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Chinese calendar
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The Chinese calendar is a lunisolar calendar, incorporating elements of a lunar calendar with those of a solar calendar. This measure of time is not exclusive to China, but followed by many other Asian cultures. However, it is often referred to by the Western cultures as the Chinese calendar. In most of Asia today, the Gregorian calendar is used for day to day activities, but the Chinese calendar is still used for marking traditional East Asian holidays such as the Lunar New Year (Spring Festival), and in China 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.

In China, the traditional calendar is known as the "agricultural calendar" (traditional Chinese: 農曆; simplified Chinese: 农历; pinyin: nónglì) while the Gregorian calendar is known as the "common calendar" (traditional Chinese: 公曆; simplified Chinese: 公历; pinyin: gōnglì) or "Common calendar" . Another name for the Chinese calendar is the "Yin Calendar" (traditional Chinese: 陰曆; simplified Chinese: 阴历; pinyin: yīnlì) in reference to the lunar aspect of the calendar, whereas the Gregorian calendar is the "Yang Calendar" (traditional Chinese: 陽曆; simplified Chinese: 阳历; pinyin: yánglì) in reference to its solar properties. The Chinese calendar was also called the "old calendar" (traditional Chinese: 舊曆; simplified Chinese: 旧历; pinyin: jìulì) after the "new calendar" (traditional Chinese: 新曆; simplified Chinese: 新历; pinyin: xīnlì), i.e. the Gregorian calendar, was adopted as the official calendar. The traditional calendar is also often referred to as "the Xia Calendar", following a comment in the Shiji which states that under the Xia Dynasty, the year began on the second moon after the winter solstice (just as in the modern calendar).

The current year in the Chinese calendar is the Year of the Earth Rat (year of Wù Zǐ, 戊子). It lasts from 7 February 2008 to 25 January 2009. Based on traditional beliefs, some form of the calendar has been in use for almost five millennia. Based on archaeological evidence some form of it has been in use for three and a half millennia.
A lunar calendar is a calendar that is based on cycles of the moon phase. The only widely used purely lunar calendar is the Islamic calendar, whose year always consists of 12 lunar months. A feature of a purely lunar year, on the Islamic calendar model, is that the calendar ceases to be linked to the seasons, and drifts each year by 11 or 12 days, and comes back to the position it had in relation to the solar year every 33 or 34 Islamic years. It is used predominantly for religious purposes. In Saudi Arabia it is also used for commercial purposes.

Most lunar calendars are in fact lunisolar calendars. That is, months are kept on a lunar cycle, but then intercalary months are added to bring the lunar cycles into synchronisation with the solar year.
S
ince there are about twelve lunations (synodic months) in a solar year, this period (354.37 days) is sometimes referred to as a lunar year.

Start of the lunar month
Lunar calendars differ as to which day is the first day of the month.
For some lunar calendars, such as the Chinese calendar, the first day of a month is the day when a new moon appears in a particular time zone.
Many other lunar calendars are based on the first sighting of a lunar crescent.

Length of the lunar month
The length of a month orbit/cycle is difficult to predict and varies from its average value. Because observations are subject to uncertainty and weather conditions, and astronomical methods are highly complex, there have been attempts to create fixed arithmetical rules.
The average length of the synodic month is 29.530589 days. This means the length of a month is alternately 29 and 30 days (termed respectively hollow and full). The distribution of hollow and full months can be determined using continued fractions, and examining successive approximations for the length of the month in terms of fractions of a day.
 

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