11||甲戌||jiǎ-xū||gapsul 갑술||{{unbulleted list|kōjutsu|kinoe-inu}}||Giáp Tuất||Yang Wood [[Unsolved:Dog (zodiac)|Dog]]||14||47||1994
|- align="center"
|12||乙亥||yǐ-hài||eulhae 을해||{{unbulleted list|itsugai|kinoto-i}}||Ât Hợi||Yin Wood [[Unsolved:Pig (zodiac)|Pig]]||15||46||1995
|- align="center"
|13||丙子||bǐng-zǐ||byeongja 병자||{{unbulleted list|heishi|hinoe-ne}}||Bính Tý||Yang Fire [[Unsolved:Rat (zodiac)|Rat]]||16||45||1996
|- align="center"
|14||丁丑||dīng-chǒu||jeongchuk 정축||{{unbulleted list|teichū|hinoto-ushi}}||Đinh Sửu||Yin Fire [[Biology:Ox (zodiac)|Ox]]||17||44||1997
|- align="center"
|15||戊寅||wù-yín||muin 무인||{{unbulleted list|boin|tsuchinoe-tora}}||Mậu Dần||Yang Earth [[Unsolved:Tiger (zodiac)|Tiger]]||18||43||1998
|- align="center"
|16||己卯||jǐ-mǎo||gimyo 기묘||{{unbulleted list|kibō|tsuchinoto-u}}||Kỷ Mão||Yin Earth [[Unsolved:Rabbit (zodiac)|Rabbit]]||19||42||1999
|- align="center"
|17||庚辰||gēng-chén||gyeongjin 경진||{{unbulleted list|kōshin|kanoe-tatsu}}||Canh Thìn||Yang Metal [[Unsolved:Dragon (zodiac)|Dragon]]||20||41||2000
|- align="center"
|18||辛巳||xīn-sì||sinsa 신사||{{unbulleted list|shinshi|kanoto-mi}}||Tân Tỵ||Yin Metal [[Unsolved:Snake (zodiac)|Snake]]||21||40||2001
|- align="center"
|19||壬午||rén-wǔ||imo 임오||{{unbulleted list|jingo|mizunoe-uma}}||Nhâm Ngọ||Yang Water [[Unsolved:Horse (zodiac)|Horse]]||22||39||2002
|- align="center"
|20||癸未||guǐ-wèi||gyemi 계미||{{unbulleted list|kibi|mizunoto-hitsuji}}||Quý Mùi||Yin Water [[Unsolved:Goat (zodiac)|Goat]]||23||38||2003
|- align="center"
|21||甲申||jiǎ-shēn||gapsin 갑신||{{unbulleted list|kōshin|kinoe-saru}}||Giáp Thân||Yang Wood [[Unsolved:Monkey (zodiac)|Monkey]]||24||37||2004
|- align="center"
|22||乙酉||yǐ-yǒu||euryu 을유||{{unbulleted list|itsuyū|kinoto-tori}}||Ất Dậu||Yin Wood [[Unsolved:Rooster (zodiac)|Rooster]]||25||36||2005
|- align="center"
|23||丙戌||bǐng-xū||byeongsul 병술||{{unbulleted list|heijutsu|hinoe-inu}}||Bính Tuất||Yang Fire [[Unsolved:Dog (zodiac)|Dog]]||26||35||2006
|- align="center"
|24||丁亥||dīng-hài||jeonghae 정해||{{unbulleted list|teigai|hinoto-i}}||Đinh Hợi||Yin Fire [[Unsolved:Pig (zodiac)|Pig]]||27||34||2007
|- align="center"
|25||戊子||wù-zǐ||muja 무자||{{unbulleted list|boshi|tsuchinoe-ne}}||Mậu Tý||Yang Earth [[Unsolved:Rat (zodiac)|Rat]]||28||33||2008
|- align="center"
|26||己丑||jǐ-chǒu||gichuk 기축||{{unbulleted list|kichū|tsuchinoto-ushi}}||Kỷ Sửu||Yin Earth [[Biology:Ox (zodiac)|Ox]]||29||32||2009
|- align="center"
|27||庚寅||gēng-yín||gyeongin 경인||{{unbulleted list|kōin|kanoe-tora}}||Canh Dần||Yang Metal [[Unsolved:Tiger (zodiac)|Tiger]]||30||31||2010
|- align="center"
|28||辛卯||xīn-mǎo||sinmyo 신묘||{{unbulleted list|shinbō|kanoto-u}}||Tân Mão||Yin Metal [[Unsolved:Rabbit (zodiac)|Rabbit]]||31||30||2011
|- align="center"
|29||壬辰||rén-chén||imjin 임진||{{unbulleted list|jinshin|mizunoe-tatsu}}||Nhâm Thìn||Yang Water [[Unsolved:Dragon (zodiac)|Dragon]]||32||29||2012
|- align="center"
|30||癸巳||guǐ-sì||gyesa 계사||{{unbulleted list|kishi|mizunoto-mi}}||Quý Tỵ||Yin Water [[Unsolved:Snake (zodiac)|Snake]]||33||28||2013
|- align="center" 
|31||甲午||jiǎ-wǔ||gabo 갑오||{{unbulleted list|kōgo|kinoe-uma}}||Giáp Ngọ||Yang Wood [[Unsolved:Horse (zodiac)|Horse]]||34||27||2014
|- align="center" 
|32||乙未||yǐ-wèi||eulmi 을미||{{unbulleted list|itsubi|kinoto-hitsuji}}||Ất Mùi||Yin Wood [[Unsolved:Goat (zodiac)|Goat]]||35||26||2015
|- align="center"
|33||丙申||bǐng-shēn||byeongsin 병신||{{unbulleted list|heishin|hinoe-saru}}||Bính Thân||Yang Fire [[Unsolved:Monkey (zodiac)|Monkey]]||36||25||2016
|- align="center"
|34||丁酉||dīng-yǒu||jeongyu 정유||{{unbulleted list|teiyū|hinoto-tori}}||Đinh Dậu||Yin Fire [[Unsolved:Rooster (zodiac)|Rooster]]||37||24||2017
|- align="center"
|35||戊戌||wù-xū||musul 무술||{{unbulleted list|bojutsu|tsuchinoe-inu}}||Mậu Tuất||Yang Earth [[Unsolved:Dog (zodiac)|Dog]]||38||23||2018
|- align="center"
|36||己亥||jǐ-hài||gihae 기해||{{unbulleted list|kigai|tsuchinoto-i}}||Kỷ Hợi||Yin Earth [[Unsolved:Pig (zodiac)|Pig]]||39||22||2019
|- align="center"
|37||庚子||gēng-zǐ||gyeongja 경자||{{unbulleted list|kōshi|kanoe-ne}}||Canh Tý||Yang Metal [[Unsolved:Rat (zodiac)|Rat]]||40||21||2020
|- align="center"
|38||辛丑||xīn-chǒu||sinchuk 신축||{{unbulleted list|shinchū|kanoto-ushi}}||Tân Sửu||Yin Metal [[Biology:Ox (zodiac)|Ox]]||41||20||2021
|- align="center" 
|39||壬寅||rén-yín||imin 임인||{{unbulleted list|jin'in|mizunoe-tora}}||Nhâm Dần||Yang Water [[Unsolved:Tiger (zodiac)|Tiger]]||42||19||2022
|- align="center" 
|40||癸卯||guǐ-mǎo||gyemyo 계묘||{{unbulleted list|kibō|mizunoto-u}}||Quý Mão||Yin Water [[Unsolved:Rabbit (zodiac)|Rabbit]]||43||18||2023
|- align="center" style="background: cadetblue; color: white"
|41||甲辰||jiǎ-chén||gapjin 갑진||{{unbulleted list|kōshin|kinoe-tatsu}}||Giáp Thìn||Yang Wood [[Unsolved:Dragon (zodiac)|Dragon]]||44||17||2024
|- align="center"
|42||乙巳||yǐ-sì||eulsa 을사||{{unbulleted list|itsushi|kinoto-mi}}||Ất Tỵ||Yin Wood [[Unsolved:Snake (zodiac)|Snake]]||45||16||2025
|- align="center"
|43||丙午||bǐng-wǔ||byeongo 병오||{{unbulleted list|heigo|hinoe-uma}}||Bính Ngọ||Yang Fire [[Unsolved:Horse (zodiac)|Horse]]||46||15||2026
|- align="center"
|44||丁未||dīng-wèi||jeongmi 정미||{{unbulleted list|teibi|hinoto-hitsuji}}||Đinh Mùi||Yin Fire [[Unsolved:Goat (zodiac)|Goat]]||47||14||2027
|- align="center"
|45||戊申||wù-shēn||musin 무신||{{unbulleted list|boshin|tsuchinoe-saru}}||Mậu Thân||Yang Earth [[Unsolved:Monkey (zodiac)|Monkey]]||48||13||2028
|- align="center"
|46||己酉||jǐ-yǒu||giyu 기유||{{unbulleted list|kiyū|tsuchinoto-tori}}||Kỷ Dậu||Yin Earth [[Unsolved:Rooster (zodiac)|Rooster]]||49||12||2029
|- align="center"
|47||庚戌||gēng-xū||gyeongsul 경술||{{unbulleted list|kōjutsu|kanoe-inu}}||Canh Tuất||Yang Metal [[Unsolved:Dog (zodiac)|Dog]]||50||11||2030
|- align="center"
|48||辛亥||xīn-hài||sinhae 신해||{{unbulleted list|shingai|kanoto-i}}||Tân Hợi||Yin Metal [[Unsolved:Pig (zodiac)|Pig]]||51||10||2031
|- align="center"
|49||壬子||rén-zǐ||imja 임자||{{unbulleted list|jinshi|mizunoe-ne}}||Nhâm Tý||Yang Water [[Unsolved:Rat (zodiac)|Rat]]||52||9||2032
|- align="center"
|50||癸丑||guǐ-chǒu||gyechuk 계축||{{unbulleted list|kichū|mizunoto-ushi}}||Quý Sửu||Yin Water [[Biology:Ox (zodiac)|Ox]]||53||8||2033
|- align="center"
|51||甲寅||jiǎ-yín||gabin 갑인||{{unbulleted list|kōin|kinoe-tora}}||Giáp Dần||Yang Wood [[Unsolved:Tiger (zodiac)|Tiger]]||54||7||2034
|- align="center"
|52||乙卯||yǐ-mǎo||eulmyo 을묘||{{unbulleted list|itsubō|kinoto-u}}||Ất Mão||Yin Wood [[Unsolved:Rabbit (zodiac)|Rabbit]]||55||6||2035
|- align="center"
|53||丙辰||bǐng-chén||byeongjin 병진||{{unbulleted list|heishin|hinoe-tatsu}}||Bính Thìn||Yang Fire [[Unsolved:Dragon (zodiac)|Dragon]]||56||5||2036
|- align="center"
|54||丁巳||dīng-sì||jeongsa 정사||{{unbulleted list|teishi|hinoto-mi}}||Đinh Tỵ||Yin Fire [[Unsolved:Snake (zodiac)|Snake]]||57||4||2037
|- align="center"
|55||戊午||wù-wǔ||muo 무오||{{unbulleted list|bogo|tsuchinoe-uma}}||Mậu Ngọ||Yang Earth [[Unsolved:Horse (zodiac)|Horse]]||58||3||2038
|- align="center"
|56||己未||jǐ-wèi||gimi 기미||{{unbulleted list|kibi|tsuchinoto-hitsuji}}||Kỷ Mùi||Yin Earth [[Unsolved:Goat (zodiac)|Goat]]||59||2||2039
|- align="center"
|57||庚申||gēng-shēn||gyeongsin 경신||{{unbulleted list|kōshin|kanoe-saru}}||Canh Thân||Yang Metal [[Unsolved:Monkey (zodiac)|Monkey]]||60||1||2040
|- align="center"
|58||辛酉||xīn-yǒu||sinyu 신유||{{unbulleted list|shin'yū|kanoto-tori}}||Tân Dậu||Yin Metal [[Unsolved:Rooster (zodiac)|Rooster]]||1||60||2041
|- align="center"
|59||壬戌||rén-xū||imsul 임술||{{unbulleted list|jinjutsu|mizunoe-inu}}||Nhâm Tuất||Yang Water [[Unsolved:Dog (zodiac)|Dog]]||2||59||2042
|- align="center"
|60||癸亥||guǐ-hài||gyehae 계해||{{unbulleted list|kigai|mizunoto-i}}||Quý Hợi||Yin Water [[Unsolved:Pig (zodiac)|Pig]]||3||58||2043
|}
[[File:China 24 cardinal directions.png|100px|thumb|right|24 cardinal directions]]

==Conversion between cyclic years and Western years==
[[File:sexagenary cycle years spirals.svg|thumb|250px|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 [[History:Chinese era name|Chinese era name]] (年号; "niánhào") to specify a year.<ref name="aslaksen">{{cite web |url=http://www.math.nus.edu.sg/aslaksen/calendar/chinese.shtml |title=Mathematics of the Chinese calendar |last=Aslaksen |first=Helmer |date=July 17, 2010 |format=PDF |language=en |website=www.math.nus.edu.sg/aslaksen |publisher=Department of Maths, National University of Singapore |access-date=December 12, 2011 |archive-url=https://web.archive.org/web/20060424100637/http://www.math.nus.edu.sg/aslaksen/calendar/chinese.shtml |archive-date=April 24, 2006 |url-status=dead |df=mdy-all }}</ref> 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, one has to consider what their "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 calendar|Gregorian]] year's equivalent in the sexagenary cycle use the appropriate method below.
# 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|remainder]]. See example below. 
# 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. 
# 1 AD, 2 AD and 3 AD correspond respectively to the 58th, 59th and 60th years of the sexagenary cycle.
#The formula for years AD is (year – 3 or + 57) mod 60 and for years BC is 60 – (year + 2) mod 60.
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) [[Modulo operation|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).

===Examples===
Step-by-step example to determine the sign for 1967:
#1967 – 3 = 1964 ("subtracting 3 from the Gregorian year")
#1964 ÷ 60 = 32 ("divide by 60 and discard any fraction")
#1964 – (60 × 32) = 44 ("taking the [[Remainder|remainder]]")
#Show one of the Sexagenary Cycle tables (the following section), look for 44 in the first column (No) and obtain Fire [[Unsolved:Goat (zodiac)|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):
#246 + 2 = 248  ("adding 2 to the Gregorian year number (in BC)")
#248 ÷ 60 = 4 ("divide by 60 and discard any fraction")
#248 – (60 × 4) = 8 ("taking the [[Remainder|remainder]]")
#60 – 8 = 52 ("subtract the remainder from 60")
#Show one of the Sexagenary Cycle table (the following section), look for 52 in the first column (No) and obtain Wood [[Unsolved:Rabbit (zodiac)|Rabbit]] (乙卯; ''yǐ-mǎo'').

===A shorter equivalent method===
Start from the AD year (1967), take directly the remainder mod 60, and look into column AD of the table "Sexagenary years" (just above).
*1967 = 60 × 32 + 47. 
Remainder is therefore 47 and the AD column says 'Fire [[Unsolved:Goat (zodiac)|Goat]]' as it should be.

For a BC year: discard the minus sign, take the remainder of the year mod 60 and look into column BC. Applied to year -246, this gives:
*246 = 60 × 4 + 6. Remainder is therefore 6 and the BC column of table "Sexagenary years" (just above) gives 'Wood [[Unsolved:Rabbit (zodiac)|Rabbit]]'.
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:

===1804–1923===
{| class="wikitable collapsible collapsed"
!No.||1804–1863||Heavenly stem||Earthly branch||1864–1923
|- align="center"
| ||Year ||(Elements)||(Animals)||Year
|- align="left"
|1||Feb 11 '''1804''' – Jan 30 1805||甲 Yang Wood ||子 [[Unsolved:Rat (zodiac)|Rat]]||Feb 8 '''1864''' – Jan 26 1865
|- align="left"
|2||Jan 31 '''1805''' – Feb 17 1806||乙 Yin Wood ||丑 [[Biology:Ox (zodiac)|Ox]]||Jan 27 '''1865''' – Feb 14 1866
|- align="left"
|3||Feb 18 '''1806''' – Feb 6 1807||丙 Yang Fire ||寅 [[Unsolved:Tiger (zodiac)|Tiger]]||Feb 15 '''1866''' – Feb 4 1867
|- align="left"
|4||Feb 7 '''1807''' – Jan 27 1808||丁 Yin Fire ||卯 [[Unsolved:Rabbit (zodiac)|Rabbit]]||Feb 5 '''1867''' – Jan 24 1868
|- align="left"
|5||Jan 28 '''1808''' – Feb 14 1809||戊 Yang Earth ||辰 [[Unsolved:Dragon (zodiac)|Dragon]]||Jan 25 '''1868''' – Feb 10 1869
|- align="left"
|6||Feb 15 '''1809''' – Feb 3 1810||己 Yin Earth ||巳 [[Unsolved:Snake (zodiac)|Snake]]||Feb 11 '''1869''' – Jan 31 1870
|- align="left"
|7||Feb 4 '''1810''' – Jan 24 1811||庚 Yang Metal ||午 [[Unsolved:Horse (zodiac)|Horse]]||Feb 01 '''1870''' – Feb 19 1871
|- align="left"
|8||Jan 25 '''1811''' – Feb 12 1812||辛 Yin Metal ||未 [[Unsolved:Goat (zodiac)|Goat]]||Feb 20 '''1871''' – Feb 8 1872
|- align="left"
|9||Feb 13 '''1812''' – Jan 31 1813||壬 Yang Water ||申 [[Unsolved:Monkey (zodiac)|Monkey]]||Feb 9 '''1872''' – Jan 28 1873
|- align="left"
|10||Feb 1 '''1813''' – Jan 20 1814||癸 Yin Water ||酉 [[Unsolved:Rooster (zodiac)|Rooster]]||Jan 29 '''1873''' – Feb 16 1874
|- align="left"
|11||Jan 21 '''1814''' – Feb 8 1815||甲 Yang Wood ||戌 [[Unsolved:Dog (zodiac)|Dog]]||Feb 17 '''1874''' – Feb 5 1875
|- align="left"
|12||Feb 9 '''1815''' – Jan 28 1816 ||乙 Yin Wood ||亥 [[Unsolved:Pig (zodiac)|Pig]]||Feb 6 '''1875''' – Jan 25 1876
|- align="left"
|13||Jan 29 '''1816''' – Feb 15 1817||丙 Yang Fire ||子 [[Unsolved:Rat (zodiac)|Rat]]||Jan 26 '''1876''' – Feb 12 1877
|- align="left"
|14||Feb 16 '''1817''' – Feb 5 1818||丁 Yin Fire ||丑 [[Biology:Ox (zodiac)|Ox]]||Feb 13 '''1877''' – Feb 1 1878
|- align="left"
|15||Feb 6 '''1818''' – Jan 25 1819||戊 Yang Earth ||寅 [[Unsolved:Tiger (zodiac)|Tiger]]||Feb 2 '''1878''' – Jan 22 1879
|- align="left"
|16||Jan 26 '''1819''' – Feb 13 1820||己 Yin Earth ||卯 [[Unsolved:Rabbit (zodiac)|Rabbit]]||Jan 23 '''1879''' – Feb 9 1880
|- align="left"
|17||Feb 14 '''1820''' – Feb 2 1821||庚 Yang Metal ||辰 [[Unsolved:Dragon (zodiac)|Dragon]]||Feb 10 '''1880''' – Jan 29 1881
|- align="left"
|18||Feb 3 '''1821''' – Jan 22 1822||辛 Yin Metal ||巳 [[Unsolved:Snake (zodiac)|Snake]]||Jan 30 '''1881''' – Feb 17 1882
|- align="left"
|19||Jan 23 '''1822''' – Feb 10 1823||壬 Yang Water ||午 [[Unsolved:Horse (zodiac)|Horse]]||Feb 18 '''1882''' – Feb 7 1883
|- align="left"
|20||Feb 11 '''1823''' – Jan 30 1824||癸 Yin Water ||未 [[Unsolved:Goat (zodiac)|Goat]]||Feb 8 '''1883''' – Jan 27 1884
|- align="left"
|21||Jan 31 '''1824''' – Feb 17 1825||甲 Yang Wood ||申 [[Unsolved:Monkey (zodiac)|Monkey]]||Jan 28 '''1884''' – Feb 14 1885
|- align="left"
|22||Feb 18 '''1825''' – Feb 6 1826||乙 Yin Wood ||酉 [[Unsolved:Rooster (zodiac)|Rooster]]||Feb 15 '''1885''' – Feb 3 1886
|- align="left"
|23||Feb 7 '''1826''' – Jan 26 1827||丙 Yang Fire ||戌 [[Unsolved:Dog (zodiac)|Dog]]||Feb 4 '''1886''' – Jan 23 1887
|- align="left"
|24||Jan 27 '''1827''' – Feb 15 1828||丁 Yin Fire ||亥 [[Unsolved:Pig (zodiac)|Pig]]||Jan 24 '''1887''' – Feb 11 1888
|- align="left"
|25||Feb 16 '''1828''' – Feb 3 1829||戊 Yang Earth ||子 [[Unsolved:Rat (zodiac)|Rat]]||Feb 12 '''1888''' – Jan 30 1889
|- align="left"
|26||Feb 4 '''1829''' – Jan 24 1830||己 Yin Earth ||丑 [[Biology:Ox (zodiac)|Ox]]||Jan 31 '''1889''' – Jan 20 1890
|- align="left"
|27||Jan 25 '''1830''' – Feb 12 1831||庚 Yang Metal ||寅 [[Unsolved:Tiger (zodiac)|Tiger]]||Jan 21 '''1890''' – Feb 08 1891
|- align="left"
|28||Feb 13 '''1831''' – Feb 1 1832||辛 Yin Metal ||卯 [[Unsolved:Rabbit (zodiac)|Rabbit]]||Feb 09 '''1891''' – Jan 29 1892
|- align="left"
|29||Feb 2 '''1832''' – Feb 19 1833||壬 Yang Water ||辰 [[Unsolved:Dragon (zodiac)|Dragon]]||Jan 30 '''1892''' – Feb 16 1893
|- align="left"
|30||Feb 20 '''1833''' – Feb 8 1834||癸 Yin Water ||巳 [[Unsolved:Snake (zodiac)|Snake]]||Feb 17 '''1893''' – Feb 5 1894
|- align="left"
|31||Feb 9 '''1834''' – Jan 28 1835||甲 Yang Wood ||午 [[Unsolved:Horse (zodiac)|Horse]]||Feb 6 '''1894''' – Jan 25 1895
|- align="left"
|32||Jan 29 '''1835''' – Feb 16 1836||乙 Yin Wood ||未 [[Unsolved:Goat (zodiac)|Goat]]||Jan 26 '''1895''' – Feb 12 1896
|- align="left"
|33||Feb 17 '''1836''' – Feb 5 1837||丙 Yang Fire ||申 [[Unsolved:Monkey (zodiac)|Monkey]]||Feb 13 '''1896''' – Feb 01 1897
|- align="left"
|34||Feb 6 '''1837''' – Jan 25 1838||丁 Yin Fire ||酉 [[Unsolved:Rooster (zodiac)|Rooster]]||Feb 02 '''1897''' – Jan 21 1898
|- align="left"
|35||Jan 26 '''1838''' – Feb 13 1839||戊 Yang Earth ||戌 [[Unsolved:Dog (zodiac)|Dog]]||Jan 22 '''1898''' – Feb 09 1899
|- align="left"
|36||Feb 14 '''1839''' – Feb 2 1840||己 Yin Earth ||亥 [[Unsolved:Pig (zodiac)|Pig]]||Feb 10 '''1899''' – Jan 30 1900
|- align="left"
|37||Feb 3 '''1840''' – Jan 22 1841||庚 Yang Metal ||子 [[Unsolved:Rat (zodiac)|Rat]]||Jan 31 '''1900''' – Feb 18 1901
|- align="left"
|38||Jan 23 '''1841''' – Feb 9 1842||辛 Yin Metal ||丑 [[Biology:Ox (zodiac)|Ox]]|| Feb 19 '''1901''' – Feb 07 1902
|- align="left"
|39||Feb 10 '''1842''' – Jan 29 1843||壬 Yang Water ||寅 [[Unsolved:Tiger (zodiac)|Tiger]]|| Feb 08 '''1902''' – Jan 28 1903
|- align="left"
|40||Jan 30 '''1843''' – Feb 17 1844||癸 Yin Water ||卯 [[Unsolved:Rabbit (zodiac)|Rabbit]]|| Jan 29 '''1903''' – Feb 15 1904
|- align="left"
|41||Feb 18 '''1844''' – Feb 6 1845||甲 Yang Wood ||辰 [[Unsolved:Dragon (zodiac)|Dragon]]|| Feb 16 '''1904''' – Feb 03 1905
|- align="left"
|42||Feb 7 '''1845''' – Jan 26 1846||乙 Yin Wood ||巳 [[Unsolved:Snake (zodiac)|Snake]]|| Feb 04 '''1905''' – Jan 24 1906
|- align="left"
|43||Jan 27 '''1846''' – Feb 15 1847||丙 Yang Fire ||午 [[Unsolved:Horse (zodiac)|Horse]]|| Jan 25 '''1906''' – Feb 12 1907
|- align="left"
|44||Feb 16 '''1847''' – Feb 4 1848||丁 Yin Fire ||未 [[Unsolved:Goat (zodiac)|Goat]]|| Feb 13 '''1907''' – Feb 01 1908
|- align="left"
|45||Feb 5 '''1848''' – Jan 23 1849||戊 Yang Earth ||申 [[Unsolved:Monkey (zodiac)|Monkey]]|| Feb 02 '''1908''' – Jan 21 1909
|- align="left"
|46||Jan 24 '''1849''' – Feb 11 1850||己 Yin Earth ||酉 [[Unsolved:Rooster (zodiac)|Rooster]]|| Jan 22 '''1909''' – Feb 09 1910
|- align="left"
|47||Feb 12 '''1850''' – Jan 31 1851||庚 Yang Metal ||戌 [[Unsolved:Dog (zodiac)|Dog]]|| Feb 10 '''1910''' – Jan 29 1911
|- align="left"
|48||Feb 1 '''1851''' – Feb 19 1852||辛 Yin Metal ||亥 [[Unsolved:Pig (zodiac)|Pig]]|| Jan 30 '''1911''' – Feb 17 1912
|- align="left"
|49||Feb 20 '''1852''' – Feb 7 1853||壬 Yang Water ||子 [[Unsolved:Rat (zodiac)|Rat]]|| Feb 18 '''1912''' – Feb 05 1913
|- align="left"
|50||Feb 8 '''1853''' – Jan 28 1854||癸 Yin Water ||丑 [[Biology:Ox (zodiac)|Ox]]|| Feb 06 '''1913''' – Jan 25 1914
|- align="left"
|51||Jan 29 '''1854''' – Feb 16 1855||甲 Yang Wood ||寅 [[Unsolved:Tiger (zodiac)|Tiger]]|| Jan 26 '''1914''' – Feb 13 1915
|- align="left"
|52||Feb 17 '''1855''' – Feb 6 1856||乙 Yin Wood ||卯 [[Unsolved:Rabbit (zodiac)|Rabbit]]|| Feb 14 '''1915''' – Feb 02 1916
|- align="left"
|53||Feb 7 '''1856''' – Jan 25 1857||丙 Yang Fire ||辰 [[Unsolved:Dragon (zodiac)|Dragon]]|| Feb 03 '''1916''' – Jan 22 1917
|- align="left"
|54||Jan 26 '''1857''' – Feb 13 1858||丁 Yin Fire ||巳 [[Unsolved:Snake (zodiac)|Snake]]|| Jan 23 '''1917''' – Feb 10 1918
|- align="left"
|55||Feb 14 '''1858''' – Feb 2 1859||戊 Yang Earth ||午 [[Unsolved:Horse (zodiac)|Horse]]|| Feb 11 '''1918''' – Jan 31 1919
|- align="left"
|56||Feb 3 '''1859''' – Jan 22 1860||己 Yin Earth ||未 [[Unsolved:Goat (zodiac)|Goat]]|| Feb 01 '''1919''' – Feb 19 1920
|- align="left"
|57||Jan 23 '''1860''' – Feb 9 1861||庚 Yang Metal ||申 [[Unsolved:Monkey (zodiac)|Monkey]]|| Feb 20 '''1920''' – Feb 07 1921
|- align="left"
|58||Feb 10 '''1861''' – Jan 29 1862||辛 Yin Metal ||酉 [[Unsolved:Rooster (zodiac)|Rooster]]|| Feb 08 '''1921''' – Jan 27 1922
|- align="left"
|59||Jan 30 '''1862''' – Feb 17 1863||壬 Yang Water ||戌 [[Unsolved:Dog (zodiac)|Dog]]|| Jan 28 '''1922''' – Feb 15 1923
|- align="left"
|60||Feb 18 '''1863''' – Feb 7 1864||癸 Yin Water ||亥 [[Unsolved:Pig (zodiac)|Pig]]|| Feb 16 '''1923''' – Feb 04 1924
|}

===1924–2043===
{| class="wikitable collapsible collapsed"
!No.||1924–1983||Heavenly stem||Earthly branch||1984–2043
|- align="center"
| ||Year ||(Elements)||(Animals)||Year
|- align="left"
|1||Feb 05 '''1924''' – Jan 23 1925||甲 Yang Wood ||子 [[Unsolved:Rat (zodiac)|Rat]]||Feb 02 '''1984''' – Jan 20 1985
|- align="left"
|2||Jan 24 '''1925''' – Feb 12 1926||乙 Yin Wood ||丑 [[Biology:Ox (zodiac)|Ox]]||Jan 21 '''1985''' – Feb 08 1986
|- align="left"
|3||Feb 13 '''1926''' – Feb 01 1927||丙 Yang Fire ||寅 [[Unsolved:Tiger (zodiac)|Tiger]]||Feb 09 '''1986''' – Jan 29 1987
|- align="left"
|4||Feb 02 '''1927''' – Jan 22 1928||丁 Yin Fire ||卯 [[Unsolved:Rabbit (zodiac)|Rabbit]]||Jan 30 '''1987''' – Feb 17 1988
|- align="left"
|5||Jan 23 '''1928''' – Feb 09 1929||戊 Yang Earth ||辰 [[Unsolved:Dragon (zodiac)|Dragon]]||Feb 18 '''1988''' – Feb 05 1989
|- align="left"
|6||Feb 10 '''1929''' – Jan 29 1930||己 Yin Earth ||巳 [[Unsolved:Snake (zodiac)|Snake]]||Feb 06 '''1989''' – Jan 26 1990
|- align="left"
|7||Jan 30 '''1930''' – Feb 16 1931||庚 Yang Metal ||午 [[Unsolved:Horse (zodiac)|Horse]]||Jan 27 '''1990''' – Feb 14 1991
|- align="left"
|8||Feb 17 '''1931''' – Feb 06 1932||辛 Yin Metal ||未 [[Unsolved:Goat (zodiac)|Goat]]||Feb 15 '''1991''' – Feb 03 1992
|- align="left"
|9||Feb 07 '''1932''' – Jan 25 1933||壬 Yang Water ||申 [[Unsolved:Monkey (zodiac)|Monkey]]||Feb 04 '''1992''' – Jan 22 1993
|- align="left"
|10||Jan 26 '''1933''' – Feb 13 1934||癸 Yin Water ||酉 [[Unsolved:Rooster (zodiac)|Rooster]]||Jan 23 '''1993''' – Feb 10 1994
|- align="left"
|11||Feb 14 '''1934''' – Feb 03 1935||甲 Yang Wood ||戌 [[Unsolved:Dog (zodiac)|Dog]]||Feb 11 '''1994''' – Jan 30 1995
|- align="left"
|12||Feb 04 '''1935''' – Jan 23 1936 ||乙 Yin Wood ||亥 [[Unsolved:Pig (zodiac)|Pig]]||Jan 31 '''1995''' – Feb 18 1996
|- align="left"
|13||Jan 24 '''1936''' – Feb 10 1937||丙 Yang Fire ||子 [[Unsolved:Rat (zodiac)|Rat]]||Feb 19 '''1996''' – Feb 06 1997
|- align="left"
|14||Feb 11 '''1937''' – Jan 30 1938||丁 Yin Fire ||丑 [[Biology:Ox (zodiac)|Ox]]||Feb 07 '''1997''' – Jan 27 1998
|- align="left"
|15||Jan 31 '''1938''' – Feb 18 1939||戊 Yang Earth ||寅 [[Unsolved:Tiger (zodiac)|Tiger]]||Jan 28 '''1998''' – Feb 15 1999
|- align="left"
|16||Feb 19 '''1939''' – Feb 07 1940||己 Yin Earth ||卯 [[Unsolved:Rabbit (zodiac)|Rabbit]]||Feb 16 '''1999''' – Feb 04 2000
|- align="left"
|17||Feb 08 '''1940''' – Jan 26 1941||庚 Yang Metal ||辰 [[Unsolved:Dragon (zodiac)|Dragon]]||Feb 05 '''2000''' – Jan 23 2001
|- align="left"
|18||Jan 27 '''1941''' – Feb 14 1942||辛 Yin Metal ||巳 [[Unsolved:Snake (zodiac)|Snake]]||Jan 24 '''2001''' – Feb 11 2002
|- align="left"
|19||Feb 15 '''1942''' – Feb 04 1943||壬 Yang Water ||午 [[Unsolved:Horse (zodiac)|Horse]]||Feb 12 '''2002''' – Jan 31 2003
|- align="left"
|20||Feb 05 '''1943''' – Jan 24 1944||癸 Yin Water ||未 [[Unsolved:Goat (zodiac)|Goat]]||Feb 01 '''2003''' – Jan 21 2004
|- align="left"
|21||Jan 25 '''1944''' – Feb 12 1945||甲 Yang Wood ||申 [[Unsolved:Monkey (zodiac)|Monkey]]||Jan 22 '''2004''' – Feb 08 2005
|- align="left"
|22||Feb 13 '''1945''' – Feb 01 1946||乙 Yin Wood ||酉 [[Unsolved:Rooster (zodiac)|Rooster]]||Feb 09 '''2005''' – Jan 29 2006
|- align="left"
|23||Feb 02 '''1946''' – Jan 21 1947||丙 Yang Fire ||戌 [[Unsolved:Dog (zodiac)|Dog]]||Jan 30 '''2006''' – Feb 17 2007
|- align="left"
|24||Jan 22 '''1947''' – Feb 09 1948||丁 Yin Fire ||亥 [[Unsolved:Pig (zodiac)|Pig]]||Feb 18 '''2007''' – Feb 06 2008
|- align="left"
|25||Feb 10 '''1948''' – Jan 28 1949||戊 Yang Earth ||子 [[Unsolved:Rat (zodiac)|Rat]]||Feb 07 '''2008''' – Jan 25 2009
|- align="left"
|26||Jan 29 '''1949''' – Feb 16 1950||己 Yin Earth ||丑 [[Biology:Ox (zodiac)|Ox]]||Jan 26 '''2009''' – Feb 13 2010
|- align="left"
|27||Feb 17 '''1950''' – Feb 05 1951||庚 Yang Metal ||寅 [[Unsolved:Tiger (zodiac)|Tiger]]||Feb 14 '''2010''' – Feb 02 2011
|- align="left"
|28||Feb 06 '''1951''' – Jan 26 1952||辛 Yin Metal ||卯 [[Unsolved:Rabbit (zodiac)|Rabbit]]||Feb 03 '''2011''' – Jan 22 2012
|- align="left"
|29||Jan 27 '''1952''' – Feb 13 1953||壬 Yang Water ||辰 [[Unsolved:Dragon (zodiac)|Dragon]]||Jan 23 '''2012''' – Feb 09 2013
|- align="left"
|30||Feb 14 '''1953''' – Feb 03 1954||癸 Yin Water ||巳 [[Unsolved:Snake (zodiac)|Snake]]||Feb 10 '''2013''' – Jan 30 2014
|- align="left"
|31||Feb 04 '''1954''' – Jan 23 1955||甲 Yang Wood ||午 [[Unsolved:Horse (zodiac)|Horse]]||Jan 31 '''2014''' – Feb 18 2015
|- align="left"
|32||Jan 24 '''1955''' – Feb 11 1956||乙 Yin Wood ||未 [[Unsolved:Goat (zodiac)|Goat]]||Feb 19 '''2015''' – Feb 07 2016
|- align="left"
|33||Feb 12 '''1956''' – Jan 30 1957||丙 Yang Fire ||申 [[Unsolved:Monkey (zodiac)|Monkey]]||Feb 08 '''2016''' – Jan 27 2017
|- align="left"
|34||Jan 31 '''1957''' – Feb 18 1958||丁 Yin Fire ||酉 [[Unsolved:Rooster (zodiac)|Rooster]]||Jan 28 '''2017''' – Feb 15 2018
|- align="left"
|35||Feb 19 '''1958''' – Feb 07 1959||戊 Yang Earth ||戌 [[Unsolved:Dog (zodiac)|Dog]]||Feb 16 '''2018''' – Feb 04 2019
|- align="left"
|36||Feb 08 '''1959''' – Jan 27 1960||己 Yin Earth ||亥 [[Unsolved:Pig (zodiac)|Pig]]||Feb 05 '''2019''' – Jan 24 2020
|- align="left"
|37||Jan 28 '''1960''' – Feb 14 1961||庚 Yang Metal ||子 [[Unsolved:Rat (zodiac)|Rat]]||Jan 25 '''2020''' – Feb 11 2021
|- align="left"
|38||Feb 15 '''1961''' – Feb 04 1962||辛 Yin Metal ||丑 [[Biology:Ox (zodiac)|Ox]]||Feb 12 '''2021''' – Jan 31 2022
|- align="left"
|39||Feb 05 '''1962''' – Jan 25 1963||壬 Yang Water ||寅 [[Unsolved:Tiger (zodiac)|Tiger]]||Feb 01 '''2022''' – Jan 21 2023
|- align="left"
|40||Jan 26 '''1963''' – Feb 12 1964||癸 Yin Water ||卯 [[Unsolved:Rabbit (zodiac)|Rabbit]]||Jan 22 '''2023''' – Feb 09 2024
|- align="left"
|41||Feb 13 '''1964''' – Feb 01 1965||甲 Yang Wood ||辰 [[Unsolved:Dragon (zodiac)|Dragon]]||Feb 10 '''2024''' – Jan 28 2025
|- align="left"
|42||Feb 02 '''1965''' – Jan 21 1966||乙 Yin Wood ||巳 [[Unsolved:Snake (zodiac)|Snake]]||Jan 29 '''2025''' – Feb 16 2026
|- align="left"
|43||Jan 22 '''1966''' – Feb 08 1967||丙 Yang Fire ||午 [[Unsolved:Horse (zodiac)|Horse]]||Feb 17 '''2026''' – Feb 05 2027
|- align="left"
|44||Feb 09 '''1967''' – Jan 29 1968||丁 Yin Fire ||未 [[Unsolved:Goat (zodiac)|Goat]]||Feb 06 '''2027''' – Jan 25 2028
|- align="left"
|45||Jan 30 '''1968''' – Feb 16 1969||戊 Yang Earth ||申 [[Unsolved:Monkey (zodiac)|Monkey]]||Jan 26 '''2028''' – Feb 12 2029
|- align="left"
|46||Feb 17 '''1969''' – Feb 05 1970||己 Yin Earth ||酉 [[Unsolved:Rooster (zodiac)|Rooster]]||Feb 13 '''2029''' – Feb 02 2030
|- align="left"
|47||Feb 06 '''1970''' – Jan 26 1971||庚 Yang Metal ||戌 [[Unsolved:Dog (zodiac)|Dog]]|| Feb 03 '''2030''' – Jan 22 2031
|- align="left"
|48||Jan 27 '''1971''' – Feb 14 1972||辛 Yin Metal ||亥 [[Unsolved:Pig (zodiac)|Pig]]||Jan 23 '''2031''' – Feb 10 2032
|- align="left"
|49||Feb 15 '''1972''' – Feb 02 1973||壬 Yang Water ||子 [[Unsolved:Rat (zodiac)|Rat]]||Feb 11 '''2032''' – Jan 30 2033
|- align="left"
|50||Feb 03 '''1973''' – Jan 22 1974||癸 Yin Water ||丑 [[Biology:Ox (zodiac)|Ox]]||Jan 31 '''2033''' – Feb 18 2034
|- align="left"
|51||Jan 23 '''1974''' – Feb 10 1975||甲 Yang Wood ||寅 [[Unsolved:Tiger (zodiac)|Tiger]]||Feb 19 '''2034''' – Feb 07 2035
|- align="left"
|52||Feb 11 '''1975''' – Jan 30 1976||乙 Yin Wood ||卯 [[Unsolved:Rabbit (zodiac)|Rabbit]]||Feb 08 '''2035''' – Jan 27 2036
|- align="left"
|53||Jan 31 '''1976''' – Feb 17 1977||丙 Yang Fire ||辰 [[Unsolved:Dragon (zodiac)|Dragon]]||Jan 28 '''2036''' – Feb 14 2037
|- align="left"
|54||Feb 18 '''1977''' – Feb 06 1978||丁 Yin Fire ||巳 [[Unsolved:Snake (zodiac)|Snake]]||Feb 15 '''2037''' – Feb 03 2038
|- align="left"
|55||Feb 07 '''1978''' – Jan 27 1979||戊 Yang Earth ||午 [[Unsolved:Horse (zodiac)|Horse]]||Feb 04 '''2038''' – Jan 23 2039
|- align="left"
|56||Jan 28 '''1979''' – Feb 15 1980||己 Yin Earth ||未 [[Unsolved:Goat (zodiac)|Goat]]||Jan 24 '''2039''' – Feb 11 2040
|- align="left"
|57||Feb 16 '''1980''' – Feb 04 1981||庚 Yang Metal ||申 [[Unsolved:Monkey (zodiac)|Monkey]]||Feb 12 '''2040''' – Jan 31 2041
|- align="left"
|58||Feb 05 '''1981''' – Jan 24 1982||辛 Yin Metal ||酉 [[Unsolved:Rooster (zodiac)|Rooster]]||Feb 01 '''2041''' – Jan 21 2042
|- align="left"
|59||Jan 25 '''1982''' – Feb 12 1983||壬 Yang Water ||戌 [[Unsolved:Dog (zodiac)|Dog]]||Jan 22 '''2042''' – Feb 09 2043
|- align="left"
|60||Feb 13 '''1983''' – Feb 01 1984||癸 Yin Water ||亥 [[Unsolved:Pig (zodiac)|Pig]]||Feb 10 '''2043''' – Jan 29 2044
|}

==Sexagenary months==
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, ({{lang|und-Hani|建子月}}: ''jiànzǐyuè'', {{lang|und-Hani|建丑月}}: ''jiànchǒuyuè'', etc.).{{sfn|Smith|2011|pages=28, 29 fn2}}<ref>{{cite dictionary |dictionary=Kōjien |publisher=Iwanami Shoten |place=Tokyo |script-title=ja:建す}}</ref> 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 ({{zh|labels=no|中氣}}; ''zhōngqì''). The ''jiànzǐyuè'' (({{lang|und-Hani|建}}){{lang|und-Hani|子月}}) is the month containing the winter solstice (i.e. the {{lang|und-Hani|冬至}} Dōngzhì) ''zhōngqì''. The ''jiànchǒuyuè'' (({{lang|und-Hani|建}}){{zh|labels=no|丑月}}) is the month of the following ''zhōngqì'', which is Dàhán ({{lang|und-Hani|大寒}}), while the ''jiànyínyuè'' (({{lang|und-Hani|建}}){{lang|und-Hani|寅月}}) is that of the Yǔshuǐ ({{lang|und-Hani|雨水}}) ''zhōngqì'', etc. Intercalary months have the same branch as the preceding month.
<ref>{{cite book |script-title=zh:新唐書 |title=Xīn Tángshū |trans-title=New Book of Tang|chapter=Records part 6 |script-chapter=zh:本紀第六 肅宗 代宗 |chapter-url=https://zh.wikisource.org/wiki/%E6%96%B0%E5%94%90%E6%9B%B8/%E5%8D%B7006 |quote={{zh|labels=no|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。<br />　　元年建子月癸巳，曹州刺史常休明及史朝义将薛崿战，败之。己亥，朝圣皇天帝于西内。丙午，卫伯玉及史朝义战于永宁，败之。己酉，朝献于太清宫。庚戌，朝享于太庙及元献皇后庙。建丑月辛亥，有事于南郊。己未，来瑱及史朝义战于汝州，败之。乙亥，侯希逸及朝义将李怀仙战于范阳，败之。宝应元年建寅月甲申，追册靖德太子琮为皇帝，妃窦氏为皇后。乙酉，葬王公妃主遇害者。丙戌，盗发敬陵、惠陵。甲辰，李光弼克许州。吐蕃请和。戊申，史朝义陷营州。建卯月辛亥，大赦。赐文武官阶、爵。五品以上清望及郎官、御史荐流人有行业情可矜者。停贡鹰、鹞、狗、豹。以京兆府为上都，河南府为东都，凤翔府为西都，江陵府为南都，太原府为北都。壬子，羌、浑、奴剌寇梁州。癸丑，河东军乱，杀其节度使邓景山，都知兵马使辛云京自称节度使。乙丑，河中军乱，杀李国贞及其节度使荔非元礼。戊辰，淮西节度使王仲升及史朝义将谢钦让战于申州，败绩。庚午，敦子仪知朔方、河中、北庭、潞仪泽沁节度行营，兴平、定国军兵马副元帅。壬申，鄜州刺史成公意及党项战，败之。建辰月壬午，大赦，官吏听纳赃免罪，左降官及流人罚镇效力者还之。甲午，奴剌寇梁州。戊申，萧华罢。户部侍郎元载同中书门下平章事。建巳月庚戌，史朝义寇泽州，刺史李抱玉败之。壬子，楚州献定国宝玉十有三。甲寅，圣皇天帝崩。乙丑，皇太子监国。大赦，改元年为宝应元年，复以正月为岁首，建巳月为四月。丙寅，闲厩使李辅国、飞龙厩副使程元振迁皇后于别殿，杀越王系、兗王亻闲。是夜，皇帝崩于长生殿，年五十二。查《壽星萬年曆》，<br />唐肅宗之元年<br />冬至所在月（761.12）：初一壬午大雪，十三癸巳，十七冬至，十九己亥，廿五丙午，廿八己酉，廿九庚戌<br />大寒所在月（762.02）：初一辛亥，初三小寒，初九己未，十八大寒，廿五乙亥<br />雨水所在月（762.03）：初一辛巳，初三立春，初四甲申，初五乙酉，初六丙戌，十八雨水，廿四甲辰，廿八戊申<br />春分所在月（762.3）：初一辛亥，初四驚蜇，初二壬子，初三癸丑，十五乙丑，十八戊辰，十九春分，二十庚午，廿一壬申，<br />穀雨所在月（762.4）：初一庚辰，初三壬午，初五清明，十五甲午，二十穀雨，廿九戊申<br />小滿所在月（762.5）：初一庚戌，初三壬子，初五甲寅立夏，初五乙丑，十六丙寅。<br />大寒所在月初一辛亥，已稱建丑月，初三才小寒<br />春分所在月初一辛亥，已稱建卯月，初四才驚蜇<br />穀雨所在月初三壬午，已稱建辰月，初五才清明<br />小滿所在月初一庚戌、初三壬子，已稱建巳月，初五才立夏<br />由此可見，唐代地支紀月自朔日始，非自節氣始。}}}}</ref>
In the other system ({{lang|und-Hani|節月}}; ''jiéyuè'') the "month" lasts for the period of two solar terms (two {{lang|und-Hani|氣策}} ''qìcì''). The ''zǐyuè'' ({{lang|und-Hani|子月}}) is the period starting with Dàxuě ({{lang|und-Hani|大雪}}), i.e. the solar term ''before'' the winter solstice. The ''chǒuyuè'' ({{lang|und-Hani|丑月}}) starts with Xiǎohán ({{lang|und-Hani|小寒}}), the term before Dàhán ({{lang|und-Hani|大寒}}), while the ''yínyuè'' ({{lang|und-Hani|寅月}}) starts with Lìchūn ({{lang|und-Hani|立春}}), the term before Yǔshuǐ ({{lang|und-Hani|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.<ref>{{citation |script-title=ja:三正 |dictionary=Kōjien |publisher=Iwanami Shoten |place=Tokyo}}</ref>

For astrological purposes stems are also necessary, and the months are named using the sexagenary cycle following a five-year cycle starting in a ''jiǎ'' ({{lang|und-Hani|甲}}; 1st) or ''jǐ'' ({{zh|labels=no|己}}; 6th) year. The first month of the ''jiǎ'' or ''jǐ''  year is a  ''bǐng-yín'' ({{lang|und-Hani|丙寅}}; 3rd) month, the next one is a ''dīng-mǎo'' ({{lang|und-Hani|丁卯}}; 4th) month, etc., and the last month of the year is a ''dīng-chǒu'' ({{lang|und-Hani|丁丑}}, 14th) month. The next year will start with a ''wù-yín'' ({{lang|und-Hani|戊寅}}; 15th) month, etc. following the cycle. The 5th year will end with a ''yǐ-chǒu'' ({{lang|und-Hani|乙丑}}; 2nd) month. The following month, the start of a ''jǐ'' 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.
{| class=wikitable
!Earthly Branches of the certain months||Solar term||Zhongqi (the Middle solar term)||Starts at||Ends at||Names in year of Jia or Ji({{lang|und-Hani|甲}}/{{lang|und-Hani|己年}})||Names in year of Yi or Geng ({{lang|und-Hani|乙}}/{{lang|und-Hani|庚年}})||Names in year of Bing or Xin ({{lang|und-Hani|丙}}/{{lang|und-Hani|辛年}})||Names in year of Ding or Ren ({{lang|und-Hani|丁}}/{{lang|und-Hani|壬年}})||Names in year of Wu or Gui ({{lang|und-Hani|戊}}/{{lang|und-Hani|癸年}})
|-
||Month of Yin ({{lang|und-Hani|寅月}}) ||Lichun – Jingzhe||Yushui / 雨水||February 4||March 6||Bingyin / {{lang|und-Hani|丙寅月}}||Wuyin / {{lang|und-Hani|戊寅月}}||Gengyin / {{lang|und-Hani|庚寅月}}||Renyin / {{lang|und-Hani|壬寅月}}||Jiayin / {{lang|und-Hani|甲寅月}}
|-
|
Month of Mao ({{lang|und-Hani|卯月}})
||Jingzhe – Qingming ||Chunfen / 春分||March 6||April 5||Dingmao / {{lang|und-Hani|丁卯月}}||Jimao / {{lang|und-Hani|己卯月}}||Xinmao / {{lang|und-Hani|辛卯月}}||Guimao / {{lang|und-Hani|癸卯月}}||Yimao / {{lang|und-Hani|乙卯月}}
|-
|Month of Chen ({{lang|und-Hani|辰月}})||Qingming – Lixia||Guyu / 谷雨||April 5||May 6||Wuchen / {{lang|und-Hani|戊辰月}}||Gengchen / {{lang|und-Hani|庚辰月}}||Renchen / {{lang|und-Hani|壬辰月}}||Jiachen / {{lang|und-Hani|甲辰月}}||Bingchen / {{lang|und-Hani|丙辰月}}
|-
|Month of Si ({{lang|und-Hani|巳月}})||Lixia – Mangzhong||Xiaoman / 小满||May 6||June 6||Jisi / {{lang|und-Hani|己巳月}}||Xinsi / {{lang|und-Hani|辛巳月}}||Guisi / {{lang|und-Hani|癸巳月}}||Yisi / {{lang|und-Hani|乙巳月}}||Dingsi / {{lang|und-Hani|丁巳月}}
|-
|Month of Wu ({{lang|und-Hani|午月}})||Mangzhong – Xiaoshu||Xiazhi / 夏至||June 6||July 7||Gengwu / {{lang|und-Hani|庚午月}}||Renwu / {{lang|und-Hani|壬午月}}||Jiawu / {{lang|und-Hani|甲午月}}||Bingwu / {{lang|und-Hani|丙午月}}||Wuwu / {{lang|und-Hani|戊午月}}
|-
|Month of Wei ({{lang|und-Hani|未月}})||Xiaoshu – Liqiu||Dashu / 大暑||July 7||August 8||Xinwei / {{lang|und-Hani|辛未月}}||Guiwei / {{lang|und-Hani|癸未月}}||Yiwei / {{lang|und-Hani|乙未月}}||Dingwei / {{lang|und-Hani|丁未月}}||Jiwei / {{lang|und-Hani|己未月}}
|-
|Month of Shen ({{lang|und-Hani|申月}})||Liqiu – Bailu||Chushu / 处暑||August 8||September 8||Renshen / {{lang|und-Hani|壬申月}}||Jiashen / {{lang|und-Hani|甲申月}}||Bingshen / {{lang|und-Hani|丙申月}}||Wushen / {{lang|und-Hani|戊申月}}||Gengshen / {{lang|und-Hani|庚申月}}
|-
|Month of You ({{lang|und-Hani|酉月}})||Bailu – Hanlu||Qiufen / 秋分||September 8||October 8||Guiyou / {{lang|und-Hani|癸酉月}}||Yiyou / {{lang|und-Hani|乙酉月}}||Dingyou / {{lang|und-Hani|丁酉月}}||Jiyou / {{lang|und-Hani|己酉月}}||Xinyou / {{lang|und-Hani|辛酉月}}
|-
|Month of Xu ({{lang|und-Hani|戌月}})||Hanlu – Lidong||Shuangjiang / 霜降||October 8||November 7||Jiaxu / {{lang|und-Hani|甲戌月}}||Bingxu / {{lang|und-Hani|丙戌月}}||Wuxu / {{lang|und-Hani|戊戌月}}||Gengxu / {{lang|und-Hani|庚戌月}}||Renxu / {{lang|und-Hani|壬戌月}}
|-
|Month of Hai ({{lang|und-Hani|亥月}})||Lidong – Daxue||Xiaoxue / 小雪||November 7||December 7||Yihai / {{lang|und-Hani|乙亥月}}||Dinghai / {{lang|und-Hani|丁亥月}}||Jihai / {{lang|und-Hani|己亥月}}||Xinhai / {{lang|und-Hani|辛亥月}}||Guihai / {{lang|und-Hani|癸亥月}}
|-
|Month of Zi ({{lang|und-Hani|子月}})||Daxue – Xiaohan||Dongzhi / 冬至||December 7||January 6||Bingzi / {{lang|und-Hani|丙子月}}||Wuzi / {{lang|und-Hani|戊子月}}||Gengzi / {{lang|und-Hani|庚子月}}||Renzi / {{lang|und-Hani|壬子月}}||Jiazi / {{lang|und-Hani|甲子月}}
|-
|Month of Chou ({{lang|und-Hani|丑月}})||Xiaohan – Lichun||Dahan / 大寒||January 6||February 4||Dingchou / {{lang|und-Hani|丁丑月}}||Jichou / {{lang|und-Hani|己丑月}}||Xinchou / {{lang|und-Hani|辛丑月}}||Guichou / {{lang|und-Hani|癸丑月}}||Yichou / {{lang|und-Hani|乙丑月}}
|}

==Sexagenary days==
{| class="wikitable collapsible"
|+ Table for sexagenary days 
|-
! colspan="4" rowspan="2" | Day<br />(stem)!! colspan="4" rowspan="2"| Month<br />(stem)!! colspan="4" rowspan="2"| 2-digit year<br />[[Modulo operation|mod]] 40<br />(stem)!! colspan="5" | Century<br />(stem)!! rowspan="2" {{yes|N}} !!  colspan="5" | Century<br />(branch)!! colspan="7" rowspan="2"| 2-digit year<br />[[Modulo operation|mod]] 16<br />(branch)!! colspan="4" rowspan="2"| Month<br />(branch)!! colspan="3" rowspan="2"| Day<br />(branch)
|-
!Julian<br />[[Modulo operation|mod]] 2<br />!! colspan="4" | Gregorian!!Julian<br />[[Modulo operation|mod]] 4!! colspan="4" | Gregorian
|-
| 00 || 10 || 20 || 30 || Aug || colspan="3" | || {{tooltip|2=May be a leap year if occurring in a century divisible by 400|00}} || 02 || {{maybe|}}21 || 23 || style="text-align:center| 00 || {{tooltip|2=1600 is a leap year|16}} || colspan="3" | || {{yes|'''00'''}} || 00 || colspan="4"|  || {{tooltip|2=May be a leap year if occurring in a century divisible by 400|00}} || colspan="2"| || 07 ||colspan="3"| ||colspan="3" | || Nov || 00 || 12 || 24
|-
| 01 || 11 || 21 || 31 || Sep  || Oct || colspan="2" | || {{tooltip|2=leap year|04}} || 06 || 25 || 27 ||  || colspan="2" | || 21 ||  || {{yes|'''01'''}} || ||    colspan="4"| ||colspan="6"| || 14 || colspan="4" | || 01 || 13 || 25
|-
| 02 || 12 || 22 ||  || Nov ||  Dec || colspan="2" |  || {{tooltip|2=leap year|08}} || 10 || 29 || 31 || ||  || 19 || colspan="2" | || {{yes|'''02'''}} ||  ||  {{tooltip|2=1600 is a leap year|16}} || 19 || colspan="2" | ||colspan="2"| || {{maybe|}}05 ||colspan="4"|  || {{tooltip|2=In a leap year|'''''Feb'''''}} || Apr || colspan="2" | || 02 || 14 || 26
|-
| 03 || 13 || 23 ||  || colspan="4"| || {{tooltip|2=leap year|12}} || 14 || 33 || 35 ||  || colspan="4" | || {{yes|'''03'''}} || 03 || colspan="2" | || 22 || || || 03 ||colspan="3"| || {{tooltip|2=leap year|12}} ||  || Feb || Jun || colspan="2" | || 03 || 15 || 27
|-
| 04 || 14 || 24 ||  || colspan="4"| || {{tooltip|2=leap year|16}} || 18 || 37 || 39 || || 17 ||colspan="2" | ||  {{tooltip|2=2400 is a leap year|24}} || {{yes|'''04'''}} || || colspan="4"|  ||colspan="4"| || 10 ||colspan="2"| || colspan="2" | || Aug ||  || 04 || 16 || 28
|-
| 05 || 15 || 25 ||  || colspan="4"|  || 01 || 03 || {{tooltip|2=leap year|20}} || 22 || style="text-align:center| 01 || colspan="2" | || 22 || 15 || {{yes|'''05'''}} ||  || 15 || colspan="3"|  || 01 ||colspan="6"| || colspan="3" | || Oct || 05 || 17 || 29
|-
| 06 || 16 || 26 ||  || colspan="4"| || 05 || 07 || {{tooltip|2=leap year|24}} || 26 || || colspan="4"| || {{yes|'''06'''}} ||  02 || ||18 || colspan="2" |   || colspan="3"| || {{tooltip|2=leap year|08}}||colspan="2"| || 15 || colspan="3" | || Dec || 06 || 18 || 30
|-
| 07 || 17 || 27 || ||  || Mar ||  || {{tooltip|2=In a leap year|'''''Jan'''''}}  || 09 || 11 || {{tooltip|2=leap year|28}} || 30 || || || {{maybe|}}{{tooltip|2=2000 is a leap year|20}} || colspan="2" | || {{yes|'''07'''}} || || colspan="2" | || 21 ||  ||colspan="2"| || 06 ||colspan="4"| || {{tooltip|2=In a leap year|'''''Jan'''''}} || Mar || colspan="2" | || 07 || 19 || 31
|-
| 08 || 18 || 28 ||  || Jan  || Apr  || May || {{tooltip|2=In a leap year|'''''Feb'''''}} || 13 || 15 || {{tooltip|2=leap year|32}} || 34 ||  || 18 || colspan="3" | || {{yes|'''08'''}} ||  || colspan="3" | || {{tooltip|2=2400 is a leap year|24}}  ||colspan="5"| || 13 || || Jan || May || colspan="2" | || 08 || 20 
|rowspan="5" colspan="1"|
|-
| 09 || 19 || 29 ||  || Feb  || Jun  || Jul ||  || 17 || 19 || {{tooltip|2=leap year|36}}|| 38 || || colspan="2" | || 23 ||  || {{yes|'''09'''}} || 01 || colspan="4"| || || {{tooltip|2=leap year|04}}  ||colspan="2"| || 11 ||colspan="2"| || colspan="2" | || Jul ||  || 09 || 21 
|-
|rowspan="2" colspan="17"| Dates with the pale yellow background indicate they are for this year. 
| {{yes|'''10'''}} || ||17 || colspan="3" | || 02 ||colspan="6"| || colspan="4"| || 10 || 22 
|-
| {{yes|'''11'''}} ||  || colspan="2" | || {{maybe|}}{{tooltip|2=2000 is a leap year|20}} || 23  ||colspan="3"| || 09 ||colspan="3"| || colspan="2" | || Sep ||  || 11 || 23
|}
*N for the year: (5y + [y/4]) mod 10, y = 0–39 (stem); (5y + [y/4]) mod 12, y = 0–15 (branch)
*N for the Gregorian century: (4c + [c/4] + 2) mod 10 (stem); (8c + [c/4] + 2) mod 12 (branch), c ≥ 15 
*N for the Julian century: 5c mod 10, c = 0–1 (stem); 9c mod 12, c = 0–3 (branch)
The table above allows one to find the stem & branch for any given date. For both the stem and the branch, find the N for the row for the century, year, month, and day, then add them together. If the sum for the stems' N is above 10, subtract 10 until the result is between 1 and 10. If the sum for the branches' N is above 12, subtract 12 until the result is between 1 and 12.

For any date before October 15, 1582, use the [[Julian calendar|Julian century]] column to find the row for that century's N. For dates after October 15, 1582, use the [[Gregorian calendar|Gregorian century]] column to find the century's N. When looking at dates in January and February of leap years, use the bold & italic '''''Feb''''' and '''''Jan'''''.

===Examples===
* Step-by-step example to determine the stem-branch for October 1, 1949.
**Stem 
***(day stem N + month stem N + year stem N + century stem N) = number of stem. If over 10, subtract 10 until within 1 – 10.
****Day 1: N = 1,
****Month of October: N = 1,
****Year 49: N = 7, 
*****49 isn't on the table, so we'll have to [[Modulo operation|mod]] 49 by 40. This gives us year 9, which we can follow to find the N for that row.
****Century 19: N = 2. 
***(1 + 1 + 7 + 2) = 11. This is more than 10, so we'll subtract 10 to bring it between 1 and 10. 
****11 – 10 = 1,
****Stem = 1, {{zh| labels=no|c=甲}}.
**Branch
***(day branch N + month branch N + year branch N + century branch N)= number of branch. If over 12, subtract 12 until within 1 – 12. 
****Day 1: N = 1,
****Month of October: N = 5,
****Year 49: N = 5, 
*****Again, 49 is not in the table for year. Modding 49 by 16 gives us 1, which we can look up to find the N of that row. 
****Century 19: N = 2.
***(1 + 5 + 5 + 2) = 13. Since 13 is more than 12, we'll subtract 12 to bring it between 1 and 12. 
****13 – 12 = 1,
****Branch = 1, {{zh| labels=no|c=子}}.
**Stem-branch = 1, 1 ({{zh| labels=no|c=甲子}}, 1 in sexagenary cycle = 32 – 5 + 33 + 1 – 60).
{{collapse top |title=More detailed examples}}
*Stem-branch for December 31, 1592
**Stem = (day stem N + month stem N + year stem N + century stem N)
***Day 31: N = 1; month of December: N = 2; year 92 (92 mod 40 = 12): N = 3; century 15: N = 5.
***(1 + 2 + 3 + 5) = 11;  11 – 10 = 1.
***Stem = 1, {{zh| labels=no|c=甲}}.
**Branch = (day branch N + month branch N + year branch N + century branch N)
***Day 31: N = 7; month of December: N = 6; year 92 (92 mod 16 = 12): N = 3; century 15: N = 5.
***(7 + 6 + 3 + 5) = 21; 21 – 12 = 9.
***Branch = 9, {{zh| labels=no|c=申}}
**Stem-branch = 1, 9 ({{zh| labels=no|c=甲申}}, 21 in cycle = – 42 – 2 + 34 + 31 = 21)
*Stem-branch for August 4, 1338
**Stem = 8, {{zh|labels=no|c=辛}}
***Day 4: N = 4; month of August: N = 0; year 38: N = 9; century 13 (13 mod 2 = 1): N = 5.
***(4 + 0 + 9 + 5) = 18; 18 – 10 = 8.
**Branch = 12, {{zh|labels=no|c=亥}}
***Day 4: N = 4; month of August: N = 4; year 38 (38 mod 16 = 6): N = 7; century 13 (13 mod 4 = 1): N = 9.
***(4 + 4 + 7 + 9) = 24; 24 – 12 = 12
**Stem-branch = 8, 12 ({{zh|labels=no|c=辛亥}}, 48 in cycle = 4 + 8 + 32 + 4)
*Stem-branch for May 25, 105 BC (−104).
**Stem = 7, {{zh|labels=no|c=庚}}
***Day 25: N = 5; month of May: N = 8; year −4 (−4 mod 40 = 36): N = 9; century −1 (−1 mod 2 = 1): N = 5.
***(5 + 8 + 9 + 5) = 27; 27 – 10 = 17; 17 – 10 = 7.
**Branch = 3, {{zh|labels=no|c=寅}}
***Day 25: N = 1; month of May: N = 8; year −4 (−4 mod 16 = 12): N = 3; century −1 (−1 mod 4 = 3): N = 3.
***(1 + 8 + 3 + 3) = 15; 15 – 12 = 3.
**Stem-branch = 7, 3 ({{zh|labels=no|c=庚寅}}, 27 in cycle = – 6 + 8 + 0 + 25)
**Alternately, instead of doing both century and year, one can exclude the century and simply use −104 as the year for both the stem and the branch to get the same result.

'''Algorithm for mental calculation'''
:<math>SB = (y + c + m + day) \bmod 60</math>
:<math>S = SB \bmod 10, B = SB \bmod 12</math>
:<math>y = (year(\bmod 400) \bmod 80 (\bmod 12) \times 5 + \left\lfloor\frac{year(\bmod 400) \bmod 80}{4}\right\rfloor) \bmod 60</math>
:<math>c = \left\lfloor\frac{year}{400}\right\rfloor - \left\lfloor\frac{year}{100}\right\rfloor + 10 </math> for Gregorian calendar and <math>c = 8 </math> for Julian calendar.
:<math>m =(month + 1)\bmod 2\times 30+\left\lfloor{0.6\times (month + 1) - 3}\right\rfloor - i </math> <br/> <math>i = 5</math> for Jan or Feb in a common year and <math>i = 6 </math> in a leap year.
{| class="wikitable" style="text-align:center"
|-
! Month
|Jan<br/>13||Feb<br/>14||Mar<br/>03||Apr<br/>04||May<br/>05||Jun<br/>06||Jul<br/>07||Aug<br/>08||Sep<br/>09||Oct<br/>10||Nov<br/>11||Dec<br/>12
|-
! m
|00||31||−1||30||00||31||01||32||03||33||04||34
|-
!Leap year
||−1||30||colspan="10"|<math>m =\left\lfloor{30.6 \times (month + 1)} -
 3 \right\rfloor \bmod 60 - i </math>
|}
*Stem-branch for February 22, 720 BC (−719).
:y = 5 x (720–719) + [1/4] = 5
:c = 8
:m = 30 + [0.6 x 15 – 3] – 5 = 31
:d = 22
:SB = 5 + 8 + 31 + 22 – 60 = 6
:S = B = 6, 己巳
*Stem-branch for November 1, 211 BC (−210).
:y = 5 x (240–210) + [30/4] = 5 x 6 + 7 = 37
:c = 8
:m = 0 + [0.6 x 12 – 3] = 4
:d = 1
:SB = 37 + 8 + 4 + 1 = 50
:S = 0, B = 2, 癸丑
*Stem-branch for February 18, 1912.
:y = 5 x (1912–1920) + [-8/4] + 60 = 18
:c = 4 – 19 + 10 = -5
:m = 30 + [0.6 x 15 – 3] – 6 = 30
:d = 18
:SB = 18 – 5 + 30 + 18 – 60 = 1
:S = B = 1, 甲子
*Stem-branch for October 1, 1949.
:y = 5 x (1949–1920) + [29/4] = 5 x 5 + 7 = 32
:c = -5
:m = 30 + [0.6 x 11 -3] = 33
:d = 1
:SB = 32 – 5 + 33 + 1 – 60 = 1
:S = B = 1, 甲子
{{collapse bottom}}

{| class="wikitable" style="text-align:center"
|+Look up table for sexagenary days
|'''Gregorian''' || || 17<br/>'''24''' || 15<br/>22 || || <br/>'''20''' || 18<br/><br/> || <br/>23<br/> || '''16'''<br/><br/> || <br/>21<br/> || 19<br/><br/> ||rowspan=2 colspan=10| '''Centuries'''
|-
| '''Julian''' || || || '''01''' || || || || || '''00''' || || 
|-
|rowspan=2|'''Dates''' || Mar<br/>'''Jan'''<br/><br/><br/> || || || || || Nov<br/>Dec<br/><br/><br/> || Sep<br/>Oct<br/><br/><br/> || Aug<br/><br/><br/><br/> || Feb<br/>Jun<br/>Jul<br/><br/> || Jan<br/>Apr<br/>May<br/>'''Feb''' || rowspan=3 colspan=10| '''Years of the century'''
|-
| 01<br/>11<br/>21<br/>31 || 02<br/>12<br/>22<br/><br/> || 03<br/>13<br/>23<br/><br/> || 04<br/>14<br/>24<br/><br/> || 05<br/>15<br/>25<br/><br/> || 06<br/>16<br/>26<br/><br/> || 07<br/>17<br/>27<br/><br/> || 08<br/>18<br/>28<br/><br/> || 09<br/>19<br/>29<br/><br/> || 10<br/>20<br/>30<br/><br/>
|-
| '''天干''' || '''甲''' || '''乙''' || '''丙''' || '''丁''' || '''戊''' || '''己''' || '''庚''' || '''辛''' || '''壬''' || '''癸'''
|-
|rowspan=10|'''Heavenly stems''' || '''A''' || '''B''' || '''C''' || '''D''' || '''E''' || '''F''' || '''G''' || '''H''' || '''I''' || '''J''' || '''0'''0 || 02 || 21 || 23 || '''40''' || 42 || 61 || 63 || '''80''' || 82 
|-
| B || C || D || E || F || G || H || I || J || A || '''04''' || 06 || 25 || 27 || '''44''' || 46 || 65 || 67 || '''84''' || 86
|-
| C || D || E || F || G || H || I || J ||A || B || '''08''' || 10 || 29 || 31 || '''48''' || 50 || 69 || 71 || '''88''' || 90
|-
| D || E || F || G || H || I || J || A || B || C || '''12''' || 14 || 33 || 35 || '''52''' || 54 || 73 || 75 || '''92''' || 94
|-
| E || F || G || H || I || J || A || B || C || D || '''16''' || 18 || 37 || 39 || '''56''' || 58 || 77 || 79 || '''96''' || 98
|-
| F || G || H || I || J || A || B || C || D || E || 01 || 03 || '''20''' || 22 || 41 || 43 || '''60''' || 62 || 81 || 83
|-
| G || H || I || J || A || B || C || D || E || F || 05 || 07 || '''24''' || 26 || 45 || 47 || '''64''' || 66 || 85 || 87
|-
| H || I || J || A || B || C || D || E || F || G || 09 || 11 || '''28''' || 30 || 49 || 51 || '''68''' || 70 || 89 || 91
|-
| I || J || A || B || C || D || E || F || G || H || 13 || 15 || '''32''' || 34 || 53 || 55 || '''72''' || 74 || 93 || 95
|-
| J || A || B || C || D || E || F || G || H || I || 17 || 19 || '''36''' || 38 || 57 || 59 || '''76''' || 78 || 97 || 99
|-
| '''地支''' || '''子''' || '''丑''' || '''寅''' || '''卯''' || '''辰''' || '''巳''' || '''午''' || '''未''' || '''申''' || '''酉''' || '''戌''' || '''亥''' ||colspan=13| '''干支纪日速查表'''
|-
|rowspan=12|'''Earthly branches''' || '''A''' || '''B''' || '''C''' || '''D''' || '''E''' || '''F''' || '''G''' || '''H''' || '''I''' || '''J''' || '''K''' || '''L''' || '''0'''0 || 07 || '''16''' || 23 || '''32''' || 39 || '''48''' || 55 || '''64''' || 71 || '''80''' || 87 || '''96''' 
|-
| B || C || D || E || F || G || H || I || J || K || L || A || || 14 || || 30 || || 46 || || 62 || || 78 || || 94 ||
|-
| C || D || E || F || G || H || I || J || K || L || A || B || 05 || || 21 || || 37 || || 53 || || 69 || || 85 || || 
|-
| D || E || F || G || H || I || J || K ||L || A || B || C || 03 || '''12''' || 19 || '''28''' || 35 || '''44''' || 51 || '''60''' || 67 || '''76''' || 83 || '''92''' || 99
|-
| E || F || G || H || I || J || K ||L || A || B || C || D || || 10 || || 26 || || 42 ||  || 58 || || 74 || || 90 || 
|-
| F || G || H || I || J || K || L || A || B || C || D || E || 01 || || 17 ||  || 33 ||  || 49 ||  || 65 || || 81 || || 97
|-
| G || H || I || J || K || L || A || B || C || D || E || F || '''08''' || 15 || '''24''' || 31 || '''40''' || 47 || '''56''' || 63 || '''72''' || 79 || '''88''' || 95 || 
|-
| H || I || J || K || L || A || B || C || D || E || F || G || 06 || || 22 || || 38 || || 54 || || 70 || || 86 || || 
|-
| I || J || K || L || A || B || C || D || E || F || G || H || || 13 ||  || 29 ||  || 45 ||  || 61 || || 77 || || 93 || 
|-
| J || K || L || A || B || C || D || E || F || G || H || I || '''04''' || 11 || '''20''' || 27 || '''36''' || 43 || '''52''' || 59 || '''68''' || 75 || '''84''' || 91 || 
|-
| K || L || A || B || C || D || E || F || G || H || I || J || 02 || || 18 || || 34|| || 50 || || 66 || || 82 || || 98
|-
| L || A || B || C || D || E || F || G || H || I || J || K || || 09 || || 25 || || 41 || || 57 || || 73 || || 89 || 
|-
|rowspan=2|'''Dates''' || 01<br/>13<br/>25 || 02<br/>14<br/>26 || 03<br/>15<br/>27 || 04<br/>16<br/>28 || 05<br/>17<br/>29 || 06<br/>18<br/>30 || 07<br/>19<br/>31 || 08<br/>20<br/><br/> || 09<br/>21<br/><br/> || 10<br/>22<br/><br/> || 11<br/>23<br/><br/> || 12<br/>24<br/><br/> ||rowspan=2 colspan=13|'''Years of the century'''
|-
| Mar<br/>'''Jan''' || <br/>Dec || <br/>Oct || <br/>Aug || Feb<br/>Jun || Apr<br/>'''Feb''' || || <br/>Nov || <br/>Sep || || <br/>Jul ||Jan<br/>May
|-
| '''Gregorian''' || || 15<br/>18<br/><br/> || <br/><br/>21 || <br/><br/>'''24''' || || 17<br/><br/><br/> || <br/>'''20'''<br/>23 || || || '''16'''<br/>19<br/><br/> || <br/><br/>22 || ||rowspan=2 colspan=13| '''Centuries'''
|-
| '''Julian''' || || '''02''' || || || '''01''' || || || '''00''' || || || '''03''' || 
|}

==Sexagenary hours==
{| class="wikitable"
|+ Table for sexagenary hours (5-day cycle)
|-
!Stem of the day!!Zǐ hour<br />{{lang|und-Hani|子时}}<br/>23:00–1:00!!Chǒu hour<br />{{lang|und-Hani|丑时}}<br/>1:00–3:00!!Yín hour<br />{{lang|und-Hani|寅时}}<br/>3:00–5:00!! Mǎo hour<br />{{lang|und-Hani|卯时}}<br/>5:00–7:00!!Chén hour<br />{{lang|und-Hani|辰时}}<br/>7:00–9:00!!Sì hour<br />{{lang|und-Hani|巳时}}<br/>9:00–11:00!!Wǔ hour<br />{{lang|und-Hani|午时}}<br/>11:00–13:00!!Wèi hour<br />{{lang|und-Hani|未时}}<br/>13:00–15:00!!Shēn hour<br/>{{lang|und-Hani|申时}}<br/>15:00–17:00!!Yǒu hour<br />{{lang|und-Hani|酉时}}<br/>17:00–19:00!!Xū hour<br />{{lang|und-Hani|戌时}}<br/>19:00–21:00!!Hài hour<br />{{lang|und-Hani|亥时}}<br/>21:00–23:00
|-
!Jia or Ji day<br />({{lang|und-Hani|甲/己}})
|1 {{lang|und-Hani|甲子}}||2{{lang|und-Hani|乙丑}}||3 {{lang|und-Hani|丙寅}}||4 {{lang|und-Hani|丁卯}}||5 {{lang|und-Hani|戊辰}}||6 {{lang|und-Hani|己巳}}||7 {{lang|und-Hani|庚午}}||8 {{lang|und-Hani|辛未}}||9 {{lang|und-Hani|壬申}}||10 {{lang|und-Hani|癸酉|}}||11 {{lang|und-Hani|甲戌}}||12 {{lang|und-Hani|乙亥}}
|-
!Yi or Geng day<br />({{lang|und-Hani|乙/庚}})
|13 {{lang|und-Hani|丙子}}||14 {{lang|und-Hani|丁丑}}||15 {{lang|und-Hani|戊寅}}||16 {{lang|und-Hani|己卯}}||17 {{lang|und-Hani|庚辰}}||18 {{lang|und-Hani|辛巳}}||19 {{lang|und-Hani|壬午}}||20 {{lang|und-Hani|癸未}}||21 {{lang|und-Hani|甲申}}||22 {{lang|und-Hani|乙酉}}||23 {{lang|und-Hani|丙戌}}||24 {{lang|und-Hani|丁亥}}
|-
!Bing or Xin day<br />({{lang|und-Hani|丙/辛}})
|25 {{lang|und-Hani|戊子}}||26 {{lang|und-Hani|己丑}}||27 {{lang|und-Hani|庚寅}}||28 {{lang|und-Hani|辛卯}}||29 {{lang|und-Hani|壬辰}}||30 {{lang|und-Hani|癸巳}}||31 {{lang|und-Hani|甲午}}||32 {{lang|und-Hani|乙未}}||33 {{lang|und-Hani|丙申}}||34 {{lang|und-Hani|丁酉}}||35 {{lang|und-Hani|戊戌}}||36 {{lang|und-Hani|己亥}}
|-
!Ding or Ren day<br />({{lang|und-Hani|丁/壬}})
|37 {{lang|und-Hani|庚子}}||38 {{lang|und-Hani|辛丑}}||39 {{lang|und-Hani|壬寅}}||40 {{lang|und-Hani|癸卯}}||41 {{lang|und-Hani|甲辰}}||42 {{lang|und-Hani|乙巳}}||43 {{lang|und-Hani|丙午}}||44 {{lang|und-Hani|丁未}}||45 {{lang|und-Hani|戊申}}||46 {{lang|und-Hani|己酉}}||47 {{lang|und-Hani|庚戌}}||48 {{lang|und-Hani|辛亥}}
|-
!Wu or Gui day<br />({{lang|und-Hani|戊/癸}})
|49 {{lang|und-Hani|壬子}}||50 {{lang|und-Hani|癸丑}}||51 {{lang|und-Hani|甲寅}}||52 {{lang|und-Hani|乙卯}}||53 {{lang|und-Hani|丙辰}}||54 {{lang|und-Hani|丁巳}}||55 {{lang|und-Hani|戊午}}||56 {{lang|und-Hani|己未}}||57 {{lang|und-Hani|庚申}}||58 {{lang|und-Hani|辛酉}}||59 {{lang|und-Hani|壬戌}}||60 {{lang|und-Hani|癸亥}}
|}

==See also==
* [[Religion:Doumu|Doumu]] (斗母元君)
* [[Astronomy:Tai Sui|Tai Sui]] (太歲)
* Chinese calendar
* [[History:Chinese era name|Chinese era name]]
* Japanese invasions of Korea (1592–1598), known in Korean as the "Imjin War", after the "Yang Water (im) [[Unsolved:Dragon (zodiac)|Dragon]] (jin)" year 1592.
* Koshien Stadium (Japan), named after the "Yang Wood (kō) Rat (shi)" year 1924. One of the last examples of general usage of the cycle in Japan.
* [[Astronomy:Lunisolar calendar|Lunisolar calendar]]
* Tet Offensive – Vietnamese name of the event, "Tết Mậu Thân Event", named after the "Yang Earth (mậu) [[Unsolved:Monkey (zodiac)|Monkey]] (thân)" year 1968.
* Xinhai Revolution (China), named after the "Yin Metal (xin) [[Unsolved:Pig (zodiac)|Pig]] (hai)" year 1911<ref>{{Cite book|url=https://books.google.com/books?id=0fP_DwAAQBAJ&pg=PA640|title=Conflicting Memories: Tibetan History under Mao Retold|date=2020-09-07|publisher=BRILL|isbn=978-90-04-43324-3|pages=640|language=en}}</ref>

== References ==
=== Citations ===
{{Reflist|1}}

=== Sources ===
{{refbegin}}
* {{cite journal | volume = 48 | issue = 1 | pages = 80–84 | last = Bartle | first = P. F. W. | title = Forty days: the Akan calendar | journal = Africa: Journal of the International African Institute | year = 1978 | doi = 10.2307/1158712 | jstor = 1158712 | s2cid = 143751434 }}
* {{cite book | publisher = Brill | isbn = 978-90-04-16063-7 | pages = 137–168 | editor = Francesca Bray | last = Kalinowski | first = Marc | title = Graphics and text in the production of technical knowledge in China : the warp and the weft | chapter = Time, space and orientation: figurative representations of the sexagenary cycle in ancient and medieval China | location = Leiden |year = 2007 }}
* {{cite book | publisher = Oxbow | isbn = 978-1-84217-987-1 | pages = 1–37 | editor-first = John |editor-last = Steele | last = Smith | first = Adam | title = Calendars and years II : astronomy and time in the ancient and medieval world |chapter = The Chinese sexagenary cycle and the ritual origins of the calendar |location = Oxford |year = 2011 |chapter-url = https://academiccommons.columbia.edu/catalog/ac:128930 }}
{{refend}}

==External links==
* {{cite web|url=http://www.hko.gov.hk/gts/time/stemsandbranches.htm|title=Heavenly Stems and Earthly Branches|website=Hong Kong Observatory|language=en|access-date=2018-11-04|url-status=live|archive-url=https://web.archive.org/web/20181104043156/http://www.hko.gov.hk/gts/time/stemsandbranches.htm|archive-date=2018-11-04}}
* [https://ganzhi.io/ganzhi Ganzhi.io] An Open Source application and implementation of Gan & Zhi as well as Jeiqi

{{-}}
{{chronology}}


[[Category:Units of time]]

{{Sourceattribution|Sexagenary cycle}}