Chinese calendar

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Shíyīyuè, Jiǎwǔnián
Today is
01-07-12-10 / 01-11-07-01
2014-12-28 (Sunday)
Rabi' al-awwal 6, 1436AH
Now is
44 mils am, chǒushí
94 mils, 3 gēng 2 diǎn

Chinese calendar may refer to any of the official and civil calendars used in China and some neighbouring countries in different periods of history; however, the phrase is generally synonymous with Han calendar.

The official calendar in China today is the Gregorian calendar, which is a solar calendar. It is used for public and business affairs.

The civil calendar in much of China is the Han calendar, which is a lunisolar calendar. It is used for selecting the day of a wedding or funeral, for opening a venture, or a relocation. A similar calendar is used in Japan, Korea, and Vietnam for these purposes. Muslims living in Xinjiang, Ningxia and other parts of northern China use the Islamic calendar, which is a mean moon lunar calendar, as their civil calendar. The civil calendar for Tibet is the Tibetan calendar, which is a lunisolar calendar.

In China, some public holidays relate to the Gregorian calendar, such as Labor Day and National Day while others relate to the Chinese Calendar, such as Chinese New Year, Duanwu Festival, and the Mid-Autumn Festival. In specified provinces of China, some extra public holidays related to Islamic calendar or Tibetan calendar, such as Islamic New Year and the Major Festival in Ningxia and Xinjiang, Tibetan New Year and Summer Assembly in Tibet.

The Han calendar is a lunisolar calendar, which indicates both the moon phases and the solar terms. In Han calendar, a year usually begins on the second dark moon after the winter solstice but occasionally on the third dark moon after the winter solstice.

The year from January 31, 2014 to February 18, 2015 is a Jiǎwǔnián or Mùmǎnián (Year of wooden horse), a year with dual Vernal Commences(traditional Chinese: 两頭春; simplified Chinese: 两头春).

An example of a Gregorian calendar and Chinese lunisolar calendar below it
A combination calendar, with Gregorian system below and a Chinese zodiac chart above.

Early Chinese calendars[edit]

The evolution route of Chinese calendars is five phases calendar-> seasonal solar calendar-> lunisolar calendar-> seasonal lunisolar calendar. And the calendars were evolving to more sophisticated and closer to the astronomical phenomena all the way.

Five Phases calendar[edit]

In Five Phases, Guǎnzǐ says: " After the Solstice, the phase of from Zǐrì of Jiǎ , …. The phase ends 72 days later. …. The phase of Huǒ from Zǐrì of Bǐng , …. The phase ends 72 days later. …. The phase of from Zǐrì of , …. The phase ends 72 days later. …. The phase of Jīn from Zǐrì of Gēng , …. The phase ends 72 days later. …. The phase of Shuǐ from Zǐrì of Rèn , …. The phase ends 72 days later."

In the Inner Canon of Huangdi(traditional Chinese: 黄帝内經; simplified Chinese: 黄帝内经), it says that: spring contains the days of Jiǎ and ; summer contains the days of Bǐng and Dīng; growing phase contains the days of and ; autumn contains the days of Gēng and Xīn; and winter contains the days of Rèn and Guì(Chinese: 春,其日甲乙;夏,其日丙丁;长夏,其日戊己;秋,其日庚辛;冬,其日壬癸).

In Xiàxiǎozhāng, it mentions that the Solstices are in the 5th and 10th month, and records the star images and phenological phenomenon upon a frame of 10 months calendar.

In Astronomical Notes(traditional Chinese: 天文訓; simplified Chinese: 天文训), Huáinánzǐ says: "In general, the Winter Solstice is at Zǐrì or Wǔrì, the Summer Solstice is at Mǎorì or Yǒurì. The date of the Winter Solstice plus 3 is the date of the Summer Solstice. The dates of the Solstices shift 6 days forward each year, and starts from beginning after the last date. For example, in 147BC, the Winter Solstice is Rènwǔrì. In this year, the phase of begins from Jiǎzǐrì, …. 72 days later, the phase of Huǒ begins from Bǐngzǐrì, …. 72 days later, the phase of begins from Wùzǐrì, …. 72 days later, the phase of Jīn begins from Gēngzǐrì, …. 72 days later, the phase of Shuǐ begins from Rènzǐrì, …. 72 days later, the year ends, and new phases begins from Gēngwǔrì. the dates shifts 6 days forward each year, reckons with numbers, the date returns back to Jiǎzǐrì at 10th year.

These essays described a five phases calendar(traditional Chinese: 五行曆; simplified Chinese: 五行历) or a ten-month solar calendar. The rough outline of the five phases calendar is that the year begins at the Vernal Commences. There're 10 months and a transition in a year. The months are 36 days long each, and named with the 10 heavenly stems. The days in the months are named with 12 earthly branches. The days in the transition are not counted. Each phase contains 2 months. And, in each month, there're 3 twelve-day week. In Yòuguān, Guǎnzí listed the name of the nodes of week. The five phases calendar derived some festivals base on Earthly Branches, such as Shàngsì and Duānwǔ

In Yi areas, a 10-month calendar was found in the early 1980s. It was a solar calendar that contained 10 months of 36 days, and 2/3 transition days before the winter solstice (the minor year) and summer solstice (the major year). The 36 days were named with the 12 earthly branches (from tiger to ox), repeated 3 times. The 27/28 mansions are used to mark days too, two 27 mansions and one 28 mansions combined into a 82 days week, which are about 3 sidereal months.

The 10 months were named with 10 animals (tiger, oter, crocodile, boa, pangolin, muntjac, bharal, ape, panther, and lizard). The 10 months were divided into five phases, which were named with the five phases (earth, bronze, water, wood, and fire).

Seasonal calendar[edit]

In Part eight of Priority(traditional Chinese: 輕重己; simplified Chinese: 轻重己), Guǎnzǐ Says "46 days after the Winter Solstice, winter ends and spring commences. …. 92 days after the Winter Solstice is the Vernal Equinox. …. 46 days after the Vernal Equinox, spring ends and summer commences. …. 92 days after the Vernal Equinox is the Summer Solstice. …. 46 days after the Summer Solstice, the summer ends and autumn commences. …. 92 days after the Summer Solstice is Autumnal Equinox. …. 46 days after the Autumnal Equinox, autumn ends and winter commences. …. 92 days after the Autumnal Equinox, the emperor offers sacrifice to Heaven". The article introduced a seasonal calendar(traditional Chinese: 四時曆; simplified Chinese: 四时历), and raised 4 seasons and 8 solar terms(traditional Chinese: 四時八節; simplified Chinese: 四时八节). In the calendar, Each year is divided into 4 seasons and a sacrificial day. Each season is divided into 2 terms. Each season is 91 days, and the first term of each season is 91-45=46 days.

In Monthly Memo(Chinese: 月令), Record of Rites divided each year into 12 months. The 12 months are the month of Early spring(Chinese: 孟春之月), the month of Mid spring(Chinese: 仲春之月), the month of Late spring(Chinese: 季春之月), the month of Early summer(Chinese: 孟夏之月), the month of Mid summer(Chinese: 仲夏之月), the month of Late summer(Chinese: 季夏之月), the month of Early autumn(Chinese: 孟秋之月), the month of Mid autumn(Chinese: 仲秋之月), the month of Late autumn(Chinese: 季秋之月), the month of Early winter(Chinese: 孟冬之月), the month of Mid winter(Chinese: 仲冬之月), the month of Late winter(Chinese: 季冬之月). The Vernal Equinox is in the month of Mid spring, the Summer Solstice is in the month of Mid summer, the Autumnal Equinox is in the month of Mid autumn, and the Winter Solstice is in the month of Mid winter.

So, the rough sketch of the seasonal calendar is that the year begins at the Veral Commences (the 46 days after the Winter Solstice), and is divided into 12 months. The month length is 30 or 31 days. The seasonal calendar derived some festival upon the eight solar terms and Heavenly Stems, such as spring Sacrifice, autumn Sacrifice , Hánshí and Winter Solstice.

The Miao solar calendar is used in Miao area for thousands years, and retired at Guāngxù 33 (traditional Chinese: 光緒三十三年; simplified Chinese: 光绪三十三年, 1907). The New Year's Day in Miao calendar is the winter solstice. And Miao calendar is similar with Gregorian calendar.

In Miao solar calendar, a year is divided into 12 months, which are January(the unformatted month), February(the 0th month), March(the 1st month), April(the 2nd month), May(the 3rd month), June(the 4th month), July(the 5th month), August(the 6th month), September(the 7th month), October(the 8th month), November(the 9th month), December(the 10th month).All odd months(the 1st,3rd,5th,7th,9th month) are 31 days, and all even months(the 0th,2nd,4th,6th,8th,10th month) are 30 days. January is an unformatted month, it's 30 days in common year, and an intercalary day is set at the end of January each 4 year(Zǐnián, Chénnián, and Shēnnián). So, the average solar year of Miao solar calendar is (365*3+366)/4=365.25 days.

Huángdì Schedule[edit]

Huángdì Schedule (traditional Chinese: 黄帝調曆; simplified Chinese: 黄帝调历; pinyin: Huángdì Diàolì) is ancient calendar which mentioned in the annals in Hàn Dynasty. In Huángdì Schedule, a tàisuì contains 12 years, and 8 years are common year, and 4 years are leap year. the common year is 356 days, and the leap year is 383 or 384 days. The month with the winter solstice is the first month of the year, and the intercalary is placed in the end of the year. The calendar in Shāng Dynasty, Zhōu Dynasty, Spring and Autumn period, Warring States Period, Qín Dynasty and early stage of Hàn Dynasty, follows the system in general except that the first month is different. Huángdì Schedule is reckoned to be issued at Jan 15, 4377BC.

It is found on the oracle bones of the Shang Dynasty (late 2nd millennium BC), which seem to describe a lunisolar year of 12 months, with a possible intercalary 13th, or even 14th, added empirically to prevent calendar drift. The Sexagenary cycle for recording days was already in use. Tradition holds that, in that era, the year began on the first new moon after the winter solstice.

Early Eastern Zhou texts, such as the Spring and Autumn Annals, provide better understanding of the calendars used in the Zhou dynasty. One year usually had 12 months, which were alternately 29 and 30 days long (with an additional day added from time to time, to catch up with "drifts" between the calendar and the actual moon cycle), and intercalary months were added in an arbitrary fashion at the end of the year.

These arbitrary rules on day and month intercalation caused the calendars of each state to be slightly different, at times. Thus, texts like the Annals will often state whether the calendar they use (the calendar of Lu) is in phase with the Royal calendar (used by the Zhou kings).

Although tradition holds that in the Zhou, the year began on the new moon which preceded the winter solstice, the Spring and Autumn Annals seem to indicate that (in Lu at least) the Yin calendar (the calendar used in Shang dynasty, with years beginning on the first new moon after the winter solstice) was in use until the middle of the 7th century, and that the beginning of the year was shifted back one month around 650 BC.

By the beginning of the Warring States, progress in astronomy and mathematics allowed the creation of calculated calendars (where intercalary months and days are set by a rule, and not arbitrarily). The quarter remainder calendar (traditional Chinese: 四分曆; simplified Chinese: 四分历; pinyin: sìfēnlì), which began about 484 BC, was the first calculated Chinese calendar, so named because it used a solar year of 365¼ days (the same as the 1st-century BC Julian Calendar of Rome), along with a 19-year (235-month) Rule Cycle (Chinese: ; pinyin: zhāng), known in the West as the Metonic cycle.[1] The year began on the new moon preceding the winter solstice, and intercalary months were inserted at the end of the year.

In 256 BC, as the last Zhou king ceded his territory to Qin, a new calendar (the Qin calendar) began to be used. It followed the same principles as the Sifen calendar, except that the year began at Shíyuè 1(Chinese: 十月朔; pinyin: shíyuèshuò, the closest new moon of the winter beginning). The Qin calendar was used during the Qin dynasty, and in the beginning of the Western Han dynasty. According to the Han Records(traditional Chinese: 漢書; simplified Chinese: 汉书; pinyin: Hànshū)21a, 973, for the moment of unification the Middle kingdoms had 6 different calendars: those of the mythological progenitors Yellow Emperor (traditional Chinese: 黃帝曆; simplified Chinese: 黄帝历) and Zhuanxu(traditional Chinese: 顓頊曆; simplified Chinese: 颛顼历); of the dynasties Xia (traditional Chinese: 夏曆; simplified Chinese: 夏历), Yin (traditional Chinese: 殷曆; simplified Chinese: 殷历), and Zhou (traditional Chinese: 周曆; simplified Chinese: 周历), and Lu state (traditional Chinese: 魯曆; simplified Chinese: 鲁历)of the Zhou Dynasty . Of those, the second was taken to substitute the rest. The Han imperial library is said to contain 82 volumes of descriptions of all those systems (Han Shu 30, 1765-6), now mostly lost.[2]

The two oldest printed Chinese calendars are dated 877 and 882; they were found at the Buddhist pilgrimage site of Dunhuang; Patricia Ebrey writes that it is no surprise that some of the earliest printed items were calendars, since the Chinese found it necessary to calculate and mark which days were auspicious and which were not.[3][4]

In Miao lunisolar calendar, A year is divided into 12 or 13 months, which are January(the unformatted month), February(the 0th month), March(the 1st month), April(the 2nd month), May(the 3rd month), June(the 4th month), July(the 5th month), August(the 6th month), September(the 7th month), October(the 8th month), November(the 9th month), December(the 10th month) and the intercalary month. January, February and the intercalary month are 29 days, and the other month are 30days. The intercalary months were set after January each 4 years(Zǐnián, Chénnián, and Shēnnián). So, the average solar year is (358*3+387)/4=365.25 days.

Late Chinese calendar and related calendars[edit]

Han calendar[edit]

Emperor Wu of the Han dynasty introduced reforms in the halfway of his administration. His Grand Inception Calendar (traditional Chinese: 太初曆; simplified Chinese: 太初历; pinyin: Tàichū Lì) introduced 24 solar terms which decides the month names. The solar year was defined as 365 \tfrac{385}{1539} days, and divided into 24 solar terms. Each couples of solar terms are associated into 12 climate terms. The lunar month was defined as 29 \tfrac{43}{81} days and named according to the closest climate term. The mid-climate in the month decides the month name, and a month without mid-climate is an intercalary.

Ever since then, there are over 100 official calendars in Chinese which are consecutive and follow the structure of Tàichū calendar both. There're several innovation in calendar calculation in the history of over 2100 years, such as:

In the Dàmíng Calendar released in Tiānjiān 9(Chinese: 天监九年, 510) of Liáng Dynasty, Zhǔ Chōngzhī introduced the equation of equinoxes.

Actual syzygy method was adopted to decide the month from the Wùyín Yuán Calendar, which was released in Wǔdé 2(Chinese: 武德二年, 619) of Táng Dynasty.

The real measured data was used in calendar calculation from Shòushí Calendar, which was released in Zhìyuán 18(Chinese: 至元十八年,1281) of Yuán Dynasty.

the ecliptic longitude is introduced and adopted to determine the solar term from the Shíxiàn calendar which was released in Shùnzhì 2(1645) of Qīng Dynasty.

Japanese, Korean, and Vietnamese Calendar[edit]

Japan found their own tradition calendar which follows the algorithm of Táng dynasty from Edo period.

Korea and Vietnam adopts the Han calendar except that Vietnam substitutes the cat for the Rabbit in the Chinese zodiac.

Tibetan Calendar[edit]

In the Tubo Dynasty, princess Wencheng and Jincheng brought Han calendar to Tibet. And Tibetan built Tibet calendar with the Tibetan calendar with the characters of phenological, Kalachakra, and Han calendar. The Tibetan calendar was finalized before Yuan Dynasty.

The specialty of Han and Tibetan calendar[edit]

the moon phases, and tidal phenomena is much easier to reckon in the Han calendar, such as spring and neap tides, fall on approximately the same day in each lunar month, and the times of high and low water and the tidal streams experienced in a certain location on a certain day of the lunar month are likely to be similar to those for the same place and lunar day in any month. For many years, therefore, mariners in East and South-East Asia have related their tidal observations to the Chinese calendar, so as to be able to provide quick, rule-of-thumb approximations of tides and tidal conditions from memory, based on the day of the Lunar month, without needing to refer to tide tables. Certain inshore passages on the China coast, for example, where there are strong tidal streams associated with spring tides, were regarded by mariners to be passable on certain days of the lunar month, and impassable on others.

Tibetan calendar is used to forecast the climate and earthquake in Tibet.

Current Chinese Calendar[edit]

On January 1, 1912, the Republic of China adopted the Gregorian calendar for official business as Japan did during Meiji Restoration. But, the Gregorian calendar wasn't fully adopted by the various provinces of China until 1929 because of incessant fighting between warlords. The People's Republic of China adopt the Gregorian calendar in 1949.

In the mainland of China, the Gregorian calendar is called as the public calendar(traditional Chinese: 公曆; simplified Chinese: 公历), and it has have adopted the Christian era which is called as the common era(Chinese: 公元). In Taiwan, the Gregorian calendar is called as the national calendar(traditional Chinese: 國曆; simplified Chinese: 国历), and adopt the republic era(traditional Chinese: 民國紀年; simplified Chinese: 民国纪年).

Although the official calendar is the Gregorian calendar, the Han calendar is used in China widely, especially rural areas. In general, in "modern" metropolitan regions, such as Beijing and Shanghai, many people are not familiar with the Han calendar. People call the Han calendar the "Former Calendar" (traditional Chinese: 舊曆; simplified Chinese: 旧历; pinyin: Jìulì), the "Traditional Calendar" (traditional Chinese: 老曆; simplified Chinese: 老历; pinyin: Lǎolì), or the "Yin Calendar" (traditional Chinese: 陰曆; simplified Chinese: 阴历; pinyin: Yīnlì). In the public media, the Han calendar is usually referred as the "Rural Calendar" (traditional Chinese: 農曆; simplified Chinese: 农历; pinyin: Nónglì). In addition, some regions also call it the Xià Calendar (traditional Chinese: 夏曆; simplified Chinese: 夏历), on the pretext of the calendar of Xià Dynasty.

The Han calendar remains culturally essential today. For example, most of the traditional festivals, such as Chinese New Year and the Mid-Autumn Festival, occur on new moons or full moons. The Han calendar, as an element of traditional culture, has much cultural and nationalistic sentiment invested in it. The Han calendar is still used in the more traditional Chinese households around the world to pick "auspicious dates" for important events such as weddings, funerals, and business deals. A special calendar is used for this purpose, called the Imperial Calendar (traditional Chinese: 皇曆; simplified Chinese: 皇历; pinyin: huánglì), which contains auspicious activities, times, and directions for each day. The calendar follows the Gregorian dates but has the corresponding Chinese dates. Every date would have a comprehensive listing of astrological measurements and fortune elements.

Japan moved all traditional festival to the same date in Gregorian calendar after the Meiji Restoration. But, in China, all traditional festivals are upon Chinese calendar. In China, 3 statutory public holidays(5 days) are upon Gregorian calendar, 3 statutory public holidays(5 days) are upon Chinese calendar, and a statutory public holidays(1 days) upon solar term. It means the official calendar is a dual-calendar system in fact, and the Chinese calendar and Gregorian calendar have equal status in China.

On the other hand, dual-calendar system(in fact, triple-calendar system, solar-lunar-week) give the authority more trouble. The authority of China have to issue the holiday arrangement year by year. But, the compromise between solar holiday, lunar holiday and weekend are complex, and difficult for all to accept it. Almost all annual holiday arrangements are be blamed to be Chinese-style vacations(Chinese: 中国式休假). For example, the arrangement(v1w3v3w6v7w2v1) of September 22 to October 10, 2010 is called as the most chaotic period in the history; and the title is taken over by the arrangement(v2w3v3w6v1w2v7w5v1) of September 14 to October 13, 2013 just 3 years later. Actually, the median date of mid autumn festival is the Autumnal Equinox(about September 23), so the intertwining between mid autumn festival and national day will occur in about half of all years.

Holidays according to Han calendar[edit]

In Sinosphere(China, Japan, Korea, Vietnam and Ryukyu), there're many traditional festivals common, and upon Chinese calendar or solar terms.

ring the old year out and the new year inthe month and day number of festival below is alike and odd
New Year's EveNew Year's DayShangsi FestivalDragon Boat FestivalNight of SevensDouble Ninth Festival
Vietnamesetrừ tịch(除夕)Nguyên Đán(元旦)unknownĐoan ngọThất tịchTrùng Cửu(重九)
Datethe last day in LàyuèZhēngyuè 1Sānyuè 3Wǔyuè 5Qīyuè 7Jǐuyuè 9
2014Jan 30Jan 31Apr 2Jun 2Aug 2Oct 2
2015Feb 18Feb 19Apr 21Jun 20Aug 20Oct 21
the festival below is on the day with half or full moon
Laba FestivalPreliminary EveLantern FestivalBuddha's BirthdayGhost FestivalMid-Autumn FestivalSpirit Festival
VietnameseTáo Quân(竈君)unknownNguyên TieuPhật ĐảnTrung NguyênTrung thuHạ Nguyên
DateLàyuè 8Làyuè 23[1]Zhēngyuè 15Sìyuè 8[2] or 15[3]Qīyuè 15Bāyuè 15Shíyuè 15
2014Jan 8Jan 23Feb 14May 6 or 13Aug 10Sept 8Dec 6
2015Jan 27Feb 11Mar 5May 25 or Jun 1Aug 28Sept 27Nov 26
the festival below is upon the solar terms
Vernal SacrificeCold Food FestivalQingming FestivalAutumn SacrificeWinter Solstice
VietnameseunknownHàn ThựcThanh MinhunknownĐông Chí
DateMar 18 or 19 even yearMar 23 or 24 odd yearApr 3 or 4Apr 4 or 5Sept 24 or 25even yearSept 19 or 20odd yearDecember 21 or 22
Remarkthe 5th Wùrì after Vernal Commences,
near Vernal Equinox
105th day after WS
near Bright and Clear
Bright and Clearthe 5th Wùrì after Autumn Commences,
near Autumn Equinox
Winter Solstice
Notes[1] In South China, the Preliminary Eve is the following day(Làyuè 23). [2] Buddha's Birthday in China and Korea is Sìyuè 8. [3] Buddha's Birthday in Vietnam is Sìyuè 15

Structure of Han and Tibetan calendar[edit]


In Han calendar, a day runs from midnight to midnight(Chinese: 下中天). Currently, midnight is based on Chinese Standard Time, the mean solar time at longitude 120° east (equivalent to UTC+08).

In Tibetan calendar, a day runs from dawn to dawn.

Subdivisions of a day[edit]

In modern China, people use the hour-minute-second system to mark and describe the time. But, people use other system to mark and describe time.

At early stage, a day is divided into 4 sections, morning, daytime, evening, night.

In ancient, the sundial and water clock is main timing device. On the relic of earlier sundial, there're 69 radial scales which covers 68% circumference. It means that China adopt centesimal system to measure the time. And in the water clock, There're 100 scales(Chinese: ; pinyin: ) on the rule to measure the water level. The time between 2 scales is a centiday(Chinese: ; pinyin: ) or 14.4 minutes.

At pre-Qin, a day is divided into 10 sections. The 5 sections in daytime are morn, fore, noon, post, and eve; the 5 sections in night are Jiǎ, , Bǐng, Dīng, and . The authority gives the time of the five section in the daytime with drum, and gives the time of the five sections in the night with gong in the city. The five section in the night were renamed with the ordinal number, such as 1 gēng(Chinese: 一更), 2 gēng(Chinese: 二更), 3 gēng(Chinese: 三更), 4 gēng(Chinese: 四更), 5 gēng(Chinese: 五更). The idiom Sāngēng bànyè.(Chinese: 三更半夜) means that in the dead night of 3 gēng.

In Han dynasty, a day is divided into 12 sections, midnight, crowing, daybreak, sunrise, morning, fore noon, noon, post noon, late afternoon, sunset, dusk, dead night. The 12 sections are renamed with 12 Earthly Branches later. And the 12 sections system is the mainstream, and is called as 12 shí. Each shí is 2 hours.

After Song Dynasty, each shí is divided into two hour. The halfway point is mid-shí(traditional Chinese: 正時; simplified Chinese: 正时; pinyin: zhèngshí), for example, midday is mid-wǔshí(traditional Chinese: 正午時; simplified Chinese: 正午时; pinyin: zhèngwǔshí). The first hour is ante mid-shí(traditional Chinese: 時初; simplified Chinese: 时初; pinyin: shíchū); and the second hour is post mid-shí(traditional Chinese: 時正; simplified Chinese: 时正; pinyin: shízhèng).

With the Buddhism's introduction into China, the bell began to used for giving time. The toll point is called as diǎn(traditional Chinese: ; simplified Chinese: ). The time between two diǎns is 24 minutes, which is called as diǎn too.

In the calendar calculate, a are divided into finer unit. Generally, a are divided into 60 mils(Chinese: ; pinyin: fēn). So, a gēng is 600 mils, a shí is 500 mils, and a diǎn is 100 mils.

The current Chinese standard time is 2014-11-7 01:10:37; or 44 mils am, chǒushí, Shíyīyuè 7, Jiǎwǔnián; or 94 mils, 3 gēng 2 diǎn, Shíyīyuè 7, 2014. Purge
True solar time of shí - kè and gēng - diǎn
(am=ante median, pm=post median)
0 kè1 kè2 kè3 kè4 kè1 gēng19:12
Zǐshípm00:0000:14:2400:28:4800:43:1200:57:361 diǎn19:36
am01:0001:12:0001:26:2401:40:4801:55:122 diǎn20:00
pm02:0002:09:3602:24:0002:38:2402:52:483 diǎn20:24
am03:0003:07:1203:21:3603:36:0003:50:244 diǎn20:48
pm04:0004:04:4804:19:1204:33:3604:48:005 diǎn21:12
am05:0005:02:2405:16:4805:31:1205:45:362 gēng21:36
pm06:0006:14:2406:28:4806:43:1206:57:361 diǎn22:00
am07:0007:12:0007:26:2407:40:4807:55:122 diǎn22:24
pm08:0008:09:3608:24:0008:38:2408:52:483 diǎn22:48

am09:0009:07:1209:21:3609:36:0009:50:244 diǎn23:12
pm10:0010:04:4810:19:1210:33:3610:48:005 diǎn23:36

am11:0011:02:2411:16:4811:31:1211:45:363 gēng00:00
pm12:0012:14:2412:28:4812:43:1212:57:361 diǎn00:24
am13:0013:12:0013:26:2413:40:4813:55:122 diǎn00:48
pm14:0014:09:3614:24:0014:38:2414:52:483 diǎn01:12
am15:0015:07:1215:21:3615:36:0015:50:244 diǎn01:36
pm16:0016:04:4816:19:1216:33:3616:48:005 diǎn02:00
am17:0017:02:2417:16:4817:31:1217:45:364 gēng02:24
pm18:0018:14:2418:28:4818:43:1218:57:361 diǎn02:48

am19:0019:12:0019:26:2419:40:4819:55:122 diǎn03:12
pm20:0020:09:3620:24:0020:38:2420:52:483 diǎn03:36
am21:0021:07:1221:21:3621:36:0021:50:244 diǎn04:00
pm22:0022:04:4822:19:1222:33:3622:48:005 diǎn04:24
Zǐshíam23:0023:02:2423:16:4823:31:1223:45:365 gēng04:48

The sundial and water clock shows shí and together. So, people always described the time with shí and together. The shí - kè system is exact time description.

Before Song Dynasty, the format is shí + kè, for example, in Section 2, Calendar Records, Yuán History(traditional Chinese: 元史·曆誌二; simplified Chinese: 元史·历志二) According to the estimation of Shòushí calendar, the sun eclipsed at the 8 kè, Yínshí(04:48). According to the estimation of Dàmíng Calendar, the sun eclipsed at 0 kè, Mǎoshí(05:00). (traditional Chinese: 《授時曆》,食甚寅八刻。《大明曆》,食甚卯初刻; simplified Chinese: 《授时历》,食甚寅八刻。《大明历》,食甚卯初刻)

After Song Dynasty, the format is shí + am/pm + kè, for example, in Section 2, Calendar Records, Yuán History(traditional Chinese: 元史·曆誌二; simplified Chinese: 元史·历志二) According to the estimation of Shòushí calendar, the sun eclipsed at the 1 kè am, Sìshí(09:07). According to the estimation of Dàmíng Calendar, the sun eclipsed at the 0 kè am, Sìshí(09:00). (traditional Chinese: 《授時曆》,食甚巳初一刻。《大明曆》,食甚巳初初刻; simplified Chinese: 《授时历》,食甚巳初一刻。《大明历》,食甚巳初初刻)

The authorities built bell and drum tower to give times. The drum signals each gēng, and bell signals each diǎn. So, people always described the time in night with gēng and diǎn together. The gēng - diǎn system is rough timing system in ancient. For example, in Section 4, Military Records, Yuán History (traditional Chinese: 元史·兵誌四; simplified Chinese: 元史·兵志四) The curfew rule: after 1 gēng 3 diǎn(20:24) when the bell tone stopped, walking is forbidden; after 5 gēng 3 diǎn (06:00) when the bell tone rang, walking is allowed. (traditional Chinese: 其夜禁之法,一更三點,鐘聲絕,禁人行;五更三點,鐘聲動,聽人行; simplified Chinese: 其夜禁之法,一更三点,钟声绝,禁人行;五更三点,钟声动,听人行)

In the water clock, the rules for day and night are separate, and the rules for deferent season are separate too. In general, the rules were changed each 9 days, corresponding the daytime change. The night-rule is 55 , and day-rule is 45 in the Winter Solstice. The night-rule is 35 , and day-rule is 65 in the Summer Solstice. The night-rule is 45 , and day-rule is 55 in the Vernal/Autumn Equinox. For the purposes of calculating the calendar, a day starts at midnight or mid-zǐshí(traditional Chinese: 正子時; simplified Chinese: 正子时; pinyin: zhèngzǐshí), but people tend to regard a day as starting at from dawn (during 5 gēng). For example, In a familiar couplet for New Year's Eve, it's written as "a night connects double ages, 5 gēng divides two years"(traditional Chinese: 一夜連雙歲,五更分兩年; simplified Chinese: 一夜连双岁,五更分两年)

The shí-kè and gēng - diǎn system is not in use in modern China. And shí and diǎn is denote a hours, is denote a quarter, and fēn is denote a minute after the western-style clock and watch was introduced into China. But, the traditional time system impress daily life. For example, the word Zhōngwǔ(Chinese: 中午) which means noon comes from the gēng and shí; the word Xīyáng(traditional Chinese: 夕陽; simplified Chinese: 夕阳) which means the sun of the evening comes from the gēng.


Days are grouped within several kinds of weeks.

The days are grouped within a 7-days week, which is called a Luminaries week (Chinese: 星期/七曜; pinyin: Xīngqī/Qīyào).

The name of the weekdays are Sun-day (Chinese: 日曜; pinyin: Rìyào), Moon-day (Chinese: 月曜; pinyin: Yuèyào), Mars-day(Chinese: 火曜; pinyin: Huǒyào), Mercury-day(Chinese: 水曜; pinyin: Shuǐyào), Jupiter-day (Chinese: 木曜; pinyin: Mùyào), Venus-day (Chinese: 金曜; pinyin: Jīnyào), and Saturn-day (Chinese: 土曜; pinyin: Tǔyào).In modern China, the names are identified by ordinal numbers, such as: First-day (Chinese: 星期一; pinyin: Xīngqīyī), Second-day (Chinese: 星期二; pinyin: Xīngqīèr), Third-day (Chinese: 星期三; pinyin: Xīngqīsān), Fourth-day (Chinese: 星期四; pinyin: Xīngqīsì), Fifth-day (Chinese: 星期五; pinyin: Xīngqīwǔ), Sixth-day (Chinese: 星期六; pinyin: Xīngqīlìu). The exception is Sunday, which is known as Sunday (Chinese: 星期日; pinyin: Xīngqīrì). 19 February 2015 is Xīngqīsì (Thursday).

Each 4 weeks are grouped within a 28-days week. the week days of a 28-days week are marked with Twenty-eight mansions(Chinese: 二十八宿; pinyin: Èrshíbāxìu). For example, 31 January 2013 is Níujīnníu (牛金牛).

28 mansions
QuadrantEast 青龙North 玄武West 白虎South 朱雀



















The days are grouped within a 10-days week, and is called Heavenly stems. The names of the weekdays are Jiǎrì, Yǐrì, Bǐngrì, Dīngrì, Wùrì, Jǐrì, Gēngrì, Xīnrì, Rénrì, and Guìrì. 19 February 2015 is Bǐngrì.

Some tradition holiday is established according to Heavenly Stems week. Such as the Vernal/Autumn Sacrifice(Chinese: 春社/秋社; pinyin: Chūnshè/Qīushè) is the fifth Wùrì after the Vernal/Autumn Commence.

The days are grouped within a 12-days week, which are called Earthly Branches. The names of the weekdays are Zǐrì, Chǒurì, Yínrì, Mǎorì, Chénrì, Sìrì, Wǔrì, Wèirì, Shēnrì, Yǒurì, Xūrì, and Hàirì. 19 February 2015 is Yínrì.

Some traditional holidays are established according to Earthly Branches week at first. Such as the Shàngsì Festival is the first Sìrì in Sānyuè, and the Duānwǔ Festival is the first Wǔrì in Wǔyuè at first. These festivals are moved to the fixed calendar later. The Shàngsì Festival is fixed to Sānyuè 3rd, and the Duānwǔ Festival is fixed to Wǔyuè 5th.

The Heavenly stems and Earthly Branches run together and, when combined, make a 60-day week which is called stem-branches week.


19 February 2015 is Bǐngyíngrì.

The earliest evidence of stem-branches week was found on oracle bones dated c. 1350 BC in the Shang Dynasty. The stem-branches week continues to this day, and can still be found on Chinese calendars today.

Although the stem-branches week cannot decide the actual date alone in historical events, it can locate the accurate date along with context and other statement about time, and the difference between versions of the calendar may be neglected. For this reason, the stem-branches week is always used to mark date in the annals. Such as:

Chronicle of Pope Rén, Sòng History (traditional Chinese: 宋史·仁宗本紀; simplified Chinese: 宋史·仁宗本纪)

In the Bǐngyínrì of vernal Zhēngyuè in the first year of Tiānshèng, which is the first day of the month, changed the era name; ...(traditional Chinese: 天聖元年春正月丙寅朔,改元; simplified Chinese: 天圣元年春正月丙寅朔,改元)

In the Wùxūrì of Èryuè, accepted the rule of Gusiluo '​s annual tribute; in Dīngsìrì, established the portrait of Grand Chris and Grand Pope at Hóngqìng Palace of the Southern Capital (Suiyang); lunched the Monopolizing-Tea-Discount Law at the 13 tea plantations of Huáinán (traditional Chinese: 二月戊戌,許唃廝囉歲一入貢;丁巳,奉安太祖、太宗御容於南京鴻慶宫;行淮南十三山場貼射茶法; simplified Chinese: 二月戊戌,许唃厮啰岁一入贡;丁巳,奉安太祖、太宗御容于南京鸿庆宫;行淮南十三山场贴射茶法)

In the Jiǎxūrì of Sānyuè, established the portrait of Pope Zhēn at Yìngtiān Temple of the Western Capital (Loyang); ...; in the Xīnmǎorì, the Imperial Astronomer present the Chóngtiān Calendar for the approval to issue; ...(traditional Chinese: 三月甲戌,奉安真宗御容於西京應天院;……;辛卯,司天監上《崇天曆》; ……; simplified Chinese: 三月甲戌,奉安真宗御容于西京应天院;……;辛卯,司天监上崇天历; ……)

Lunar phase and lunar month[edit]

The lunar phase refers to the shape of the illuminated (sunlit) portion of the Moon as seen by an observer on Earth. The lunar phases corresponds to the celestial longitude difference of the moon and sun. The principal lunar phases are new moon (0° celestial longitude difference), first quarter moon (90° celestial longitude difference), full moon (180° celestial longitude difference) and last quarter moon (270° celestial longitude difference).

The lunar month is the time from a day between two identical syzygies or principal phase (new moons or full moons).

In Han calendar, a lunar month corresponds to a variation cycle (0°~360°) of the celestial longitude difference. So, the month always starts on the day of with a new astronomical moon.

    Synodic month      2013-01-12 03:43:36 ~ 2013-02-10 15:20:06(29.48 days)|  2013-02-10 15:20:06 ~ 2013-03-12 03:51:00(29.52 days)  +      New moon day  2013-01-12 00:00:00 ~ 2013-01-13 00:00:00            |+ 2013-02-10 00:00:00 ~ 2013-02-11 00:00:00  - Next new moon day  2013-02-10 00:00:00 ~ 2013-02-11 00:00:00            |- 2013-03-12 00:00:00 ~ 2013-03-13 00:00:00   -------------------------------------------------------------------------+---------------------------------------------------------     The month         2013-01-12 00:00:00 ~ 2013-02-10 00:00:00(29    days)|  2013-02-10 00:00:00 ~ 2013-03-12 00:00:00(30    days) 

In Tibetan calendar, a lunar month corresponds to a variation cycle (-180°~180°) of the celestial longitude difference. The variation cycle is divided to 30 sections, and each section corresponds to a lunar day.

Celestial longitude difference-168°-156°-144°-132°-120°-108°-96°-84°-72°-60°-48°-36°-24°-12°
The moon phase accordinglyWaning gibbous(left)Third quarterWaning crescent(left)New moon
The lunar day accordingly16th17th18th19th20th21st22nd23rd24th25th26th27th28th29th30th
Celestial longitude difference12°24°36°48°60°72°84°96°108°120°132°144°156°168°180°
The moon phase accordinglyWaxing crescent(right)First quarterWaxing gibbous(right)Full Moon
The lunar day accordingly1st2nd3rd4th5th6th7th8th9th10th11th12th13th14th15th

The days in the month[edit]

In Han calendar, the dates in the month are arranged in an orderly row from 1 to 29 or 30, and each date are called with two characters, such as:


In the late Qīng Dynasty, selected yùnmù (韵目, the representative character of the rhymes) are on behalf of the two date characters for telegram use. It was applied into the date in the Gregorian calendar later. For example: Wénxī Fire (Chinese: 文夕大火) is a conflagration on the eve of 1938-11-12 (Evening of 1938-11-12, Chángshā was going to be occupied by the enemy, municipality burnt and fielded the city), Wén (Chinese: ) is on behalf of 12th and (Chinese: ) is on behalf of evening.

In Tibetan calendar, the dates in the month are arranged according to the lunar days. If there's a whole lunar day within a solar day, the date is arranged according the lunar day which ends in the solar day first; if there's a whole solar day within a lunar day, the date is arranged according to the lunar day; and if the solar day intersects with the lunar day, the date is arranged according to lunar day which ends in the solar day.

For example:

the number of the solar day12...9101112...2526...
The number of the lunar day12341011121325262728
The ending of the lunar day12:43⅔57:27½53:11⅓55:50⅓0:01⅚4:13⅓2:4856:53⅔50:59⅓
Celestial longitude difference12°24°36°120°132°144°300°312°324°
The date accordingly1st (skip 2nd)3rd10th11thlap 11th12th25th (skip 26th)27th
1 The time is remarked according to Tibetan time system. A day is 60 points, a point is 60 sections, and a section is 6 parts

In Tibetan calendar, the month length is decided by the number of the skipped and lapped dates. If there's no skipped and lapped date, it's a lucky month. If there's a skipped date, it's a month with 29 days. If there's a skipped and lapped date, it's a month with 30 days. If there're 2 skipped dates and a lapped date, it's a month with 29 days. If there're 2 skipped and lapped dates, it's a month with 30 days.

The dating method in Han and Tibetan calendar is different, so the date is not the same all the way. But, the bias is within 1.

Solar year and solar term[edit]

A solar year, for general purposes, is the length of time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from winter solstice to winter solstice.

In Han calendar, a solar year is the time from a winter solstice to the next. And a solar year is divided into 24 solar terms which correspond to 15° along the ecliptic. A couple of solar terms are associated into a climate term. The start point of the first term in the couple is called as pre-climate (traditional Chinese: 節氣; simplified Chinese: 节气; pinyin: Jiéqì), and the start point of the last term in the couple is called as mid-climate (traditional Chinese: 中氣; simplified Chinese: 中气; pinyin: Zhōngqì). The climate terms are marked with the 12 earthly branches. The time between two mid-climates correspond quite closely to the zodiac. The table right shows the relationship between solar terms, ecliptic positions and the zodiacs.

In the late Spring and Autumn Period (722–481 BC), the former Sìfēn calendar was established, and set the tropical year at 365.25 days, the same length as the Julian calendar which was introduced in 46 BC.[1] The Taichu calendar of 104 BC under Emperor Wu of Han rendered the solar year at roughly the same ( 365\tfrac{385}{1539}).[1]

Many other calendars were established between then and the Yuan Dynasty (1271–1368), including those established by Li Chunfeng (602–670) and Yi Xing (683–727).[1] In 1281, the Yuan astronomer Guo Shoujing (1233–1316) fixed the calendar at 365.2425 days, the same as the Gregorian calendar established in 1582; this calendar, the Shoushi calendar, would be used in China for the next 363 years.[1][5] Guo Shoujing established the new calendar with the aid of his own achievements in spherical trigonometry, which he derived largely from the work of Shen Kuo (1031–1095) who established trigonometry in China.[6][7][8]

In Tibetan calendar, a solar year is divided into 12 solar months (climate terms) equally. A solar month is about 30.4 days

The ecliptic position of each solar term
Solar MonthSolar termDateLongitudeZodiacSolar MonthSolar termDateLongitudeZodiac
Early Spring
VC, Vernal CommencesFeb 3-5315°AquariusShēn
Early Autumn
AC, Autumn CommencesAug 7-9135°Leo
VS, Vernal ShowersFeb 18-20330°330-360°
EH, End of HeatAug 22-24150°150-180°
Mid Spring
IA, Insects WakenMar 5-7345°Yǒu
Mid Autumn
WD, White DewSep 7-9165°
VE, Vernal EquinoxMar 20-22360°/0°0-30°
AE, Autumnal EquinoxSep 22-24180°180-210°
Late Spring
BC, Bright and ClearApr 4-615°
Late Autumn
CD, Cold DewOct 8-9195°
CR, Corn RainApr 19-2130°30-60°
FF, First FrostOct 23-24210°210-240°

Early Summer
SC, Summer CommencesMay 5-745°Hài
Early Winter
WC,Winter CommencesNov 7-8225°
CF, Corn FormsMay 20-2260°60-90°
LS, Light SnowNov 22-23240°240-270°

Mid Summer
CE, Corn on EarJun 5-775°
Mid Winter
HS, Heavy SnowDec 6-8255°
SS, Summer SolsticeJun 21-2290°90-120°
WS, Winter SolsticeDec 21-23270°270-300°
Late Summer
MH, Moderate HeatJul 6-8105°Chǒu
Late Winter
MC, Moderate ColdJan 5-7285°
GH, Great HeatJul 22-24120°LeoGC, Great ColdJan 20-21300°Aquarius

Month names[edit]

An astronomical year is approximately 365¼ days, a period between 12 and 13 lunar months. So, to keep the pace with the astronomical year in a long term, common years (a year with 12 months) and leap years (a year with 13 months) are interleaved. Generally, in each 19 years, there're 7 leap years and 12 common years.

In Han and Tibetan calendar, the month name corresponds to the climate term. The closest climate to the moon decides the month name, and the mid-climate in the month is regarded as the key point to choose the closest climate. Generally, the month with the Vernal Showers is Zhēngyuè or Dangpo (the 1st month), the month with the Vernal Equinox is Èryuè or Gnyispa ( the 2nd month), the month with the Corn Rain is Sānyuè or Gsumpa (the 3rd month), the month with the Corn Forms is Sìyuè or Bzhipa ( the 4th month), the month with the Summer Solstice is Wǔyuè or Lngapa (the 5th month), the month with the Moderate Heat is Lìuyuè or Drugpa ( the 6th month), the month with the End of Heat is Qīyuè or Ddunpa (the 7th month), the month with the Autumnal Equinox is Bāyuè or Brgyadpa (the 8th month), the month with the First Frost term is Jǐuyuè or Dgupa (the 9th month), the month with the Light Snow is Shíyuè Bcupa (the 10th month), the month with the Winter Solstice is Shíyīyuè or Bcugcigpa (the 11th month), the month with the Great Cold term is Làyuè or Bcugnyispa (the 12th month), and the month without a mid-climate is Rùnyuè (an intercalary month). For example, the table below show the information of 2014.

          Month Date              mid-Climate     Month name      |      Month Date              mid-Climate     Month name      A  2014-01-31 ~ 2014-02-28  VC: 2014-02-19  Zhēngyuè(1st)   |  G  2014-07-27 ~ 2014-08-24  EH: 2014-08-23     Qīyuè(7th)      B  2014-03-01 ~ 2014-03-30  VE: 2014-03-21     Èryuè(2nd)   |  H  2014-08-25 ~ 2014-09-23  AE: 2014-09-23     Bāyuè(8th)      C  2014-03-31 ~ 2014-04-28  CR: 2014-04-20    Sānyuè(3rd)   |  I  2014-09-24 ~ 2014-10-23  FF: 2014-10-23    Jǐuyuè(9th)      D  2014-04-29 ~ 2014-05-28  CF: 2014-05-21     Sìyuè(4th)   |  J  2014-10-24 ~ 2014-11-21  N/A               Rùnyuè(leap over)      E  2014-05-29 ~ 2014-06-26  SS: 2014-06-21     Wǔyuè(5th)   |  K  2014-11-22 ~ 2014-12-21  LS: 2014-11-22    Shíyuè(10th)      F  2014-06-27 ~ 2014-07-26  GH: 2014-07-23    Lìuyuè(6th)   |  L  2014-12-22 ~ 2015-01-19  WS: 2014-12-22  Shíyīyuè(11th)                                                                  |  M  2015-01-20 ~ 2015-02-18  GC: 2015-01-20     Làyuè(12th) 

In Han calendar, the solar term are calculated with the true sun position from Shùnzhì 2 (traditional Chinese: 順治二年; simplified Chinese: 顺治二年, 1645), and the length of the solar terms are 14.7-15.7 days against 15.2 days. So, there's a possibility of 0.3% that two mid-climates enters the same month. To avoid the skipped month, the month name is arranged in orderly row from then. When there're 12 month between two winter solstice months, the first month without a mid-climate is an intercalary. The month names except the intercalary are Shíyīyuè or Bcugcigpa (the 11th month), Làyuè or Bcugnyispa (the 12th month), Zhēngyuè or Dangpo (the 1st month), Èryuè or Gnyispa (the 2nd month), Sānyuè or Gsumpa (the 3rd month), Sìyuè or Bzhipa (the 4th month), Wǔyuè or Lngapa (the 5th month), Lìuyuè or Drugpa (the 6th month), Qīyuè or Ddunpa (the 7th month), Bāyuè or Brgyadpa (the 8th month), Jǐuyuè or Dgupa (the 9th month), Shíyuè Bcupa (the 10th month). For example, the table below shows the information of 2032-2035.

    Month Date        mid-Climate             Month name      |   Month Date         mid-Climate             Month name A 2032/12/03~12/31  WS: 2032/12/21         0  Shíyīyuè(11th) | M 2033/11/22~12/21  LS: 11/22 / WS: 12/21  0  Shíyīyuè(11th) B 2033/01/01~01/30  GC: 2033/01/20         1     Làyuè(12th) | N 2033/12/22~01/19  N/A                    1    Rùnyuè(11th, Intercalary) C 2033/01/31~02/28  RW: 2033/02/18         2  Zhēngyuè( 1st) | O 2033/01/20~02/18  GC: 01/20 / RW: 02/18  2     Làyuè(12th) D 2033/03/01~03/30  VE: 2033/03/20         3     Èryuè( 2nd) | P 2034/02/19~03/19  N/A                    3  Zhēngyuè( 1st) E 2033/03/31~04/28  GR: 2033/04/20         4    Sānyuè( 3rd) | Q 2034/03/20~04/18  VE: 2034/03/20         4     Èryuè( 2nd) F 2033/04/29~05/27  GF: 2033/05/21         5     Sìyuè( 4th) | R 2034/04/19~05/17  GR: 2034/04/20         5    Sānyuè( 3rd) G 2033/05/28~06/26  SS: 2033/06/21         6     Wǔyuè( 5th) | S 2034/05/18~06/15  GF: 2034/05/21         6     Sìyuè( 4th) H 2033/06/27~07/25  GH: 2033/07/22         7    Lìuyuè( 6th) | T 2034/06/16~07/15  SS: 2034/06/21         7     Wǔyuè( 5th) I 2033/07/26~08/24  LH: 2033/08/23         8     Qīyuè( 7th) | U 2034/07/16~08/13  GH: 2034/07/23         8    Lìuyuè( 6th) J 2033/08/25~09/22  N/A                    9     Bāyuè( 8th) | V 2034/08/14~09/12  LH: 2034/08/23         9     Qīyuè( 7th) K 2033/09/23~10/22  AE: 2033/09/23        10    Jǐuyuè( 9th) | W 2034/09/13~10/11  AE: 2034/09/23        10     Bāyuè( 8th) L 2033/10/23~11/21  FF: 2033/10/23        11    Shíyuè(10th) | X 2034/10/12~11/10  FF: 2034/10/23        11    Jǐuyuè( 9th) M 2033/11/22~12/21  LS: 11/22 / WS: 12/21  0  Shíyīyuè(11th) | Y 2034/11/10~12/10  LS: 2034/11/22        12    Shíyuè(10th)      11 months between Winter Solstices, no intercalary      | Z 2034/12/11~01/08  WS: 2034/12/22         0  Shíyīyuè(11th) 

Month bias in Han and Tibetan calendar[edit]

In Han calendar, the climate terms are unequal sections; but in Tibetan calendar, the climate terms are equal sections. So, the month is not the same all the way. But, the bias is within 1.

To sum up the month and date bias, the date in Han and Tibetan calendar is the same, a bias of a day, a bias of a month, or a bias of a month and a day. Such as:

    Feb 28, 1987 is Dangpo 1st, Fire rabbit year or   Èryuè 1st, Dīngmǎonián  with a bias of a month     Feb 18, 1988 is Dangpo 1st, Earth dragon year or Zhēngyuè 2nd, Wùchénnián with a bias of a day     Feb 27, 1990 is Dangpo 1st, Iron horse year  or   Èryuè 2nd, Gēngwǔnián  with a bias of a month and a day     Feb 15, 1991 is Dangpo 1st, Iron goat year  or Zhēngyuè 1st, Xīngwèinián  without bias 

Calendric intercalary rule[edit]

For Han calendar, Ping-Tse Kao (Chinese: 高平子; pinyin: Gāo, Píngzǐ; 1888-1970, one of the founders of Purple Mountain Observatory) mentioned the calendric intercalary rule. In his the calendric intercalary rule, the month name and intercalary are decided before rounding the month start to day. For example:

         Synodic Month                      mid-Climate        Month name    Civil Month A 2032-12-03 04:52:26 ~ 01-01 18:16:36  WS:12-21 15:55:29  0  Shíyīyuè 2032-12-03 ~ 12-31  B 2033-01-01 18:16:36 ~ 01-31 05:59:26  GC:01-20 02:32:20  1    Làyuè  2033-01-01 ~ 01-30  C 2033-01-31 05:59:26 ~ 03-01 16:23:05  VS:02-18 16:33:22  2  Zhēngyuè 2033-01-31 ~ 02-28  D 2033-03-01 16:23:05 ~ 03-31 01:51:12  VE:03-20 15:22:17  3    Èryuè  2033-03-01 ~ 03-30  E 2033-03-31 01:51:12 ~ 04-29 10:45:45  CR:04-20 02:12:40  4   Sānyuè  2033-03-31 ~ 04-28  F 2033-04-29 10:45:45 ~ 05-28 19:36:06  CF:05-21 01:10:30  5    Sìyuè  2033-04-29 ~ 05-27  G 2033-05-28 19:36:06 ~ 06-27 05:06:36  SS:06-21 09:00:40  6    Wǔyuè  2033-05-28 ~ 06-26  H 2033-06-27 05:06:36 ~ 07-26 16:12:07  GH:07-22 19:52:21  7   Lìuyuè  2033-06-27 ~ 07-25  I 2033-07-26 16:12:07 ~ 08-25 05:39:21  EH:08-23 03:01:22  8    Qīyuè  2033-07-26 ~ 08-24  J 2033-08-25 05:39:21 ~ 09-23 21:39:19  AE:09-23 00:51:12  9    Bāyuè  2033-08-25 ~ 09-22  K 2033-09-23 21:39:19 ~ 10-23 15:27:58  FF:10-23 10:27:08 10   Jǐuyuè  2033-09-23 ~ 10-22  L 2033-10-23 15:27:58 ~ 11-22 09:38:40  LS:11-22 08:15:42 11   Shíyuè  2033-10-23 ~ 11-21  M 2033-11-22 09:38:40 ~ 12-22 02:46:01  WS:12-21 21:45:32  0  Shíyīyuè 2033-11-22 ~ 12-21  N 2033-12-22 02:46:01 ~ 01-20 18:01:05  GC:01-20 08:26:49  1    Làyuè  2033-12-22 ~ 01-19  O 2034-01-20 18:01:05 ~ 02-19 07:09:47  VS:02-18 22:29:43  2  Zhēngyuè 2034-01-20 ~ 02-18  P 2034-02-19 07:09:47 ~ 03-20 18:14:06                     3   Rùnyuè  2034-02-19 ~ 03-19  Q 2034-03-20 18:14:06 ~ 04-19 03:25:25  VE:03-20 21:17:01  4    Èryuè  2034-03-20 ~ 04-18  R 2034-04-19 03:25:25 ~ 05-18 11:12:07  CR:04-20 08:03:14  5   Sānyuè  2034-04-19 ~ 05-17  S 2034-05-18 11:12:07 ~ 06-16 18:25:28  CF:05-21 06:56:24  6    Sìyuè  2034-05-18 ~ 06-15  T 2034-06-16 18:25:28 ~ 07-16 02:14:47  SS:06-21 14:43:42  7    Wǔyuè  2034-06-16 ~ 07-15  U 2034-07-16 02:14:47 ~ 08-14 11:52:35  GH:07-23 01:35:51  8   Lìuyuè  2034-07-16 ~ 08-13  V 2034-08-14 11:52:35 ~ 09-13 00:13:20  EH:08-23 08:47:16  9    Qīyuè  2034-08-14 ~ 09-12 W 2034-09-13 00:13:20 ~ 10-12 15:32:10  AE:09-23 06:39:04 10    Bāyuè  2034-09-13 ~ 10-11  X 2034-10-12 15:32:10 ~ 11-11 09:15:45  FF:10-23 16:15:57 11   Jǐuyuè  2034-10-12 ~ 11-10  Y 2034-11-11 09:15:45 ~ 12-11 04:13:56  LS:11-22 14:04:28 12   Shíyuè  2034-11-11 ~ 12-10  Z 2034-12-11 04:13:56 ~ 01-09 23:02:37  SS:12-22 03:33:30  0  Shíyīyuè 2034-12-11 ~ 01-08  

The calendric intercalary rule reduced the possibility that two mid-climate enters the same month to 0.06%. And, the intercalary is the same using different standard time.


A year starts at Zhēngyuè or Dangpo 1st, and always ends at the last day of Làyuè or Bcugnyispa (if there is an intercalary month after Làyuè or Bcugnyispa, the year will end on the last day of the intercalary month).

There are 12 or 13 months in a year. If there are 12 months in year, there are 353, 354 or 355 days in this year. If there are 13 months in a year, there are 383, 384 or 385 days in this year. For example, the current year starts at 2012-1-23 and ends at 2013-02-09. There are 13 months or 384 days.

The year with 13 month is a leap year. The intercalary month of the leap year between 1905 and 2132 in Han calendar is list as below:

leap 4190641925419444196341982420014202042039520584207742096421154
leap 2/31909219282194721966319841020043202322042220613208032099221183
leap 6/7191161930619497196871987620067202562044720637208272101721207
leap 5191451933519525197151990520095202852047520665208552104521235
leap 3/4191721936319553197441993320124203132050320694208842107421264
leap 8/9/1119197193871957819768199582014920331120528207182090821099212811
leap 6192251941619606197961998520176203662055620746209362112621316

A representative sequence of common and leap years is clc clc lc clc clc lc clc, which is the classic nineteen-year Metonic cycle. Han calendar follows the rule in general.

Age recognition in China[edit]

In China, the age recognition for official use is based on the Gregorian calendar. But, for traditional use, it is based on Han calendar. From birthday to the end of the year, it's one year old. And, add one year old after each New Year Eve. Such as, if one's birthday is Làyuè 29th 2013, he is 2 years old at Zhēngyuè 1st 2014. The Chinese traditional age recognition is called as nominal age(traditional Chinese: 虛歲; simplified Chinese: 虚岁), after the actual age(traditional Chinese: 實歲; simplified Chinese: 实岁) is introduced into China.

And, the month length of Chinese calendar is float. So, if someone was born in 30th of a month, his birthday is the last day of the month, whatever it's 29th or 30th. On the other hand, if someone was born in an intercalary month, his birthday is the common month of the intercalary month for the year without intercalary month.

Year name (Chinese: 年份; pinyin: Niánfèn)[edit]

The years are named with the era name (which is a name of several years) and ordinal number generally. But, the first year of each era is called as Yuánnián (Chinese: 元年).

For the eras ante Emperor Wǔ of Hàn Dynasty, the regnal names are regard as the era names. such as Yǐngōng 1(traditional Chinese: 隱公元年; simplified Chinese: 隐公元年; pinyin: Yǐngōng Yuánnián, The first year of Duke Yǐn of Lǔ State, 722 BC).

113 BC, Emperor Wǔ of Hàn Dynasty issued the first era name, Jiànyuán (Chinese: 建元), and 140 BC is marked as Jiànyuán 1(Chinese: 建元元年; pinyin: Jiànyuán Yuánnián,140 BC).

In China, the first official era name is Jiànyuán, the last official era name is Xuāntǒng(traditional Chinese: 宣統; simplified Chinese: 宣统).

In Japan, the first era name is Taika (大化), the last era name for Han calendar is Keiō (慶応). The first era name for the Gregorian calendar is Meiji (明治). Current era name is Heisei (平成).

After Xuāntǒng Sānnián, the republic authority adopted the Gregorian calendar and establish the next year as the first year. The country name(traditional Chinese: 民國; simplified Chinese: 民国; pinyin: Mínguǒ) is regard as the era name. The time system is used in Taiwan and some overseas Chinese societies still.

Since 1949, in mainland China, the authority abolished the era name of the ROC, and specified the Chinese of Christ Era as common era (Chinese: 公元; pinyin: Gōngyuán). So, the Gōngyuán is regard as the current era name. In some Chinese society, the Western Era (Chinese: 西元; pinyin: Xīyuán) takes the place of Gōngyuán

Continuous year numbering system[edit]

There's a epoch for each version of Han Calendar, which is called as Lìyuán(traditional Chinese: 曆元; simplified Chinese: 历元). The epoch is optimal origin of the calendar, and it's a Jiǎzǐrì, the first day of a lunar month, and the dark moon and solstice is just at the mid-night(Chinese: 日得甲子夜半朔旦冬至). And tracing back to a perfect day, such as that the day with magical star sign, there's a supreme epoch(Chinese: 上元; pinyin: shàngyuán). The continuous year base on the supreme epoch is shàngyuán jīnián(traditional Chinese: 上元積年; simplified Chinese: 上元积年). More and more factors was added into the supreme epoch, and the shàngyuán jīnián became a huge number. So, the supreme epoch and shàngyuán jīnián was neglected from Shòushí calendar.

From Tàichū calendar, all Han calendar follows a same frame, and straights down. So, epoch of the Tàichū calendar (the winter solstice of 105BC),is the calendaric epoch of Han calendar.

      The years before 105 BC,       105-Gōngyuán, such as: 2698 BC is 1594th year before the calendar epoch      The year of 105 BC,            105-Gōngyuán,           105 BC is    0th year      The years form 104 BC to 1 BC, 105-Gōngyuán, Such as:   87 BC is   18th year      The years after 1 BC,          Gōngyuán+104, such as:   2013  is 2117th year 

Shao Yong (Chinese: 邵雍, 1011–1077, Courtesy name: Yáofū, Posthumous title: Kāngjié, a philosopher, cosmologist, poet and historian who greatly influenced the development of Non-Confucianism in China.) introduced a timing system in his The Ultimate which Manages the World(traditional Chinese: 皇極經世; simplified Chinese: 皇极经世; pinyin: Huángjíjīngshì )

In his time system, 1 round (Chinese: ; pinyin: yuán), which contains 12'9600 years, is a lifecycle of the world. Each yuán (round) is divided into 12 assembly(traditional Chinese: ; simplified Chinese: ; pinyin: huì), which are named with Earthly Branches.

The Hài, , and Chǒu are the Remote Ages(Chinese: 太古; pinyin: Tàigǔ),which is the opening of the world (Chinese: 天地之分) just as the winter. The Yín, Mǎo, and Chén are the Early Ages(Chinese: 上古; pinyin: Shànggǔ), which is the evolution of the world (Chinese: 天地之化) just as the spring. The , , and Wèi are the Middle Ages(Chinese: 中古; pinyin: Zhōnggǔ), which is the climax of the world (traditional Chinese: 天地之關; simplified Chinese: 天地之关) just as the summer. The Shēn, Yǒu, and are the Late Ages(Chinese: 下古; pinyin: Xiàgǔ, ), which is the closing of the world (天地之合) just as the autumn.

Each assembly is divided into 30 run(traditional Chinese: ; simplified Chinese: ; pinyin: yùn), and each run is divided into 12 generation(Chinese: ; pinyin: shì). So, each generation is equivalent to 30 years.

The Yuán-Huì-Yùn-Shì is corresponded with Nián-Yuè-Rì-Shí. So the Yuán-Huì-Yùn-Shì is called as the major tend or the numbers of the heaven, and the Nián-Yuè-Rì-Shí is called as the minor tend or the numbers of the earth.

The major tend or the numbers of the heaven is far away from people seemingly, but the minor tend or the numbers of the earth is close to people. So the minor tend or the numbers of the earth is adapted by people for predicting destiny or fate. The numbers of Nián-Yuè-Rì-Shí is marked with stem-branches. So the minor tend of the numbers of the earth is show a form of Bāzì, and the four terms are be called as Four Pillars of Destiny

For example, the eight characters of the birth of Emperor Qiánlóng is Xīnmǎo-Dīngyǒu-Gēngwǔ-Bǐngzǐ (辛卯、丁酉、庚午、丙子).

Shào '​s Huángjíjīngshì recorded the history with stem-branches cycle from the first year of the 180th run or 2149th generation (ARGY 6-30-1-1, 2577 BC) and marked the year with reign title from the Jiǎchénnián of the 2156th generation (ARGY 6-30-8-11, 2357 BC, Tángyáo 1, traditional Chinese: 唐堯元年; simplified Chinese: 唐尧元年).

According to this timing system, 2014-1-31 is ARG/YMD 7-12-10/1-1-1.

The official year system of China is divided into many division with reign titles. And there's not an official recognition continuous year system. Referring to BC and AD, many reference points were purposed in the earlier 20th century, such as:

    Huángdì Era (traditional Chinese: 黄帝紀年; simplified Chinese: 黄帝纪年), Based on the birth or regal of Huángdì  Confucius Era (traditional Chinese: 孔子紀年; simplified Chinese: 孔子纪年), Based on the birth or dead year of Confucius        Yáo Era (traditional Chinese: 帝堯紀年; simplified Chinese: 帝尧纪年), Based on the regnal of Emperor Yao        Xià Era (traditional Chinese: 夏禹紀年; simplified Chinese: 夏禹纪年), Based on the regnal of Yu of Xia        Qín Era (traditional Chinese: 秦統一紀年; simplified Chinese: 秦统一纪年), Based on the year when Qin Unified China       Yuan Era (traditional Chinese: 亡國紀年; simplified Chinese: 亡国纪年), Based on the year when Song lost China completely     Gònghé Era (traditional Chinese: 共和紀年; simplified Chinese: 共和纪年), Based on Gònghé 1 

Generally, no reference date is widely accepted. Huángdì Era has significant public implications in oversea Chinese.

In the 17th century, the Jesuits tried to determine what year should be considered the epoch of Han calendar. In his Sinicae historiae decas prima (first published in Munich in 1658), Martino Martini (1614–1661) dated the royal ascension of Huangdi to 2697 BC, but started the Chinese calendar with the reign of Fu Xi, which he claimed started in 2952 BC. Philippe Couplet's (1623–1693) Chronological table of Chinese monarchs (Tabula chronologica monarchiae sinicae; 1686) also gave the same date for the Yellow Emperor. The Jesuits' dates provoked great interest in Europe, where they were used for comparisons with Biblical chronology. Modern Chinese chronology has generally accepted Martini's dates, except that it usually places the reign of Huangdi in 2698 BC and omits Huangdi's predecessors Fu Xi and Shennong, who are considered "too legendary to include".

Starting in 1903, radical publications started using the projected date of birth of the Yellow Emperor as the first year of Han calendar. Different newspapers and magazines proposed different dates. Jiangsu, for example, counted 1905 as year 4396 (use an epoch of 2491 BC), whereas the Minbao (traditional Chinese: 明報; simplified Chinese: 明报, the organ of the Tongmenghui) reckoned 1905 as 4603 (use an epoch of 2698 BC). Liu Shipei (劉師培; 1884–1919) created the Yellow Emperor Calendar, now often used to calculate the date, to show the unbroken continuity of the Han race and Han culture from earliest times. Liu's calendar started with the birth of the Yellow Emperor, which he determined to be 2711 BC. There is no evidence that this calendar was used before the 20th century.[9] Liu calculated that the 1900 international expedition sent by eight foreign powers to suppress the Boxer Uprising entered Beijing in the 4611th year of the Yellow Emperor.

At January 2, 1912, Sun Yat-sen declared that the Republic of China adopt the Gregorian calendar, and establish Shíyīyuè 13th 4609 of Huángdì Era as the new year's day of the first year of the Republic of China (traditional Chinese: 中華民國改用陽曆,以黄帝紀元四千六百零九年十一月十三日爲中華民國元年元旦; simplified Chinese: 中华民国改用阳历,以黄帝纪元四千六百零九年十一月十三日为中华民国元年元旦). Sun Yat-sen's choice, which implied an epoch of 2698 BC, was adopted by many overseas Chinese communities outside Southeast Asia such as San Francisco's Chinatown.[10]

       Sun Yat-sen's version       Years before 2698 BC not mentioned      Years before 1 AD   HE=2699-CE      Years after 1 BC   HE=2698+CE such as 1912+2698=4610, the year after spring festival of 1912 CE is 4610 HE 

Cycle of years[edit]

The years are grouped within a 10-year cycle which is called the 10 Celestial Stems (or called as 10 Heavenly Stems). The names of each year are: Jiǎnián, Yǐnián, Bǐngnián, Dīngnián, Wùnián, Jǐnián, Gēngnián, Xīnnián, Rénnián and Guìnián.The current year (2014-1-31~2015-2-18) is Jiǎnián.

Each year corresponds to an element in Wǔxíng. Jiǎnián and Yǐnián is Wood(Chinese: ; pinyin: ), Bǐngnián and Dīngnián is Fire(Chinese: ; pinyin: Huǒ), Wùnián and Jǐnián is Earth(Chinese: ; pinyin: ), Gēngnián and Xīnnián is Metal(Chinese: ; pinyin: Jīn), Rénnián and Guìnián is Water(Chinese: ; pinyin: Shuǐ). Therefore the current year is a Mùnián.

Main article: Chinese zodiac

The years are grouped within a 12-year cycle which is called the 12 Earthly Branches. The names of the years are: Zǐnián, Chǒunián, Yínnián, Mǎonián, Chénnián, Sìnián, Wǔnián, Wèinián, Shēnnián, Yǒunián, Xūnián, and Hàinián.The current year is Wǔnián.

Each cycle year is corresponds to an animal of the Chinese zodiac. Zǐnián to Rat(Chinese: ; pinyin: Shǔ), Chǒunián to Ox(Chinese: ; pinyin: Níu), Yínnián to Tiger(Chinese: ; pinyin: ), Mǎonián to Rabbit(Chinese: ; pinyin: ), Chénnián to Dragon(traditional Chinese: ; simplified Chinese: ; pinyin: Lóng), Sìnián to Snake(Chinese: ; pinyin: Shé), Wǔnián to Horse(traditional Chinese: ; simplified Chinese: ; pinyin: ), Wèinián to Goat(Chinese: ; pinyin: Yáng), Shēnnián to Monkey(Chinese: ; pinyin: Hóu), Yǒunián to Rooster(traditional Chinese: ; simplified Chinese: ; pinyin: ), Xūnián to Dog(Chinese: ; pinyin: Gǒu) and Hàinián to Pig(traditional Chinese: ; simplified Chinese: ; pinyin: Zhū). The seal characters of the earthly branches show the figure of the animals. For example, shows the figure of the horse face.Therefore the current year is Mǎnián (Horse).

The Heavenly stems cycle and Earthly Branches cycle runs together, and become a 60-year cycle which is called the stem-branches cycle. The current year is Jiǎwǔnián, also called as Mùmǎnián (Wood Horse).

Around the Han Dynasty, the stem-branches cycle was introduced. In Míng Dynasty and Qīng Dynasty, the stem-branches cycle was used along with the year mark in the Oration to Yellow Emperor. Such as: in Oration to Yellow Emperor at the first year of Wànlì

That, at the first year of Wànlì, which is Guìyǒunián, at Sìyuè started at Gēngxūrì, at 16th day which is Yǐchǒurì, the Emperor sent... (traditional Chinese: 萬曆元年,歲次癸酉,四月庚戌朔,越十六日乙丑,皇帝遣……; simplified Chinese: 万历元年,岁次癸酉,四月庚戌朔,越十六日乙丑,皇帝遣……)

The table right shows the stem/branch year names, correspondences to the Western (Gregorian) calendar, and other related information for the current decade. Alternatively, see this larger table of the full 60-year cycle.

CE[1]Timestamp[2]AH[3]Jiǎzǐxù[4]Stem,branchYear of the[5]...AD[6]AM[7]From... to ...Notes
211401-07-12-09 /27470779:26(7,3)庚寅GY gēngyín Metal Tiger201099Feb 14 - Duo 21. calendaric year number
    from the Winter Solstice of 104BC
2. timestamp of Huángjíjīngshì system
3. Anno Huángdì, Using an epoch of 2697BC
   -60 if using an epoch of 2637BC
   +1 if using an epoch of 2698BC
4. the order in the stems-branches cycle
5. phase and zodic
6. year number upon Christian era.
   the year number of the larger overlapping
7. Anno Mínguó, year number upon Minguo era
8. Und(Undecember) is Jan of the next year
9. Duo(Duodecember) is Feb of the next year
211501-07-12-09 /28470879:27(8,4)辛卯XM   xīnmǎoMetal Rabbit2011100Feb 3 - Und[8] 22
211601-07-12-09 /29470979:28(9,5)壬辰RC  rénchénWater Dragon2012101Jan 23 - Duo[9] 9
211701-07-12-09 /30471079:29(a,6)癸巳GS    guǐsìWater Snake2013102Feb 10 - Und 30
211801-07-12-10 /01471179:30(1,7)甲午JW    jiǎwǔWood Horse2014103Jan 31 - Duo 18
211901-07-12-10 /02471279:31(2,8)乙未YW    yǐwèiWood Goat2015104Feb 19 - Duo 7
212001-07-12-10 /03471379:32(3,9)丙申BS bǐngshēnFire Monkey2016105Feb 8 - Und 27
212101-07-12-10 /04471479:33(4,a)丁酉DY  dīngyǒuFire Rooster2017106Jan 28 - Duo 15
212201-07-12-10 /05471579:34(5,b)戊戌WX     wùxūEarth Dog2018107Feb 16 - Duo 14
212301-07-12-10 /06471679:35(6,c)己亥JH    jǐhàiEarth Pig2019108Feb 5 - Und 24

Chinese-Uighur calendar[edit]

Chinese-Uighur calendar In 1258, when both North China and the Islamic world were part of the Mongol Empire, Hulagu Khan established an observatory in Maragheh for the astronomer Nasir al-Din al-Tusi at which a few Chinese astronomers were present, resulting in the Chinese-Uighur calendar that al-Tusi describes in his Zij-i Ilkhani.[11] The 12 year cycle, including Turkic/Mongolian translations of the animal names (known as sanawat-e turki سنوات ترکی,) remained in use for chronology, historiography, and bureaucratic purposes in the Persian and Turkic speaking world from Asia Minor to India and Mongolia throughout the Medieval and Early Modern periods. In Iran it remained common in agricultural records and tax assessments until a 1925 law deprecated its use.

In Chinese-Uighur calendar, the year was computed from the vernal equinox, and each month was determined by the transit of the sun into the corresponding zodiac region. So, the month in Chinese-Uighur calendar is 3 month later than that in Miao calendar, and there're 29–32 days in each month.

See also[edit]


  1. ^ a b c d e Deng, Yingke. (2005). Ancient Chinese Inventions. Translated by Wang Pingxing. Beijing: China Intercontinental Press (五洲传播出版社). ISBN 7-5085-0837-8. Page 67.
  2. ^ Cullen, Atronomy and Methematics in Ancient China. Cambridge, 1996.
  3. ^ Needham, Joseph. (1986). Science and Civilization in China: Volume 5, Chemistry and Chemical Technology, Part 6, Missiles and Sieges. Cambridge University Press., reprinted Taipei: Caves Books, Ltd.(1986). Page 151.
  4. ^ Ebrey, Patricia Buckley (1999). The Cambridge Illustrated History of China. Cambridge: Cambridge University Press. ISBN 0-521-66991-X (paperback). Pages 124–125.
  5. ^ Asiapac Editorial. (2004). Origins of Chinese Science and Technology. Translated by Yang Liping and Y.N. Han. Singapore: Asiapac Books Pte. Ltd. ISBN 981-229-376-0, p. 132.
  6. ^ Needham, Joseph. (1959). Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Cambridge University Press., reprinted Taipei: Caves Books, Ltd.(1986), pp. 109–110.
  7. ^ Ho, Peng Yoke. (2000). Li, Qi, and Shu: An Introduction to Science and Civilization in China. Mineola: Dover Publications. ISBN 0-486-41445-0. p. 105.
  8. ^ Restivo, Sal. (1992). Mathematics in Society and History: Sociological Inquiries. Dordrecht: Kluwer Academic Publishers. ISBN 1-4020-0039-1. p. 32.
  9. ^ Cohen (2012), p. 1, 4.
  10. ^ Aslaksen, p. 38.
  11. ^ Benno van Dalen, E.S. Kennedy, Mustafa K. Saiyid, "The Chinese-Uighur Calendar in Tusi's Zij-i Ilkhani", Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften 11 (1997) 111–151.

Further reading[edit]


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External links[edit]

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