# Chinese calendar

The single-page calendar of the Year of Guisi, lunar-monthly (Marked the month name in Chinese, Islamic, Tibet calendar)

The Chinese calendar is a lunisolar calendar, incorporating elements of a lunar calendar with those of a solar calendar. It is not exclusive to China, but followed by many other Asian cultures as well.[1] In most of East Asia today, the Gregorian calendar is used for day-to-day activities, but the Chinese calendar is still used for marking holidays such as the Chinese New Year, the Duan Wu festival, and the Mid-Autumn Festival, and in astrology, such as choosing the most auspicious date for a wedding or the opening of a building. Because each month follows one cycle of the moon, it is also used to determine the phases of the moon.

A year in the Chinese calendar begins on the second new moon after the winter solstice, unless an intercalary month moves it to the third new moon.

The current year (February 10, 2013 – January 30, 2014) is Guisi-year (year of the Snake).

An example of a Chinese calendar.
A combination calendar, with Gregorian system below and a Chinese Zodiac chart above.
Time Scale (Gregorian calendar vs Chinese calendar)

## History

### Early history

The earliest evidence of the Chinese calendar is found on the oracle bones of the Shang Dynasty (late second 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 sìfēn 四分 (quarter remainder) calendar, 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 zhang 章, known in the West as the Metonic cycle.[2] 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 the year began one month before (the second new moon before the winter solstice, which now fell in the second month of the year). The Qin calendar was used during the Qin dynasty, and in the beginning of the Western Han dynasty. According to the Han Shu 21a, 973, for the moment of unification the Middle kingdoms had 6 different calendars: those of the mythological progenitors Yellow Emperor (黄帝曆) and Zhuanxu (顓頊曆); of the dynasties Xia (夏曆), Yin (殷曆), and Zhou (周曆), and of the Zhou Dynasty state of Lu (鲁曆). 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.[3]

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.[4][5]

### Taichu calendar

The Emperor Wu of the Western Han dynasty(In capital of Changan) introduced reforms that have governed the Chinese calendar ever since. His Tàichū (太初, "Grand Inception") calendar introduced in 104 BC build a relationship between the solar terms and the months. The midpoints of the solar terms are defined as benchmark to evaluate the bias between the solar terms and the months. If the midpoints escape from a month, the bias between the solar terms and the month is regarded as the biggest bias, and the month is regarded as an intercalary month. A mean solar term is about 30.43685 days, and a month is about 29.530588 days, so there's an intercalary month after about 32.585 months. It means that the intercalary month was equally likely to occur after any month of the year until 1645.

The tropical year of the Taichu calendar was defined as $365\tfrac{385}{1539}$ days and the synodic month as $29\tfrac{43}{81}$ days.

### True sun and moon

Though the fact of the irregularity of the lunar orbit was known in the 1st century BC, the starts of the months were calculated using the mean motions of both the sun and moon until 619, the second year of the Tang dynasty, when chronologists began to use true motions modeled using two offset opposing parabolas (with small linear and cubic components). Unfortunately, the parabolas did not meet smoothly at the mean motion, but met with a discontinuity or jump.

With the introduction of European astronomy into China via the Jesuits, the motions of both the sun and moon began to be calculated with sinusoids in the 1645 Chongzhen calendar (時憲書, Book of the Conformity of Time) of the Qing dynasty, made by the Jesuits Adam Schall and Giacomo Rho. The true motion of the sun was now used to calculate the jiéqì, which caused the intercalary month to often occur after the second through the ninth months, but rarely after the tenth through first months. A few autumn-winter periods have two or three calendar months in which the sun stays within one sign during the month (i.e. months that would normally be treated as intercalary months), interspersed with one or two calendar months in which the sun enters two signs of the zodiac during the month, something that was impossible using mean sun motion.

### Gregorian reform

The Gregorian calendar was adopted by the nascent Republic of China effective January 1, 1912 for official business, but the general populace continued to use the traditional calendar. The status of the Gregorian calendar was unclear between 1916 and 1921 while China was controlled by several competing warlords each supported by foreign colonial powers. From about 1921 until 1928 warlords continued to fight over northern China, but the Kuomintang or Nationalist government controlled southern China and used the Gregorian calendar. After the Kuomintang reconstituted the Republic of China October 10, 1928, the Gregorian calendar was officially adopted, effective January 1, 1929. The People's Republic of China has continued to use the Gregorian calendar since 1949.

### Standard time

Before 1929, the traditional calendar was calculated by the Central Observatory (formerly the Imperial Observatory) in Beijing using Beijing local time at a longitude of 116°25'E (GMT+7h 45m 40s). From 1929 to 1949 it was calculated by the Institute of Astronomy in Nanjing and since 1949 by the Purple Mountain Observatory outside of Nanjing using Chinese standard time at a longitude of 120°E (GMT+8h). This shifted the midnight marking the beginning of each day in both the traditional and Gregorian calendars by plus 14 minutes 20 seconds. This shift meant that any dark moon which formerly occurred just before midnight Beijing local time now occurred just after midnight Chinese standard time, causing the first day of a lunar month to occur one day later. However, unlike the official tables, most public calendars relied on the old Wannian Shu (Long-term (lit. "10,000-year) Calendar；simplified Chinese: 万年书; traditional Chinese: 萬年書) last published in 1910 using Beijing time until they were forced to adopt the official traditional calendar using Chinese standard time when the two disagreed. In 1953 public calendars placed the dark moon and the first day of a lunar month on August 9, whereas the official traditional calendar placed it on August 10, which caused public calendars in most of the People's Republic of China to use the official tables and standard time after 1953. In 1978 the dates were respectively September 2 and 3, causing public calendars in the Hong Kong and Canton areas to do the same after 1978. In 1989 the dates were August 1 and 2, which caused Taiwan to do the same after 1989.[6][7]

## Structure

### Day (Rì日)

A day in the Chinese calendar runs from midnight to midnight, as in the Gregorian calendar. Currently, midnight is based on Chinese Standard Time, the mean solar time at longitude 120° east.

A day is divided into 13 parts: starting from the second half of Zi-seizsaenz(下子时, 0~1), Chou-seizsaenz(丑时, 1~3), Yin-seizsaenz(寅时, 3~5), Mao-seizsaenz(卯时, 5~7), Chen-seizsaenz(辰时, 7~9), Si-seizsaenz(巳时, 9~11), Wu-seizsaenz(午时, 11~13), Wei-seizsaenz(未时, 13~15), Shen-seizsaenz(申时, 15~17), You-seizsaenz(酉时, 17~19), Xu-seizsaenz(戌时, 19~21), Hai-seizsaenz(亥时, 21~23), and First half of Zi-seizsaenz(上子时, 23~24).

One seizsaenz is two hours.

People tend to regard a day as starting at from dawn (Yin-seizsaenz).

### Week

Days are grouped within several kinds of weeks.

• 10-day week

The days are grouped within a 10-day week, and is called the ten celestial stems. The names of the weekdays are Jia(甲)-day, Yi(乙)-day, Bin(丙)-day, Ding(丁)-day, Wu(戊)-day, Ji(己)-day, Geng(庚)-day, Xin(辛)-day, Ren(壬)-day, and Gui(癸)-day.

2013-1-31 is Ding(丁)-day.

• 12-day week

The days are grouped within a 12-day week, which is called the 12 earthly branches. The names of the weekdays are Zi(子)-day, Chou(丑)-day, Yin(寅)-day, Mao(卯)-day, Chen(辰)-day, Si(巳)-day, Wu(午)-day, Wei(未)-day, Shen(申)-day, You(酉)-day, Xu(戌)-day, and Hai(亥)-day.

2013-1-31 is You(酉)-day.

• 60-day week

The 10-day week system and 12-day week system are combined, and become a 60-day week which is called the 60 stem-branches.

2013-1-31 is Dingyou-day.

• 7-day week

The days are grouped within a 7-day week, which is called a Xingqi (星期, Luminary-day). The name of the weekdays are Sun-day, Moon-day, Mars-day, Mercury-day, Jupiter-day, Venus-day, and Saturn-day.

In modern China, the names are identified by ordinal numbers except: Xingqi Yi (星期一，First-day), Xingqi Er (星期二，Second-day), Xingqi San (星期三，Third-day), Xingqi Si (星期四，Fourth-day), Xingqi Wu (星期五，Fifth-day), Xingqi Liu (星期六，Sixth-day). The exception is Sunday, which is known as Xingqi Ri (星期日) or Xingqi Tian (星期天).

2013-1-31 is Fourth-day (Thursday).

### Month (Yuè月)

The month in the Chinese calendar is a lunar term between two dark moons.

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

### Solar year (Suì 歲) and Solar term (Jiéqì 節氣)

The solar year (Suì) in Chinese is the term between the winter solstice days.

```          Tropical year (365.25 days)           2012-12-21 19:11:35     ~     2013-12-22 01:10:59
+    The day of the winter solstice        2012-12-21 00:00:00     ~     2012-12-22 00:00:00
-    The day of the next winter solstice   2013-12-22 00:00:00     ~     2013-12-23 00:00:00
-------------------------------------------------------------------------------------------------
Solar year (366 days)                 2012-12-21 00:00:00     ~     2013-12-21 00:00:00
```

A tropical year is divided into twelve solar terms, Zi-term, Chou-term, Yin-term, Mao-term, Chen-term, Si-term, Wu-term, Wei-term, Shen-term, You-term, Xu-term, and Hai-term. There are twelve nodes between the terms and twelve midpints within the terms. The nodes are called Jieqi, and the midpoints are called Zhongqi. The nodes and midpoints correspond to each 15° points along the ecliptic.

The relationship between the nodes/midpoints, ecliptic position, and zodiac is listed below.

Solar Term Name Longitude Zodiac
Zi-term(子) Node GS, Great Snow(Dàxuě 大雪) 255°
Midpoint WS, Winter Solstice(Dōngzhì 冬至) 270° Capricornus 270-300°
Chou-term(丑) Node SC, Slight Cold(Xiǎohán 小寒) 285°
Midpoint GC, Great Cold(Dàhán 大寒) 300° Aquarius 300-330°
Yin-term(寅) Node VB, Vernal Begins(Lìchūn 立春) 315°
Midpoint RW, Rain Water(Yǔshuǐ 雨水) 330° Pisces 330-360°
Mao-term(卯) Node IA, Insects Awaken(Jīnzhé 驚蟄) 345°
Midpoint VE, Vernal Equinox(Chūnfēn 春分) 360°/0° Aries 0-30°
Chen-term(辰) Node CB, Clear and Bright(Qīngmíng 清明) 15°
Midpoint GR, Grain Rain(Gǔyǔ 穀雨) 30° Taurus 30-60°
Si-term(巳) Node SB, Summer Begins(Lìxià 立夏) 45°
Midpoint GF, Grain Full(Xiǎomǎn 小滿) 60° Gemini 60-90°
Wu-term(午) Node GE, Grain in Ear(Mángzhǒng 芒種) 75°
Midpoint SS, Summer Solstice(Xiàzhì 夏至) 90° Cancer 90-120°
Wei-term(未) Node SH, Slight Heat(Xiǎoshǔ 小暑) 105°
Midpoint GH, Great Heat(Dàshǔ 大暑) 120° Leo 120-150°
Shen-term(申) Node AB, Autumn Begins(Lìqiū 立秋) 135°
Midpoint LH, Limit of Heat(Chúshǔ 處暑) 150° Virgo 150-180°
You-term(酉) Node WD, White Dew(Báilù 白露) 165°
Midpoint AE, Autumnal Equinox(Qiūfēn 秋分) 180° Libra 180-210°
Xu-term(戌) Node CD, Cold Dew(Hánlù 寒露) 195°
Midpoint FD, Frost's Descent(Shuāngjiàng 霜降) 210° Scorpio 210-240°
Hai-term(亥) Node WB, Winter Begins(Lìdōng 立冬) 225°
Midpoint LS, Light Snow(Xiǎoxuě 小雪) 240° Sagitarius 240-270°
Node GS, Great Snow(Dàxuě 大雪) 255°

### Month name

In generally, a solar year contains 11 or 12 whole-months and 2 parts. However, if the winter solstice or the next winter solstice is on the midnight of the day with the dark moon, which is very rare, the solar year contains 12 whole-months and one part.

The month with the winter solstice, is called Dongyue (The month with the winter solstice).

If a solar year contains 11 whole-months (except Dongyue), the names of the months are: Layue, Zhengyue, Eryue, Sanyue, Siyue, Wuyue, Liuyue, Qiyue, Bayue, Jiuyue, Shiyue.

If a solar year contains 12 whole-months(except Dongyue), the first month without a midpoint of solar term is an intercalary month. The names of the other months are: Layue, Zhengyue, Eryue, Sanyue, Siyue, Wuyue, Liuyue, Qiyue, Bayue, Jiuyue, Shiyue.

If the intercalary month is the first of the 12 whole-months, it is called Run-Dongyue (Intercalary Dongyue). If the intercalary month is not the first of the 12 whole-months, it follow the name of the month before it. For example, the intercalary month after Qiyue is called Run-Qiyue.

```               2012-12-13 ~ 2013-01-11       Dongyue      WS:2012-12-21
1    2013-01-12 ~ 2013-02-09       Layue
2    2013-02-10 ~ 2013-03-11       Zhengyue
3    2013-03-12 ~ 2013-04-09       Eryue
4    2013-04-10 ~ 2013-05-09       Sanyue
5    2013-05-10 ~ 2013-06-07       Siyue
6    2013-06-08 ~ 2013-07-07       Wuyue
7    2013-07-08 ~ 2013-08-06       Liuyue
8    2013-08-07 ~ 2013-09-04       Qiyue
9    2013-09-05 ~ 2013-10-04       Bayue
10   2013-10-05 ~ 2013-11-02       Jiuyue
11   2013-11-03 ~ 2013-12-02       Shiyue
2013-12-03 ~ 2013-12-31       Dongyue      WS: 2013-12-22
```
```               2013-12-03 ~ 2013-12-31       Dongyue      WS: 2013-12-22
1    2014-01-01 ~ 2014-01-30       Layue        GC: 2014-01-20
2    2014-01-31 ~ 2014-02-28       Zhengyue     RW: 2014-02-19
3    2014-03-01 ~ 2014-03-30       Eryue        VE: 2014-03-21
4    2014-03-31 ~ 2014-04-28       Sanyue       GR: 2014-04-20
5    2014-04-29 ~ 2014-05-28       Siyue        GF: 2014-05-21
6    2014-05-29 ~ 2014-06-26       Wuyue        SS: 2014-06-21
7    2014-06-27 ~ 2014-07-26       Liuyue       GH: 2014-07-23
8    2014-07-27 ~ 2014-08-24       Qiyue        LH: 2014-08-23
9    2014-08-25 ~ 2014-09-23       Bayue        AE: 2014-09-23
10   2014-09-24 ~ 2014-10-23       Jiuyue       FD: 2014-10-23
11   2014-10-24 ~ 2014-11-21       Intercalary Jiuyue(Run-Jiuyue)
12   2014-11-22 ~ 2014-12-21       Shiyue       LS: 2014-11-22
2014-12-22 ~ 2015-01-19       Dongyue      WS: 2014-12-22
```

#### Correspondence between solar terms and lunar months

The month is a lunar term, and the Chinese calendar is a lunisolar term. Therefore the month name corresponds to the solar term.

Generally, the midpoint of the solar term decides the month name.

Winter solstice decides Dongyue. Great cold decides Layue. Rain water decides Zhengyue. Vernal equinox decides Eryue. Grain rain decides Sanyue.

Grain full decides Siyue. Summer solstice decides Wuyue. Great heat decides Liuyue. Limit of heat decides Qiyue. Autumnal equinox decides Bayue.

Frost's descent decides Jiuyue. Light snow decides Shiyue. A month without a midpoint of a solar term is an intercalary month.

However, the nodes and midpoints of the solar terms are decided by true sun position after 1645, and the days between the midpoints near the perihelion may be 29 days. However, the month length may be 30 days.

This means the there may be 2 midpoints in a month. If one of the two midpoints is the winter solstice, the month must be defined as Dongyue. The month before/after Dongyue may not correspond to the solar term. for example:

The light snow and winter solstice in 2033 occur in the same month. The month should be Dongyue. However, the months before/after the Dongyue may not correspond to the solar term.

1. There is no midpoint in the month before Autumn equinox, there is Bayue aginst the Intercalary month.

2. The month with autumn equinox is Jiuyue against Bayue

3. The month with frost's descent is Shiyue against Jiuyue

4. There is no midpoint in the month before Vernal equinox is Zhengyue against Intercalary month.

This is an exception. The exceptions are rare. In the 600 years from 1810 to 2409, there are 7421 months. Only 11 months meet the wrong midpoint of the solar term, and 19 months (except the intercalary month) miss the midpoint of the solar term.

### Year (Nián年)

A year starts on the first day of Zhengyue, and always ends on the last day of Layue (if there is an intercalary month after Layue, the year will end on the last day of Run-Layue).

There are twelve or thirteen months in a year. If there are twelve months in year, the number of days in a year is 353, 354, or 355. If there are thirteen months in a year, the number of days in a year is 383, 384, or 385.

For example, the current year starts at 2012-1-23 and ends at 2013-02-09. There are 13 months or 384 days.

### Year Name

From the ages of Han Wudi, each emperor gave a name for the following years. The name is called the era name, such as Jianyuan or Taichu.

The specified year is called the first year (Yuannian). For example there was the first year of Jianyuan (Jianyuan Yuannian) and the first year of Taichu (Taichu Yuannian).

The following years are called the 2nd year (Ernian), 3rd year (Sannian), 4th year (Sinian), and so on, such as the third year of Xuantong (Xuantong Sannian).

Since 1911, the authorities do not give names for the years of Chinese Calendar any more, so either the Common Era or Republic of China Era (now only in Taiwan and in some overseas communities) is used to indicate the years of Chinese Calendar.

### Cycle of years

• 10-year cycle

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: Jia-year, Yi-year, Bin-year, Ding-year, Wu-year, Ji-year, Geng-year, Xin-year, Ren-year, and Gui-year.

The current year (2012-1-23~2013-2-9) is Ren-year.

Each year corresponds to an element in Wuxing. Jia-year and Yi-year are wood, Bin-year and Ding-year Fire, Wu-year and Ji-year earth, Geng-year and Xin-year metal, Ren-year and Gui-year water. Therefore the current year is a water-year.

• 12-year cycle

The years are grouped within a 12-year cycle which is called the 12 Earthly braches. The names of they years are: Zi-year, Chou-year, Yin-year, Mao-year, Chen-year, Si-year, Wu-year, Wei-year, Shen-year, You-year, Xu-year, and Hai-year.

The current year is Chen-year.

Each cycle year is corresponds to an animal of the Chinese zodiac. Zi-year to the Rat, Chou-year the Ox, Yin-year the Tiger, Mao-year the Rabbit, Chen-year the Dragon, Si-year the Snake, Wu-year the Horse, Wei-year the Goat, Shen-year the Monkey, You-year the Rooster, Xu-year the Dog and Hai-year the Pig.

Therefore the current year is Dragon-year.

• 60-year cycle

The 10-year cycle system and 12-year cycle system are used together, and become a 60-year cycle which is called the stem-branches.

The current year is Renchen-year, also called as Water Dragon-year.

## Nineteen year cycle

In the early age of Chinese Calendar, the following parameter was used.

1 tropical year is $365\tfrac{1}{4}$ days. 1 synodic month is $29\tfrac{499}{940}$ days.

Therefore, 76 years =365*76+76/4= 27759 days, and 940 months = 29*940+499=27759 days.

In other words, 76 years = 940 months, meaning that 76 years is a cycle, or the sun and moon back to their original positions together after 76 years. The month name after 235 months is the same.

As, 76/4=19, and 940/4=235, 19 years forms a cycle too. The dates of the middle solar terms after 19 years are just the same.

Additionally, 235=12*19+7, It means there are 7 intercalaries each 19 years.

The 19-year-cycle is substituted with a 600 year (221 intercalary) cycle and a 391 year (144 intercalary) cycle.

After the calendar is made with the true position the cycle is not suitable again.

However the Gregorian date may be estimated with a 19-year cycle. The error is a day, or about a month

## Year markings

### Regnal years

Traditional Chinese years were not continuously numbered in the way that the BC/AD system is. More commonly, official year counting always used some form of a regnal year. This system began in 841 BC during the Zhou dynasty. Prior to this, years were not marked at all, and historical events cannot be dated exactly.

In 841 BC, the King Li of Zhou (周厲王) was ousted by a civilian uprising (國人暴動), and the country was governed for the next 14 years by a council of senior ministers, a period known as the Gonghe Regency (共和行政). In this period, years were marked as First (second, third, etc.) Year of the Regency.

Subsequently, years were marked as regnal years, e.g., the year 825 BC was marked as the 3rd Year of the Xuan King Jing of Zhou (周宣王三年). This system was used until early in the Han dynasty, when the Wen Emperor of Han (漢文帝劉恒) instituted regnal names. After this, most emperors used one or more regnal names to mark their reign. Usually, the emperor would institute a new name upon accession to the throne, and then change to new names to mark significant events, or to end a perceived cycle of bad luck. In the Ming and Qing dynasties, however,the emperor usually used only one regnal name for his reign.

This system continued until the Republic of China, which counted years as Years of the Republic, beginning in 1912. Thus, 1912 is the 1st Year of the Republic, 1949 the 38th, and 2011 the 100th. This system is still commonly used in Taiwan. In 1949 the People's Republic of China chose to use the Gregorian Calendar (equivalently, AD/BC system), in line with international standards.

### Stem-branch cycle

The other system by which years are marked historically in China was by the stem-branch or sexagenary cycle. This system is based on two forms of counting: a cycle of 10 Heavenly Stems and a cycle of 12 Earthly Branches. Each year is named by a pair of one stem and one branch called a Stem-Branch (干支 gānzhī). The Heavenly Stems are associated with Yin Yang and the Five Elements. Recent 10-year periods began in 1984, 1994, and 2004. The Earthly Branches are associated with the 12 signs of the zodiac. Each Earthly Branch is also associated with an animal, collectively known as the Twelve Animals. Recent 12-year periods began in 1984, 1996 and 2008.

Within the Heavenly Stems system the year is advanced up by one per year, cycling back to year one after the last (year ten). Similarly the Earthly Branches also advances by one per year, cyclically. Since the numbers 10 (Heavenly Stems) and 12 (Earthly Branches) have a common factor of 2, only 1/2 of the 120 possible stem-branch combinations actually occur. The resulting 60-year (or sexagesimal) cycle takes the name jiǎzǐ (甲子) after the first year in the cycle, being the Heavenly Stem of jiǎ and Earthly Branch of . The term "jiǎzǐ" is used figuratively to mean "a full lifespan"—one who has lived more than a jiǎzǐ is obviously blessed. (Compare the Biblical "three-score years and ten.")

At first, this system was used to mark days, not years. The earliest evidence of this was found on oracle bones dated c. 1350 BC in the Shang Dynasty. This system of date marking continues to this day, and can still be found on Chinese calendars today. Although a stem-branch cannot be used to deduce the actual day in historical events, it can assist in converting Chinese dates to other calendars more accurately.

Around the Han Dynasty, the stem-branch cycle also began to be used to mark years. The 60-year system cycles continuously, and determines the animal or sign under which a person is born (see Chinese Zodiac). These cycles were not named, and were used in conjunction with regnal names declared by the emperor. For example: 康熙壬寅 (Kāngxī rényín) (1662 AD) is the first 壬寅 (rényín) year during the reign of 康熙 (Kāngxī), regnal name of an emperor of the Qing Dynasty

The months, days and hours can also be denoted using Heavenly Stems and Earthly Branches, though they are commonly addressed using Chinese numerals instead. In Chinese astrology, four Stem-Branch pairs form the Eight Characters (八字 bāzì).

### Continuously numbered years

#### Huangdi era

According to the executive order for reforming the calendar and era (改历改元通电) by the Interim president of Republic of China (Sun Yat-sen), the January 1, 1912 is Dongyue 13 in the 4609th year of Huangdi Era.

So, the days after the spring festival of 1912 is the 4610th year of Huangdi Era. And, the current year (2013-02-10 to 2014-01-30) is the 4711th year of Huangdi Era.

The year AD may be caluated by the formular: HE=AD+2698 (after Spring festival).

The year after the first year of Taichu (104BC) may be caluated by the formular: HE=2699-BC (after Zhengyue 1st).

### Correspondence between systems

This table shows the stem/branch year names, correspondences to the Western (Gregorian) calendar, and other related information for the current decade.[8] (These years are all part of the 79th sexagenary cycle, or the 78th if an epoch of 2637 BC is accepted.) Or see this larger table of the full 60-year cycle.

Jiǎzǐ (甲子)
sequence
Stem/
branch
Gānzhī (干支) Year of the...
[Note 1]
Continuous
[Note 2]
Gregorian
[Note 3]
New Year's Day
(chūnjié, 春節)
15 5/3 wùyín (戊寅) Earth Tiger 4696 1998 January 28
16 6/4 jǐmǎo (己卯) Earth Rabbit 4697 1999 February 16
17 7/5 gēngchén (庚辰) Metal Dragon 4698 2000 February 5
18 8/6 xīnsì (辛巳) Metal Snake 4699 2001 January 24
19 9/7 rénwǔ (壬午) Water Horse 4700 2002 February 12
20 10/8 guǐwèi (癸未) Water Goat 4701 2003 February 1
21 1/9 jiǎshēn (甲申) Wood Monkey 4702 2004 January 22
22 2/10 yǐyǒu (乙酉) Wood Rooster 4703 2005 February 9
23 3/11 bǐngxū (丙戌) Fire Dog 4704 2006 January 29
24 4/12 dīnghài (丁亥) Fire Pig 4705 2007 February 18
25 5/1 wùzǐ (戊子) Earth Rat 4706 2008 February 7
26 6/2 jǐchǒu (己丑) Earth Ox 4707 2009 January 26
27 7/3 gēngyín (庚寅) Metal Tiger 4708 2010 February 14
28 8/4 xīnmǎo (辛卯) Metal Rabbit 4709 2011 February 3
29 9/5 rénchén (壬辰) Water Dragon 4710 2012 January 23

Notes

1 The beginning of each zodiac year should correspond to the first day of the lunar year.

2 Calculating according to the number on executive order for reforming the calendar and era.

3 In any case, the correspondence between Chinese year and Gregorian year is of course not exact. The first few weeks of each Gregorian year (the days before Chinese New Year) belong to the previous Chinese year. For example, January 1–28, 2006 correspond to yǐyǒu or 4703. Thus, it might be more precise to state that Gregorian 2006 corresponds to 4703–4704, or that continuous Chinese 4704 corresponds to 2006–2007.

### Solar year versus lunar year

There is a distinction between a solar year and a lunar year in the Chinese calendar because the calendar is lunisolar. A lunar year ( nián) is from one Chinese new year to the next. A solar year ( suì) is either the period between one Spring Equinox and the next or the period between two winter solstices (see Jiéqì section). A lunar year is exclusively used for dates, whereas a solar year, especially that between winter solstices, is used to number the months.

## Hours of the day

Under the traditional system of hour-marking, each day is divided into 12 units (時辰). Each of these units is equivalent to two hours of international time. Each is named after one of the 12 Earthly Branches. The first unit, Hour of Zi (子時), begins at 11 p.m. of the previous day and ends at 1 a.m. Traditionally, executions of condemned prisoners occur at the midpoint of Hour of Wu (正午時), i.e., noon.

A second system subdivided the day into 100 equal parts, ke, each of which equalling 14.4 minutes or about one quarter of a standard Western hour. This was used for centuries, making the Chinese first to apply decimal time – long before the French Republican Calendar. However, because 100 could not be divided equally into the 12 "double hours", the system was changed to variously 96, 108, and 120 ke in a day. During the Qing Dynasty, the number was officially settled at 96, making each ke exactly a quarter of a Western hour. Today, ke is often used to refer to a quarter of an hour.

## Number of days

In the late Spring and Autumn Period (722–481 BC), the former Sifen calendar (古四分历) was established, and set the tropical year at 365.25 days, the same length as the Julian calendar which was introduced in 46 BC.[2] The Taichu calendar (太初历) of 104 BC under Emperor Wu of Han rendered the tropical year at roughly the same ( $365\tfrac{385}{1539}$).[2]

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).[2] 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 (授時曆), would be used in China for the next 363 years.[2][9] 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.[10][11][12]

## 12 animals

The 12 animals (十二生肖 shí'èr shēngxiào, "twelve birth emblems" or colloquially 十二屬相 shí'èr shǔxiàng, "twelve signs of belonging") representing the 12 Earthly Branches are, in order, the Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Goat, Monkey, Rooster, Dog and Pig. The legend of The Great Race explains the order of the animals.

## Solar term

Chinese months follow the phases of the moon. As a result, they do not accurately follow the seasons of the solar year. To assist farmers to decide when to plant or harvest crops, the drafters of the calendar put in 24 seasonal markers, which follow the solar year, and are called jiéqì (節氣).

The term Jiéqì is usually translated as "Solar Terms" (lit. Nodes of Weather). Each node is the instant when the sun reaches one of 24 equally spaced points along the ecliptic, including the solstices and equinoxes, positioned at 15 degree intervals. Because the calculation is solar-based, these jiéqì fall around the same date every year in solar calendars (for example, the Gregorian Calendar), but do not form any obvious pattern in the Chinese calendar. The dates below are approximate and may vary slightly from year to year due to the intercalary rules (i.e. system of leap years) of the Gregorian calendar. Jiéqì are published each year in farmers' almanacs. Chinese New Year is usually the new moon closest to lìchūn.

In the table below, these measures are given in the standard astronomical convention of ecliptic longitude, zero degrees being positioned at the vernal equinox point. Each calendar month under the heading "M" contains the designated jiéqì called a principal term, which is an entry into a sign of the zodiac, also known as a cusp. Here term has the archaic meaning of a limit, not a duration. In Chinese astronomy, seasons are centered on the solstices and equinoxes, whereas in the standard Western definition, they begin at the solstices and equinoxes. Thus the term Beginning of Spring and the related Spring Festival fall in February, when it is still very chilly in temperate latitudes in the Northern Hemisphere.

Ecliptic
long.
Chinese name Gregorian
date (approx.)
Usual
translation
Remarks
315° 立春 lìchūn February 4 start of spring spring starts here according to the Chinese definition of a season
330° 雨水 yǔshuǐ February 19 rain water starting at this point, the temperature makes rain more likely than snow
345° 驚蟄 jīngzhé
(啓蟄 qǐzhé)
March 5 awakening of insects when hibernating insects awaken

15° 清明 qīngmíng April 5 clear and bright a Chinese festival where, traditionally, ancestral graves are tended
30° 穀雨 gǔyǔ or gǔyù April 20 grain rains rain helps grain grow
45° 立夏 lìxià May 6 start of summer refers to the Chinese seasonal definition
60° 小滿 xiǎomǎn May 21 grain full grains are plump
75° 芒種 mángzhòng or mángzhǒng June 6 grain in ear lit. awns (beard of grain) grow
90° 夏至 xiàzhì June 21 summer solstice lit. summer extreme (of sun's height)
105° 小暑 xiǎoshǔ July 7 minor heat when heat starts to get unbearable
120° 大暑 dàshǔ July 23 major heat the hottest time of the year
135° 立秋 lìqiū August 7 start of autumn uses the Chinese seasonal definition
150° 處暑 chùshǔ August 23 limit of heat lit. dwell in heat
165° 白露 báilù September 8 white dew condensed moisture makes dew white; a sign of autumn
180° 秋分 qiūfēn September 23 autumnal equinox lit. central divide of autumn (refers to the Chinese seasonal definition)
195° 寒露 hánlù October 8 cold dew dew starts turning into frost
210° 霜降 shuāngjiàng October 23 descent of frost appearance of frost and descent of temperature
225° 立冬 lìdōng November 7 start of winter refers to the Chinese seasonal definition
240° 小雪 xiǎoxuě November 22 minor snow snow starts falling
255° 大雪 dàxuě December 7 major snow season of snowstorms in full swing
270° 冬至 dōngzhì December 22 winter solstice lit. winter extreme (of sun's height)
285° 小寒 xiǎohán January 6 minor cold cold starts to become unbearable
300° 大寒 dàhán January 20 major cold coldest time of year

Note: The third jiéqì was originally called 啓蟄 (qǐzhé) but renamed to 驚蟄 (jīngzhé) in the era of the Emperor Jing of Han (漢景帝) to avoid writing his given name (also written as , a variant of 啓).

## Holidays

The Chinese calendar year has nine main festivals, seven determined by the lunisolar calendar, and two derived from the solar agricultural calendar. (Farmers actually used a solar calendar, and its 24 terms, to determine when to plant crops, due to the inaccuracy of the lunisolar traditional calendar. However, the traditional calendar has also come to be known as the agricultural calendar.) The two special holidays are the Qingming Festival (about 15 days after the spring equinox) and the Winter Solstice Festival, falling upon the respective solar terms, at ecliptic longitudes of 15° and 270°, respectively. As for all other calendrical calculations, the calculations use civil time in China, UTC+08:00

Date English Chinese Vietnamese Remarks 2008 2009 2010 2011 2012 2013
Zhengyue 1st Chinese New Year (Spring Festival) 春節 chūnjié Nguyên Đán (元旦) Family gathering and festivities for 3–15 days 0207 0126 0214 0203 0123 0210
Zhengyue 15th Lantern Festival
(Chap Goh Mei)

0221 0209 0228 0217 0206 0224
April 4/5 Qingming Festival 清明節 qīngmíng Thanh Minh (清明) Tomb sweeping 0404 0404 0405 0405 0404 0404
Wuyue 5th Dragon Boat Festival 端午 duānwǔ Đoan Ngọ (端午) Dragon boat racing and zongzi eating 0608 0528 0616 0606 0623 0612
Qiyue 7th Night of Sevens 七夕 qīxī Thất tịch For lovers, like Valentine's Day 0807 0826 0816 0806 0823 0813
Qiyue 15th Ghost Festival
(Spirit Festival)

Le Vu Lan (禮盂蘭)
Offer tributes and respect to the deceased 0815 0903 0824 0814 0831 0821
Bayue 15th Mid-Autumn Festival 中秋 zhōngqiū Trung Thu (中秋) Family gathering and moon cake eating 0914 1003 0922 0912 0930 0919
Jiuyue 9th Double Ninth Festival 重陽 chóngyáng Trùng Cửu (重九) Mountain climbing and flower shows 1007 1026 1016 1005 1023 1013
Shiyue 15th Peaceful Festival or Xia Yuan 下元節 xiàyuán Hạ Nguyên (下元) Pray for a peaceful year to the Water God 1112 1201 1120 1110 1128 1117
December 21/22 Winter Solstice Festival 冬至 dōngzhì Lễ hội Đông Chí Family gathering, eat Tong yuen 1221 1221 1222 1222 1221 1221
Layue 23th/24th Kitchen God Festival 小年 xiǎonián Táo Quân (竈君) Worshipping the kitchen god with thanks 0131 0119 0207 0127 0117 0204

## Purpose of the intercalary months

Most people, upon using or studying the Chinese calendar, are perplexed by the intercalary month because of its seemingly unpredictable nature. As mentioned above, the intercalary month refers to additional months added to the calendar in some years to correct for its deviation from the astronomical year, a function similar to that of the extra day in February in leap years.

However, because of the complex astronomical knowledge required to calculate if and when an intercalary month needs to be inserted, to most people, it is simply a mystery. This has led to a superstition that intercalary months in certain times of the year bring bad luck.

The main purpose of the intercalary month is to correct for deviations of the calendrical year from the astronomical year. Because the Chinese calendar is mainly a lunar calendar, its standard year is 354 days, whereas the astronomical year is approximately 365¼ days. Without the intercalary month, this deviation would build up over time, and the Spring festival, for example, would no longer fall in Spring. Thus, the intercalary month serves a valuable purpose in ensuring that the year in the Chinese calendar remains approximately in line with the astronomical year.

The intercalary month is inserted whenever the Chinese calendar moves too far from the stage of progression of the earth in its orbit. Thus, for example, if the beginning of a certain month in the Chinese calendar deviates by a certain number of days from its equivalent in a solar calendar, an intercalary month needs to be inserted.

The practical benefit of this system is that the calendar is able to approximately keep in pace with the solar cycle, while at the same time retaining months that roughly correspond with lunar cycles. Hence the term lunisolar calendar. The latter is important because many traditional festivals correspond to significant events in the moon's cycle. For example, the mid-autumn festival is always on a day of the full moon.

## Relevance of the calendar today

There have been calls for reform in recent years from experts in China, because of the increasing irrelevance of the Chinese calendar in modern life. They point to the example in Japan, where during the Meiji Restoration the nation adopted the Gregorian calendar, and simply shifted all traditional festivities onto an equivalent date. However, the Chinese calendar remains important as an element of cultural tradition, and for certain cultural activities.

### Practical uses

The original practical relevance of the lunisolar calendar for date marking has largely disappeared. First, the Gregorian calendar is much easier to compute and more in line with international standards. Its adoption for official purposes has meant that the traditional calendar is rarely used for date marking. This, in turn, means that it is more convenient to remember significant events such as birth dates by the Gregorian rather than the Chinese calendar.

Second, the 24 solar terms were important to farmers who would not be able to plan agricultural activities without foreknowledge of these terms. However, the 24 solar terms (including the solstices and equinoxes) are more predictable on the Gregorian calendar than the lunisolar calendar since they are based on the solar cycle. It is easier for the average Chinese farmer to organize their planting and harvesting with the Gregorian calendar.

However, one practical advantage of using a calendar where the months are lunar months is that the phases of the moon, and astronomical and tidal phenomena associated with them, 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.

### Cultural issues

The Chinese 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 traditional Chinese calendar, as an element of traditional culture, has much cultural and nationalistic sentiment invested in it.

The 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 Huang Li (traditional Chinese: ; simplified Chinese: ; pinyin: huánglì), literally "Imperial Calendar", 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.

## Influence

Other traditional East Asian calendars are very similar to if not identical to the Chinese calendar: the Korean calendar is identical; the Thai lunar calendar substitutes a big snake for the Dragon and a little snake for the Snake; the Vietnamese calendar substitutes the cat for the Rabbit in the Chinese zodiac; the Tibetan calendar differs slightly in animal names, and the traditional Japanese calendar uses a different method of calculation, resulting in disagreements between the calendars in some years. The 12 year cycle, with the animal names translated into the vernacular, was adopted by the Göktürks (its use there is first attested 584), and spread subsequently among many if not most Turkic peoples, as well as the Mongols. A similar calendar seems to have been used by the Bulgars, as attested in the Nominalia of the Bulgarian Khans and in some other documents. The main differences between the Bulgar and the Chinese calendar are the different calculating system, the Tiger has been replaced with a wolf, and the Dragon and Monkey with an unknown animal. Also, the Bulgar calendar is a solar one.[13]

### 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.[14] 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.

## References

1. ^ Calendars, Time, & Numerology - Egyptian Roots & Mathematical Precision of Our Modern Calendar
2. 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.
3. ^ Cullen, Atronomy and Methematics in Ancient China. Cambridge, 1996.
4. ^ 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.
5. ^ Ebrey, Patricia Buckley (1999). The Cambridge Illustrated History of China. Cambridge: Cambridge University Press. ISBN 0-521-66991-X (paperback). Pages 124–125.
6. ^ F. Richard Stephenson and Liu Baolin, "A brief contemporary history of the Chinese calendar" (unpublished paper, 1990)
7. ^ Helmer Aslaksen, The mathematics of the Chinese calendar pages 18 & 28.
8. ^ The following link provides conversion of Chinese calendar dates to Western calendar dates: [1]
9. ^ 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.
10. ^ 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.
11. ^ 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.
12. ^ Restivo, Sal. (1992). Mathematics in Society and History: Sociological Inquiries. Dordrecht: Kluwer Academic Publishers. ISBN 1-4020-0039-1. p. 32.
13. ^ Перипетиите на календара, проф. Никола Николов
14. ^ 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.