Sexagenary cycle

The sexagenary cycle, also known as the stems-and-branches or ganzhi (Chinese: 干支), 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 East Asian cultural sphere and Southeast Asia.^[1][2] 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.^[3] 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 in Mainland China.^[4] In India, the Dai-Ahom (descendants of Dai ethnic minority of Yunnan who migrated to Assam in 13th century) also used the sexagenary cycle known as Lak-Ni.^[5][6]

"Xinwei" redirects here. For the town in China, see Xinwei, Meizhou.

Sexagenary cycle
Chinese	六十干支
Transcriptions Standard Mandarin Hanyu Pinyin liùshí gānzhī IPA [ljôʊ.ʂǐ kán.ʈʂí]
stems-and-branches
Chinese	干支
Transcriptions Standard Mandarin Hanyu Pinyin gānzhī IPA [kán.ʈʂí]

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 Chinese astrology and fortune telling. There are some parallels in this with Tamil calendar.

Overview

Sexagenary cycle
1 Wood Rat	2 Wood Ox [ja]	3 Fire Tiger [ja]	4 Fire Rabbit [ja]	5 Earth Dragon	6 Earth Snake [ja]
7 Metal Horse [ja]	8 Metal Goat [ja]	9 Water Monkey [ja]	10 Water Rooster [ja]	11 Wood Dog [ja]	12 Wood Pig [ja]
13 Fire Rat [ja]	14 Fire Ox [ja]	15 Earth Tiger [ja]	16 Earth Rabbit [ja]	17 Metal Dragon [ja]	18 Metal Snake [ja]
19 Water Horse [ja]	20 Water Goat [ja]	21 Wood Monkey [ja]	22 Wood Rooster [ja]	23 Fire Dog [ja]	24 Fire Pig [ja]
25 Earth Rat [ja]	26 Earth Ox [ja]	27 Metal Tiger [ja]	28 Metal Rabbit [ja]	29 Water Dragon [ja]	30 Water Snake [ja]
31 Wood Horse [ja]	32 Wood Goat [ja]	33 Fire Monkey [ja]	34 Fire Rooster [ja]	35 Earth Dog [ja]	36 Earth Pig [ja]
37 Metal Rat [ja]	38 Metal Ox [ja]	39 Water Tiger [ja]	40 Water Rabbit [ja]	41 Wood Dragon [ja]	42 Wood Snake [ja]
43 Fire Horse	44 Fire Goat [ja]	45 Earth Monkey [ja]	46 Earth Rooster [ja]	47 Metal Dog [ja]	48 Metal Pig [ja]
49 Water Rat [ja]	50 Water Ox [ja]	51 Wood Tiger [ja]	52 Wood Rabbit [ja]	53 Fire Dragon [ja]	54 Fire Snake [ja]
55 Earth Horse [ja]	56 Earth Goat [ja]	57 Metal Monkey	58 Metal Rooster	59 Water Dog [ja]	60 Water Pig [ja]
Heavenly Stems ・ Earthly Branches

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.^[7]

History

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 c. 1100 BC.^[8] 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.^[9]

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.^{[10] [11]} 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:^[12] 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.^[13]

The Korean (환갑; 還甲 hwangap) and Japanese tradition (還暦 kanreki) of celebrating the 60th birthday (literally 'return of calendar') reflects the influence of the sexagenary cycle as a count of years.^[14]

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).^[15]

Ten Heavenly Stems

Main article: Celestial Stems

No.	Heavenly Stem	Ahom Name	Chinese name				Japanese name		Korean name		Vietnamese name	Yin Yang	Wu Xing
			Mandarin (Pinyin)	Cantonese (Jyutping)	Middle Chinese (Baxter)	Old Chinese (Baxter–Sagart)	Onyomi	Kunyomi with corresponding kanji	Romanized	Hangul
1	甲	kap	jiǎ	gaap3	kæp	*[k]ˤr[a]p	kō (こう)	kinoe (木の兄)	gap	갑	giáp	yang	wood
2	乙	dap	yǐ	jyut3	ʔit	*qrət	otsu (おつ)	kinoto (木の弟)	eul	을	ất	yin
3	丙	rai	bǐng	bing2	pjængX	*praŋʔ	hei (へい)	hinoe (火の兄)	byeong	병	bính	yang	fire
4	丁	Mueang	dīng	ding1	teng	*tˤeŋ	tei (てい)	hinoto (火の弟)	jeong	정	đinh	yin
5	戊	plaek	wù	mou6	muwH	*m(r)uʔ-s (~ *m(r)uʔ)	bo (ぼ)	tsuchinoe (土の兄)	mu	무	mậu	yang	earth
6	己	kat	jǐ	gei2	kiX	*k(r)əʔ	ki (き)	tsuchinoto (土の弟)	gi	기	kỷ	yin
7	庚	khut	gēng	gang1	kæng	*kˤraŋ	kō (こう)	kanoe (金の兄)	gyeong	경	canh	yang	metal
8	辛	rung	xīn	san1	sin	*si[n]	shin (しん)	kanoto (金の弟)	sin	신	tân	yin
9	壬	tao	rén	jam4	nyim	*n[ə]m	jin (じん)	mizunoe (水の兄)	im	임	nhâm	yang	water
10	癸	ka	guǐ	gwai3	kjwijX	*kʷijʔ	ki (き)	mizunoto (水の弟)	gye	계	quý	yin

Twelve Earthly Branches

Main article: Terrestrial Branches

No.	Earthly Branch	Chinese name				Japanese name		Korean name		Vietnamese name	Vietnamese zodiac	Chinese zodiac	Corresponding hours
		Mandarin (Pinyin)	Cantonese (Jyutping)	Middle Chinese (Baxter)	Old Chinese (Baxter–Sagart)	Onyomi	Kunyomi	Romanized	Hangul
1	子	zǐ	zi2	tsiX	*[ts]əʔ	shi (し)	ne (ね)	ja	자	tý	Rat (chuột 𤝞)	Rat (鼠)	11 p.m. to 1 a.m.
2	丑	chǒu	cau2	trhjuwX	*[n̥]ruʔ	chū (ちゅう)	ushi (うし)	chuk	축	sửu	Water buffalo (trâu 𤛠)	Ox (牛)	1 to 3 a.m.
3	寅	yín	jan4	yij	*[ɢ] (r)ər	in (いん)	tora (とら)	in	인	dần	Tiger (hổ 虎/cọp 𧲫)	Tiger (虎)	3 to 5 a.m.
4	卯	mǎo	maau5	mæwX	*mˤruʔ	bō (ぼう)	u (う)	myo	묘	mão/mẹo	Cat (mèo 猫)	Rabbit (兔)	5 to 7 a.m.
5	辰	chén	san4	dzyin	*[d]ər	shin (しん)	tatsu (たつ)	jin	진	thìn	Dragon (rồng 龍)	Dragon (龍)	7 to 9 a.m.
6	巳	sì	zi6	ziX	*s-[ɢ]əʔ	shi (し)	mi (み)	sa	사	tỵ	Snake (rắn 𧋻)	Snake (蛇)	9 to 11 a.m.
7	午	wǔ	ng5	nguX	*[m].qʰˤaʔ	go (ご)	uma (うま)	o	오	ngọ	Horse (ngựa 馭)	Horse (馬)	11 a.m. to 1 p.m.
8	未	wèi	mei6	mjɨjH	*m[ə]t-s	mi (み) or bi (び)	hitsuji (ひつじ)	mi	미	mùi	Goat (dê 羝)	Goat (羊)	1 to 3 p.m.
9	申	shēn	san1	syin	*l̥i[n]	shin (しん)	saru (さる)	sin	신	thân	Monkey (khỉ 𤠳)	Monkey (猴)	3 to 5 p.m.
10	酉	yǒu	jau5	yuwX	*N-ruʔ	yū (ゆう)	tori (とり)	yu	유	dậu	Rooster (gà 𪂮)	Rooster (雞)	5 to 7 p.m.
11	戌	xū	seot1	swit	*s.mi[t]	jutsu (じゅつ)	inu (いぬ)	sul	술	tuất	Dog (chó 㹥)	Dog (狗)	7 to 9 p.m.
12	亥	hài	hoi6	hojX	*[g]ˤəʔ	gai (がい)	i (い)	hae	해	hợi	Pig (lợn 𤞼/heo 㺧)	Pig (豬)	9 to 11 p.m.

*The names of several animals can be translated into English in several different ways. The Vietnamese Earthly Branches use cat instead of Rabbit.

Sexagenary years

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

24 cardinal directions

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.^[16] 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 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.
3. 1 AD, 2 AD and 3 AD correspond respectively to the 58th, 59th and 60th years of the sexagenary cycle.
4. The formula for years AD is (year – 3) mod 60 and for years BC is (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) 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:

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 (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 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 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.

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

1804–1923

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

1924–2043

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

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 (甲; 1st) or jǐ (己; 6th) year. The first month of the jiǎ or jǐ 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 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.

Earthly Branches of the certain months	Solar term	Zhongqi (the Middle solar term)	Starts at	Ends at	Names in year of Jia or Ji(甲/己年)	Names in year of Yi or Geng (乙/庚年)	Names in year of Bing or Xin (丙/辛年)	Names in year of Ding or Ren (丁/壬年)	Names in year of Wu or Gui (戊/癸年)
Month of Yin (寅月)	Lichun – Jingzhe	Yushui / 雨水	February 4	March 6	Bingyin / 丙寅月	Wuyin / 戊寅月	Gengyin / 庚寅月	Renyin / 壬寅月	Jiayin / 甲寅月
Month of Mao (卯月)	Jingzhe – Qingming	Chunfen / 春分	March 6	April 5	Dingmao / 丁卯月	Jimao / 己卯月	Xinmao / 辛卯月	Guimao / 癸卯月	Yimao / 乙卯月
Month of Chen (辰月)	Qingming – Lixia	Guyu / 谷雨	April 5	May 6	Wuchen / 戊辰月	Gengchen / 庚辰月	Renchen / 壬辰月	Jiachen / 甲辰月	Bingchen / 丙辰月
Month of Si (巳月)	Lixia – Mangzhong	Xiaoman / 小满	May 6	June 6	Jisi / 己巳月	Xinsi / 辛巳月	Guisi / 癸巳月	Yisi / 乙巳月	Dingsi / 丁巳月
Month of Wu (午月)	Mangzhong – Xiaoshu	Xiazhi / 夏至	June 6	July 7	Gengwu / 庚午月	Renwu / 壬午月	Jiawu / 甲午月	Bingwu / 丙午月	Wuwu / 戊午月
Month of Wei (未月)	Xiaoshu – Liqiu	Dashu / 大暑	July 7	August 8	Xinwei / 辛未月	Guiwei / 癸未月	Yiwei / 乙未月	Dingwei / 丁未月	Jiwei / 己未月
Month of Shen (申月)	Liqiu – Bailu	Chushu / 处暑	August 8	September 8	Renshen / 壬申月	Jiashen / 甲申月	Bingshen / 丙申月	Wushen / 戊申月	Gengshen / 庚申月
Month of You (酉月)	Bailu – Hanlu	Qiufen / 秋分	September 8	October 8	Guiyou / 癸酉月	Yiyou / 乙酉月	Dingyou / 丁酉月	Jiyou / 己酉月	Xinyou / 辛酉月
Month of Xu (戌月)	Hanlu – Lidong	Shuangjiang / 霜降	October 8	November 7	Jiaxu / 甲戌月	Bingxu / 丙戌月	Wuxu / 戊戌月	Gengxu / 庚戌月	Renxu / 壬戌月
Month of Hai (亥月)	Lidong – Daxue	Xiaoxue / 小雪	November 7	December 7	Yihai / 乙亥月	Dinghai / 丁亥月	Jihai / 己亥月	Xinhai / 辛亥月	Guihai / 癸亥月
Month of Zi (子月)	Daxue – Xiaohan	Dongzhi / 冬至	December 7	January 6	Bingzi / 丙子月	Wuzi / 戊子月	Gengzi / 庚子月	Renzi / 壬子月	Jiazi / 甲子月
Month of Chou (丑月)	Xiaohan – Lichun	Dahan / 大寒	January 6	February 4	Dingchou / 丁丑月	Jichou / 己丑月	Xinchou / 辛丑月	Guichou / 癸丑月	Yichou / 乙丑月

Sexagenary days

Table for sexagenary days

Day (stem)				Month (stem)				2-digit year mod 40 (stem)				Century (stem)					N	Century (branch)					2-digit year mod 16 (branch)							Month (branch)				Day (branch)
												Julian mod 2	Gregorian					Julian mod 4	Gregorian
00	10	20	30	Aug				00	02	21	23	00	16				00	00					00			07							Nov	00	12	24
01	11	21	31	Sep	Oct			04	06	25	27				21		01												14					01	13	25
02	12	22		Nov	Dec			08	10	29	31			19			02		16	19					05					Feb	Apr			02	14	26
03	13	23						12	14	33	35						03	03			22			03				12		Feb	Jun			03	15	27
04	14	24						16	18	37	39		17			24	04										10					Aug		04	16	28
05	15	25						01	03	20	22	01			22	15	05		15				01										Oct	05	17	29
06	16	26						05	07	24	26						06	02		18						08			15				Dec	06	18	30
07	17	27			Mar		Jan	09	11	28	30			20			07				21				06					Jan	Mar			07	19	31
08	18	28		Jan	Apr	May	Feb	13	15	32	34		18				08					24						13		Jan	May			08	20
09	19	29		Feb	Jun	Jul		17	19	36	38				23		09	01						04			11					Jul		09	21
Dates with the pale yellow background indicate they are for this year.																	10		17				02											10	22
																	11				20	23				09						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 century column to find the row for that century's N. For dates after October 15, 1582, use the 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 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, 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, 子.
  • Stem-branch = 1, 1 (甲子, 1 in sexagenary cycle = 32 – 5 + 33 + 1 – 60).

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, 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, 申 Stem-branch = 1, 9 (甲申, 21 in cycle = – 42 – 2 + 34 + 31 = 21) Stem-branch for August 4, 1338 Stem = 8, 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, 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 (辛亥, 48 in cycle = 4 + 8 + 32 + 4) Stem-branch for May 25, 105 BC (−104). Stem = 7, 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, 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 (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 ${\displaystyle SB=(y+c+m+day){\bmod {6}}0}$ ${\displaystyle S=SB{\bmod {1}}0,B=SB{\bmod {1}}2}$ ${\displaystyle y=(year({\bmod {4}}00){\bmod {8}}0({\bmod {1}}2)\times 5+\left\lfloor {\frac {year({\bmod {4}}00){\bmod {8}}0}{4}}\right\rfloor ){\bmod {6}}0}$ ${\displaystyle c=\left\lfloor {\frac {year}{400}}\right\rfloor -\left\lfloor {\frac {year}{100}}\right\rfloor +10}$ for Gregorian calendar and ${\displaystyle c=8}$ for Julian calendar. ${\displaystyle m=(month+1){\bmod {2}}\times 30+\left\lfloor {0.6\times (month+1)-3}\right\rfloor -i}$ ${\displaystyle i=5}$ for Jan or Feb in a common year and ${\displaystyle i=6}$ in a leap year. Month Jan 13 Feb 14 Mar 03 Apr 04 May 05 Jun 06 Jul 07 Aug 08 Sep 09 Oct 10 Nov 11 Dec 12 m 00 31 −1 30 00 31 01 32 03 33 04 34 Leap year −1 30 ${\displaystyle m=\left\lfloor {30.6\times (month+1)}-3\right\rfloor {\bmod {6}}0-i}$ 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

Look up table for sexagenary days

Gregorian		17 24	15 22		20	18	23	16	21	19	Centuries
Julian			01					00
Dates	Mar Jan					Nov Dec	Sep Oct	Aug	Feb Jun Jul	Jan Apr May Feb	Years of the century
	01 11 21 31	02 12 22	03 13 23	04 14 24	05 15 25	06 16 26	07 17 27	08 18 28	09 19 29	10 20 30
天干	甲	乙	丙	丁	戊	己	庚	辛	壬	癸
Heavenly stems	A	B	C	D	E	F	G	H	I	J	00	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	干支纪日速查表
Earthly branches	A	B	C	D	E	F	G	H	I	J	K	L	00	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
Dates	01 13 25	02 14 26	03 15 27	04 16 28	05 17 29	06 18 30	07 19 31	08 20	09 21	10 22	11 23	12 24	Years of the century
	Mar Jan	Dec	Oct	Aug	Feb Jun	Apr Feb		Nov	Sep		Jul	Jan May
Gregorian		15 18	21	24		17	20 23			16 19	22		Centuries
Julian		02			01			00			03

Sexagenary hours

Table for sexagenary hours (5-day cycle)

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

See also

• Doumu (斗母元君)
• Tai Sui (太歲)
• Chinese calendar
• Chinese era name
• Japanese invasions of Korea (1592–1598), known in Korean as the "Imjin War", after the "Yang Water (im) 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.
• Lunisolar calendar
• Tet Offensive – Vietnamese name of the event, "Tết Mậu Thân Event", named after the "Yang Earth (mậu) Monkey (thân)" year 1968.
• Xinhai Revolution (China), named after the "Yin Metal (xin) Pig (hai)" year 1911^[21]

References

Citations

1. Nussbaum, Louis-Frédéric (2005). "Jikkan-jūnishi". Japan Encyclopedia. Translated by Roth, Käthe. p. 420. ISBN 9780674017535.
2. For non-mathematical readers, a simple explanation for the number "60" in the 60-year cycle of the Lunar calendar can be found in Vu-Quoc-Loc; Vu-Quoc-Hung; Vu-Le-Thao-Uyen; Lee-Collins (2024), The triennial Hương exam: Deducing laureates' birth years, Internet Archive, retrieved 2024-05-12.
3. Smith 2011, pp. 1, 28.
4. 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).
5. "...the Ahom reckoned time by means of a sexa- genary cycle"(Kapoor 2021:666)
6. "..migration from Mong Mao in Yunnan into Mungdunshunkhām..."(Kapoor 2021:666)
7. For the Akan calendar, see (Bartle 1978).
8. Selin, Helaine (2012-12-06). Mathematics Across Cultures: The History of Non-Western Mathematics. Springer Science & Business Media. p. 390. ISBN 978-94-011-4301-1.
9. Smith 2011, pp. 24, 26–27.
10. Kalinowski 2007, p. 145, fig. 3.
11. Smith 2011, p. 29.
12. Smith 2011, p. 28.
13. "Calendar History; the Source". National Diet Library. Archived from the original on January 6, 2013. Retrieved January 1, 2013.
14. "Kanreki". Encyclopedia of Shinto. Retrieved January 1, 2013.
15. Chattopadhyaya, Alaka (1999). Atisa and Tibet: Life and Works of Dipamkara Srijnana in relation to the history and religion of Tibet. Motilal Banarsidass Publ. pp. 566–568. ISBN 9788120809284.
16. Aslaksen, Helmer (July 17, 2010). "Mathematics of the Chinese calendar". www.math.nus.edu.sg/aslaksen. Department of Maths, National University of Singapore. Archived from the original (PDF) on April 24, 2006. Retrieved December 12, 2011.
17. Smith 2011, pp. 28, 29 fn2.
18. 建す. Kōjien. Tokyo: Iwanami Shoten.
19. "Records part 6" 本紀第六 肅宗 代宗. Xīn Tángshū 新唐書 [New Book of Tang]. 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。
    　　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》，
    唐肅宗之元年
    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
    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
    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
    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，
    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
    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。
    大寒所在月初一辛亥，已稱建丑月，初三才小寒
    春分所在月初一辛亥，已稱建卯月，初四才驚蜇
    穀雨所在月初三壬午，已稱建辰月，初五才清明
    小滿所在月初一庚戌、初三壬子，已稱建巳月，初五才立夏
    由此可見，唐代地支紀月自朔日始，非自節氣始。
20. 三正, Kōjien, Tokyo: Iwanami Shoten
21. Conflicting Memories: Tibetan History under Mao Retold. BRILL. 2020-09-07. p. 640. ISBN 978-90-04-43324-3.

Sources

• Bartle, P. F. W. (1978). "Forty days: the Akan calendar". Africa: Journal of the International African Institute. 48 (1): 80–84. doi:10.2307/1158712. JSTOR 1158712. S2CID 143751434.
• Kalinowski, Marc (2007). "Time, space and orientation: figurative representations of the sexagenary cycle in ancient and medieval China". In Francesca Bray (ed.). Graphics and text in the production of technical knowledge in China : the warp and the weft. Leiden: Brill. pp. 137–168. ISBN 978-90-04-16063-7.
• Smith, Adam (2011). "The Chinese sexagenary cycle and the ritual origins of the calendar". In Steele, John (ed.). Calendars and years II : astronomy and time in the ancient and medieval world. Oxford: Oxbow. pp. 1–37. ISBN 978-1-84217-987-1.
• Kapoor, Ramesh (2021), "Fixing the chronology in Tai-Ahom chronicles by using astronomical references", Journal of Astronomical History and Heritage, 24 (3): 665–687, doi:10.3724/SP.J.1440-2807.2021.03.07

• Phukan Baruah, B. N.N. (1964). Ahom lexicon. The government of Assam in the department of historical and antiquarian studies.

External links

• "Heavenly Stems and Earthly Branches". Hong Kong Observatory. Archived from the original on 2018-11-04. Retrieved 2018-11-04.
• Ganzhi.io An Open Source application and implementation of Gan & Zhi as well as Jeiqi