The sexagenary cycle, also known as the gānzhī (干支) or stems-and-branches, is a cycle of sixty terms, each corresponding to one year, thus amounting to a total of sixty years every cycle, historically used for recording time in China and the rest of the
East Asian cultural sphere
The Sinosphere, also known as the Chinese cultural sphere, East Asian cultural sphere, or the Sinic world, encompasses multiple countries in East Asia and Southeast Asia that were historically heavily influenced by Chinese culture. The Sinosph ...
, as well as in Southeast Asia. It appears as a means of recording days in the first Chinese written texts, the
oracle bone
Oracle bones are pieces of ox scapula and turtle plastron which were used in pyromancya form of divinationduring the Late Shang period () in ancient China. '' Scapulimancy'' is the specific term if ox scapulae were used for the divination, ''p ...
s of the late second millennium BC
Shang dynasty
The Shang dynasty (), also known as the Yin dynasty (), was a Chinese royal dynasty that ruled in the Yellow River valley during the second millennium BC, traditionally succeeding the Xia dynasty and followed by the Western Zhou d ...
. Its use to record years began around the middle of the 3rd century BC. 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
Japan is an island country in East Asia. Located in the Pacific Ocean off the northeast coast of the Asia, Asian mainland, it is bordered on the west by the Sea of Japan and extends from the Sea of Okhotsk in the north to the East China Sea ...
,
Korea
Korea is a peninsular region in East Asia consisting of the Korean Peninsula, Jeju Island, and smaller islands. Since the end of World War II in 1945, it has been politically Division of Korea, divided at or near the 38th parallel north, 3 ...
, and
Vietnam
Vietnam, officially the Socialist Republic of Vietnam (SRV), is a country at the eastern edge of mainland Southeast Asia, with an area of about and a population of over 100 million, making it the world's List of countries and depende ...
, with the old Chinese system still in use in
Taiwan
Taiwan, officially the Republic of China (ROC), is a country in East Asia. The main geography of Taiwan, island of Taiwan, also known as ''Formosa'', lies between the East China Sea, East and South China Seas in the northwestern Pacific Ocea ...
, and in
Mainland China
"Mainland China", also referred to as "the Chinese mainland", is a Geopolitics, geopolitical term defined as the territory under direct administration of the People's Republic of China (PRC) in the aftermath of the Chinese Civil War. In addit ...
. In India, the
Ahom people
The Ahom (Pron: ) or Tai-Ahom (; ) is an ethnic group from the Indian states of Assam and Arunachal Pradesh. The members of this group are admixed descendants of the Tai people who reached the Brahmaputra valley of Assam in 1228 and the loc ...
(descendants of the
Dai people
The Dai people ( Burmese: ရှမ်းလူမျိုး; ; ; ; , ; , ; zh, c=, p=Dǎizú) are several Tai-speaking ethnic groups living in the Xishuangbanna Dai Autonomous Prefecture and the Dehong Dai and Jingpo Autonomous Prefecture ...
of
Yunnan
Yunnan; is an inland Provinces of China, province in Southwestern China. The province spans approximately and has a population of 47.2 million (as of 2020). The capital of the province is Kunming. The province borders the Chinese provinces ...
who migrated to
Assam
Assam (, , ) is a state in Northeast India, northeastern India, south of the eastern Himalayas along the Brahmaputra Valley, Brahmaputra and Barak River valleys. Assam covers an area of . It is the second largest state in Northeast India, nor ...
in the 13th century) also used the sexagenary cycle known as Lak-Ni.
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 1911 Revolution, also known as the Xinhai Revolution or Hsinhai Revolution, ended China's last imperial dynasty, the Qing dynasty, and led to the establishment of the Republic of China (ROC). The revolution was the culmination of a decade ...
, the Japanese
Boshin War
The , sometimes known as the Japanese Revolution or Japanese Civil War, was a civil war in Japan fought from 1868 to 1869 between forces of the ruling Tokugawa shogunate and a coalition seeking to seize political power in the name of the Impe ...
, the Korean
Imjin War
The Imjin War () was a series of two Japanese invasions of Korea: an initial invasion in 1592 also individually called the "Imjin War", a brief truce in 1596, and a second invasion in 1597 called the Chŏngyu War (). The conflict ended in 159 ...
and the Vietnamese
Famine of Ất Dậu,
Tết Mậu Thân. It also continues to have a role in contemporary
Chinese astrology
Chinese astrology is based on traditional Chinese astronomy and the Chinese calendar. Chinese astrology flourished during the Han dynasty (2nd century BC to 2nd century AD).
Chinese astrology has a close relation with Chinese philosophy (theor ...
and
fortune telling
Fortune telling is the spiritual practice of prediction, predicting information about a person's life.J. Gordon Melton, Melton, J. Gordon. (2008). ''The Encyclopedia of Religious Phenomena''. Visible Ink Press. pp. 115–116. The scope of for ...
. There are some parallels in this with
Tamil calendar
The Tamil calendar (தமிழ் நாட்காட்டி) is a Sidereal time, sidereal solar calendar used by the Tamil people of the Indian subcontinent. It is also used in Puducherry (union territory), Puducherry, and by the Tamil ...
.
Overview

Each term in the sexagenary cycle consists of two Chinese characters, the first being one of the ten
Heavenly Stems
The ten Heavenly Stems (or Celestial Stems) are a system of ordinals indigenous to China and used throughout East Asia, first attested during the Shang dynasty as the names of the ten days of the week. They were also used in Shang-era ritual ...
of the
Shang-era week and the second being one of the twelve
Earthly Branches
The Earthly Branches (also called the Terrestrial Branches or the 12-cycle) are a system of twelve ordered symbols used throughout East Asia. They are indigenous to China, and are themselves Chinese characters, corresponding to words with no co ...
representing the years of
Jupiter
Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a Jupiter mass, mass more than 2.5 times that of all the other planets in the Solar System combined a ...
's
duodecennial
An anniversary is the date on which an event took place or an institution was founded.
Most countries celebrate national anniversaries, typically called national days. These could be the date of independence of the nation or the adoption o ...
orbital cycle. The first term ''jiǎzǐ'' () combines the first heavenly stem with the first earthly branch. The second term ''yǐchǒu'' () combines the second stem with the second branch. This pattern continues until both cycles conclude simultaneously with ''guǐhài'' (), after which it begins again at ''jiǎzǐ''. This termination at ten and twelve's
least common multiple
In arithmetic and number theory, the least common multiple (LCM), lowest common multiple, or smallest common multiple (SCM) of two integers ''a'' and ''b'', usually denoted by , is the smallest positive integer that is divisible by both ''a'' and ...
leaves half of the combinations—such as ''jiǎchǒu'' ()—unused; this is traditionally explained by reference to pairing the stems and branches according to their
yin and yang
Originating in Chinese philosophy, yin and yang (, ), also yinyang or yin-yang, is the concept of opposite cosmic principles or forces that interact, interconnect, and perpetuate each other. Yin and yang can be thought of as complementary an ...
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.
History

The sexagenary cycle is attested as a method of recording days from the earliest written records in China,
records of divination on
oracle bones
Oracle bones are pieces of ox scapula and turtle plastron which were used in pyromancya form of divinationduring the Late Shang period () in ancient China. '' Scapulimancy'' is the specific term if ox scapulae were used for the divination, '' ...
, beginning . Almost every oracle bone inscription includes a date in this format. This use of the cycle for days is attested throughout the
Zhou dynasty
The Zhou dynasty ( ) was a royal dynasty of China that existed for 789 years from until 256 BC, the longest span of any dynasty in Chinese history. During the Western Zhou period (771 BC), the royal house, surnamed Ji, had military ...
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
The ''Spring and Autumn Annals'' is an ancient Chinese chronicle that has been one of the core Chinese classics since ancient times. ''The Annals'' is the official chronicle of the State of Lu, and covers a 242-year period from 722 to 481&nbs ...
'', a chronological list of events from 722 to 481 BC, use this system in combination with regnal years and months (
lunation
In lunar calendars, a lunar month is the time between two successive syzygies of the same type: new moons or full moons. The precise definition varies, especially for the beginning of the month.
Variations
In Shona, Middle Eastern, and Euro ...
s) 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.
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
Qin Shi Huang (, ; February 25912 July 210 BC), born Ying Zheng () or Zhao Zheng (), was the founder of the Qin dynasty and the first emperor of China. He is widely regarded as the first ever supreme leader of a unitary state, unitary d ...
(), 246 BC, is noted on the diagram next to the position of the 60-cycle term ''yǐmǎo'' (, 52 of 60), corresponding to that year. Use of the cycle to record years became widespread for administrative time-keeping during the
Western Han dynasty
The Han dynasty was an imperial dynasty of China (202 BC9 AD, 25–220 AD) established by Liu Bang and ruled by the House of Liu. The dynasty was preceded by the short-lived Qin dynasty (221–206 BC) and a warring in ...
(202 BC – 8 AD). The count of years has continued uninterrupted ever since: the year 1984 began the present cycle (a —''jiǎzǐ'' 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
Lunar New Year is the beginning of a new year based on lunar calendars or, informally, lunisolar calendars. Lunar calendar years begin with a new moon and have a fixed number of lunar months, usually twelve, in contrast to lunisolar calendar ye ...
of the traditional
Chinese calendar
The traditional Chinese calendar, dating back to the Han dynasty, is a lunisolar calendar that blends solar, lunar, and other cycles for social and agricultural purposes. While modern China primarily uses the Gregorian calendar for officia ...
. For example, the ''jichou'' year (coinciding roughly with 2009) began on January 26, 2009. (However, for astrology, the year begins with the first solar term "Lìchūn" (), which occurs near February 4.)
In Japan, according to ''
Nihon shoki
The or , sometimes translated as ''The Chronicles of Japan'', is the second-oldest book of classical Japanese history. It is more elaborate and detailed than the , the oldest, and has proven to be an important tool for historians and archaeol ...
'', 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
The traditional Chinese calendar, dating back to the Han dynasty, is a lunisolar calendar that blends solar, lunar, and other cycles for social and agricultural purposes. While modern China primarily uses the Gregorian calendar for officia ...
, was the first year of the cycle.
The Korean (
hwangap
In the Sinosphere, one's sixtieth birthday has traditionally held special significance. Especially when life expectancies were shorter, the sixtieth birthday was seen as a symbolic threshold for reaching old age and having lived a full life. Th ...
) and Japanese tradition ( ''kanreki'') of celebrating the 60th birthday (literally 'return of calendar') reflects the influence of the sexagenary cycle as a count of years.
The
Tibetan calendar
The Tibetan calendar (), or the Phukpa calendar, known as the ''Tibetan lunar calendar'', is a lunisolar calendar composed of either 12 or 13 lunar months, each beginning and ending with a new moon. A thirteenth month is added every two or three y ...
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 ''jiǎzǐ'' (the year of the Wood
Rat
Rats are various medium-sized, long-tailed rodents. Species of rats are found throughout the order Rodentia, but stereotypical rats are found in the genus ''Rattus''. Other rat genera include '' Neotoma'' (pack rats), '' Bandicota'' (bandicoo ...
), the first year of the Tibetan cycle is ''dīngmǎo'' (; year 4 on the Chinese cycle, year of the Fire
Rabbit
Rabbits are small mammals in the family Leporidae (which also includes the hares), which is in the order Lagomorpha (which also includes pikas). They are familiar throughout the world as a small herbivore, a prey animal, a domesticated ...
).
Heavenly Stems
Earthly Branches
*The names of several animals can be translated into English in several different ways. The Vietnamese
Earthly Branches
The Earthly Branches (also called the Terrestrial Branches or the 12-cycle) are a system of twelve ordered symbols used throughout East Asia. They are indigenous to China, and are themselves Chinese characters, corresponding to words with no co ...
use cat instead of
Rabbit
Rabbits are small mammals in the family Leporidae (which also includes the hares), which is in the order Lagomorpha (which also includes pikas). They are familiar throughout the world as a small herbivore, a prey animal, a domesticated ...
.
Sexagenary years
Conversion between cyclic years and Western 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
Chinese era names, also known as reign mottos, were titles used by various Dynasties of China, Chinese dynasties and regimes in History of China#Imperial China, Imperial China for the purpose of regnal year, year identification and numbering. Th ...
(; ) to specify a year.
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
Lunar New Year is the beginning of a new year based on lunar calendars or, informally, lunisolar calendars. Lunar calendar years begin with a new moon and have a fixed number of lunar months, usually twelve, in contrast to lunisolar calendar ye ...
. 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
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
The Yellow Emperor, also known as the Yellow Thearch, or Huangdi ( zh, t=黃帝, s=黄帝, first=t) in Chinese, is a mythical Chinese sovereign and culture hero included among the legendary Three Sovereigns and Five Emperors. He is revered as ...
, was the first year (甲子; ''jiǎzǐ'') 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.
# 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
In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient ( integer division). In a ...
. 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 and for years BC is .
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; ''rénchén''), 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; ''gēngchén''), as ''60-
221+2) mod 60
1 (one, unit, unity) is a number, numeral, and glyph. It is the first and smallest positive integer of the infinite sequence of natural numbers. This fundamental property has led to its unique uses in other fields, ranging from science to sp ...
= 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
In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient ( integer division). In a ...
")
#Show one of the Sexagenary Cycle tables (the following section), look for 44 in the first column (No) and obtain Fire
Goat
The goat or domestic goat (''Capra hircus'') is a species of Caprinae, goat-antelope that is mostly kept as livestock. It was domesticated from the wild goat (''C. aegagrus'') of Southwest Asia and Eastern Europe. The goat is a member of the ...
(丁未; ''dīngwèi'').
Step-by-step example to determine the cyclic year of first year of the reign of
Qin Shi Huang
Qin Shi Huang (, ; February 25912 July 210 BC), born Ying Zheng () or Zhao Zheng (), was the founder of the Qin dynasty and the first emperor of China. He is widely regarded as the first ever supreme leader of a unitary state, unitary d ...
(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
In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient ( integer division). In a ...
")
#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
Rabbit
Rabbits are small mammals in the family Leporidae (which also includes the hares), which is in the order Lagomorpha (which also includes pikas). They are familiar throughout the world as a small herbivore, a prey animal, a domesticated ...
(乙卯; ''yǐmǎo'').
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
The goat or domestic goat (''Capra hircus'') is a species of Caprinae, goat-antelope that is mostly kept as livestock. It was domesticated from the wild goat (''C. aegagrus'') of Southwest Asia and Eastern Europe. The goat is a member of the ...
' 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
Rabbits are small mammals in the family Leporidae (which also includes the hares), which is in the order Lagomorpha (which also includes pikas). They are familiar throughout the world as a small herbivore, a prey animal, a domesticated ...
'.
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.
Recent cycles
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
The Big Dipper (American English, US, Canadian English, Canada) or the Plough (British English, UK, Hiberno-English, Ireland) is an asterism (astronomy), asterism consisting of seven bright stars of the constellation Ursa Major; six of them ar ...
, (: ''jiànzǐyuè'', : ''jiànchǒuyuè'', etc.). 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
A solar term (or ''jiéqì'', zh, t=節氣, s=节气) is any of twenty-four periods in traditional Chinese lunisolar calendars that matches a particular astronomical event or signifies some natural phenomenon. The points are spaced 15° apart ...
(; ''zhōngqì''). The ''jiànzǐyuè'' (()) is the month containing the winter solstice (i.e. the
Dōngzhì) ''zhōngqì''. The ''jiànchǒuyuè'' (()) is the month of the following ''zhōngqì'', which is
Dàhán (), while the ''jiànyínyuè'' (()) is that of the
Yǔshuǐ () ''zhōngqì'', etc. Intercalary months have the same branch as the preceding month.
In the other system (; ''jiéyuè'') the "month" lasts for the period of two solar terms (two ''qìcì''). The ''zǐyuè'' () is the period starting with
Dàxuě (), i.e. the solar term ''before'' the winter solstice. The ''chǒuyuè'' () starts with
Xiǎohán (), the term before Dàhán (), while the ''yínyuè'' () starts with
Lìchūn (), the term before Yǔshuǐ (), 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 Han dynasty was an Dynasties of China, imperial dynasty of China (202 BC9 AD, 25–220 AD) established by Liu Bang and ruled by the House of Liu. The dynasty was preceded by the short-lived Qin dynasty (221–206 BC ...
, the first month has been ''jiànyínyuè'', but earlier the first month was ''jiànzǐyuè'' (during the
Zhou dynasty
The Zhou dynasty ( ) was a royal dynasty of China that existed for 789 years from until 256 BC, the longest span of any dynasty in Chinese history. During the Western Zhou period (771 BC), the royal house, surnamed Ji, had military ...
) or ''jiànchǒuyuè'' (traditionally during the
Shang dynasty
The Shang dynasty (), also known as the Yin dynasty (), was a Chinese royal dynasty that ruled in the Yellow River valley during the second millennium BC, traditionally succeeding the Xia dynasty and followed by the Western Zhou d ...
) as well.
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'' (; 1st) or ''jǐ'' (; 6th) year. The first month of the ''jiǎ'' or ''jǐ'' year is a ''bǐngyín'' (; 3rd) month, the next one is a ''dīngmǎo'' (; 4th) month, etc., and the last month of the year is a ''dīngchǒu'' (, 14th) month. The next year will start with a ''wùyín'' (; 15th) month, etc. following the cycle. The 5th year will end with a ''yǐchǒu'' (; 2nd) month. The following month, the start of a ''jǐ'' or ''jiǎ'' year, will hence again be a ''bǐngyín'' (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.
Sexagenary days
*N for the year: (5y +
/4 mod 10, y = 0–39 (stem); (5y +
/4 mod 12, y = 0–15 (branch)
*N for the Gregorian century: (4c +
/4+ 2) mod 10 (stem); (8c +
/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
In astronomy, a Julian year (symbol: a or aj) is a unit of measurement of time defined as exactly 365.25 days of SI seconds each.P. Kenneth Seidelmann, ed.''The explanatory supplement to the Astronomical Almanac'' (Mill Valley, Cal.: Universit ...
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, .
**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, .
**Stem-branch = 1, 1 (, 1 in sexagenary cycle = 32 – 5 + 33 + 1 – 60).
*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, .
**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,
**Stem-branch = 1, 9 (, 21 in cycle = – 42 – 2 + 34 + 31 = 21)
*Stem-branch for August 4, 1338
**Stem = 8,
***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,
***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 (, 48 in cycle = 4 + 8 + 32 + 4)
*Stem-branch for May 25, 105 BC (−104).
**Stem = 7,
***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,
***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 (, 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
:
:
:
:
for Gregorian calendar and
for Julian calendar.
:
for Jan or Feb in a common year and
in a leap year.
*Stem-branch for February 22, 720 BC (−719).
:y = 5 x (720–719) +
/4= 5
:c = 8
:m = 30 +
.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) +
0/4= 5 x 6 + 7 = 37
:c = 8
:m = 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 +
.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) +
9/4= 5 x 5 + 7 = 32
:c = -5
:m = 30 +
.6 x 11 -3= 33
:d = 1
:SB = 32 – 5 + 33 + 1 – 60 = 1
:S = B = 1, 甲子
Sexagenary hours
See also
*
Doumu
Dǒumǔ (), also known as , and , is a goddess in Chinese religion and Taoism. She is also named through the honorific Tiānhòu ( "Queen of Heaven"), shared with other Chinese goddesses, especially Mazu, who are perhaps conceived as her aspect ...
(斗母元君)
*
Tai Sui
Tai Sui is a Chinese name for stars directly opposite the planet Jupiter ( ''Mùxīng'') in its roughly 12-year orbital cycle. Personified as deities, they are important features of Chinese astrology, Feng Shui, Taoism, and to a lesser extent C ...
(太歲)
*
Chinese calendar
The traditional Chinese calendar, dating back to the Han dynasty, is a lunisolar calendar that blends solar, lunar, and other cycles for social and agricultural purposes. While modern China primarily uses the Gregorian calendar for officia ...
*
Chinese era name
Chinese era names, also known as reign mottos, were titles used by various Dynasties of China, Chinese dynasties and regimes in History of China#Imperial China, Imperial China for the purpose of regnal year, year identification and numbering. Th ...
*
Lunisolar calendar
A lunisolar calendar is a calendar in many cultures, that combines monthly lunar cycles with the solar year. As with all calendars which divide the year into months, there is an additional requirement that the year have a whole number of mont ...
*
Japanese invasions of Korea (1592–1598)
The Imjin War () was a series of two Japanese invasions of Korea: an initial invasion in 1592 also individually called the "Imjin War", a brief truce in 1596, and a second invasion in 1597 called the Chŏngyu War (). The conflict ended in 159 ...
, known in Korean as the "Imjin War", after the ''imjin'' (Yang Water
Dragon
A dragon is a Magic (supernatural), magical legendary creature that appears in the folklore of multiple cultures worldwide. Beliefs about dragons vary considerably through regions, but European dragon, dragons in Western cultures since the Hi ...
) year 1592.
*
Koshien Stadium
, commonly referred to as simply Koshien Stadium, is a baseball stadium located near Kobe in Nishinomiya, Hyōgo Prefecture, Japan. The stadium was built to host the national high school baseball tournaments, and opened on 1 August 1924. It was ...
(Japan), named after the ''kōshi'' (Yang Wood Rat) year 1924. One of the last examples of general usage of the cycle in Japan.
*
Tet Offensive
The Tet Offensive was a major escalation and one of the largest military campaigns of the Vietnam War. The Viet Cong (VC) and North Vietnamese People's Army of Vietnam (PAVN) launched a surprise attack on 30 January 1968 against the forces of ...
– Vietnamese name of the event, "Tết Mậu Thân Event", named after the ''mậuthân'' (Yang Earth
Monkey
Monkey is a common name that may refer to most mammals of the infraorder Simiiformes, also known as simians. Traditionally, all animals in the group now known as simians are counted as monkeys except the apes. Thus monkeys, in that sense, co ...
) year 1968.
*
Xinhai Revolution
The 1911 Revolution, also known as the Xinhai Revolution or Hsinhai Revolution, ended China's last imperial dynasty, the Qing dynasty, and led to the establishment of the Republic of China (ROC). The revolution was the culmination of a decade ...
(China), named after the ''xinhai'' (Yin Metal
Pig
The pig (''Sus domesticus''), also called swine (: swine) or hog, is an omnivorous, domesticated, even-toed, hoofed mammal. It is named the domestic pig when distinguishing it from other members of the genus '' Sus''. Some authorities cons ...
) year 1911
*
Samvatsara
References
Citations
Sources
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External links
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Ganzhi.ioAn Open Source application and implementation of Gan & Zhi as well as Jeiqi
{{Authority control
Chinese calendars
Chinese astrology
Units of time
Sexagenary cycle