The Chinese Calendar

Chinese Calendar Algorithm - Year 1901 to 2100

∟Chinese Calendar Background Information

∟The Chinese Calendar

This section describes The Chinese Calendar, which is a lunisolar calendar based on the tropical year and the synodic month.

The Chinese calendar is a lunisolar calendar, which is based on the tropical year and the synodic month.

The primary cycle in the Chinese calendar is the Chinese month, which is closely synchronized to the synodic month. Since the synodic month has an average of about 29.5305888531 days, the number of days in a Chinese month varies between 29 days and 30 days from month to month.

The first day of a Chinese month must be the new moon day, when the moon is completely dark, that is the moon is in conjunction with the sun.

The secondary cycle in the Chinese calendar is the solar term system, which is closely synchronized to the tropical year. The solar term system has 12 principal terms to indicate the sun's longitudes at every 30 degrees, with the first principle term defined as the day when the sun's longitude at 330 degrees.

In addition to the 12 principal terms, 12 sectional terms are added to break the sun's longitude into 24 15-degree segments. The following table lists the 24 solar terms and their approximate dates in Gregorian calendar.

Term   Long.   Greg.    Dur.   Ch. Name      En. Name

S. 1   315     Feb. 4          Lichun        Beginning of Spring
P. 1   330     Feb.19   29.8   Yushui        Rain Water
S. 2   345     Mar. 6          Jingzhi       Waking of Insects
P. 2     0     Mar.21   30.2   Chunfen       Spring Equinox
S. 3    15     Apr. 5          Qingming      Pure Brightness
P. 3    30     Apr.20   30.7   Guyu          Grain Rain
S. 4    45     May  6          Lixia         Beginning of Summer
P. 4    60     May 21   31.2   Xiaoman       Grain Full
S. 5    75     Jun. 6          Mangzhong     Grain in Ear
P. 5    90     Jun.22   31.4   Xiazhi        Summer Solstice
S. 6   105     Jul. 7          Xiaoshu       Slight Heat
P. 6   120     Jul.23   31.4   Dashu         Great Heat
S. 7   135     Aug. 8          Liqiu         Beginning of Autumn
P. 7   150     Aug.23   31.1   Chushu        Limit of Heat
S. 8   165     Sep. 8          Bailu         White Dew
P. 8   180     Sep.23   30.7   Qiufen        Autumnal Equinox
S. 9   195     Oct. 8          Hanlu         Cold Dew
P. 9   210     Oct.24   30.1   Shuangjiang   Descent of Frost
S.10   225     Nov. 8          Lidong        Beginning of Winter
P.10   240     Nov.22   29.7   Xiaoxue       Slight Snow
S.11   255     Dec. 7          Daxue         Great Snow
P.11   270     Dec.22   29.5   Dongzhi       Winter Solstice
S.12   285     Jan. 6          Xiaohan       Slight Cold
P.12   300     Jan.20   29.5   Dahan         Great Cold

The third cycle in the Chinese calendar is the Chinese year, which is closely synchronized to the tropical year. A common Chinese year has 12 Chinese months, with 353, 354, or 355 days. which is about 11 days less than a tropical year. In order to bring the Chinese year cycle in line with the tropical year cycle, a leap year is defined after about every 3 common years. A leap year has 13 months, with the extra month called leap month.

To determine which year is a leap year and after which month to add the leap month, the Chinese calendar uses the following leap year rules:

1. The 11th principle term, winter solstice, must falls in month 11. A leap year is a year that an extra month must be added to push month 11 to contain the 11th principle term.
2. In a leap year, the first month after month 11 that contains no principle term is the leap month. A leap month shares the same number and name of the preceding month.

Chinese years are counted in 60-year cycles. Each year is named with a combination of one of the 10 heavenly stems (tiangan) and one of the 12 earthly branches (dizhi) sequentially, and repeatedly. 10 heavenly stems are mapped to 5 elements as Wood, Wood, Fire, Fire, Earth, Earth, Metal, Metal, Water, and Water. 12 earthly branches are also mapped to 12 animals as Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Goat, Monkey, Chicken, Dog, and Pig.

It is believed that the Chinese calendar has completed 78 cycles so far. This year, 1999 in Gregorian calendar, is the 16th year in the 79th cycle, or year 4696. Note that January 1, 1999 was still in year 4695, because the Chinese year is about one month behind.

The Chinese calendar rules can be summarized as:

1. New moon rule - The first day of the month is when the moon is completely dark. This defines the Chinese month cycle.
2. Solar term rule - 24 solar terms divide the tropical year into 15-degree longitude segments. This links the Chinese calendar to the tropical year cycle.
3. Winter solstice rule - The winter solstice must falls in month 11. This defines leap years.
4. Leap month rule - The first month after month 11 that contains no principle term is a leap month in a leap year.
5. Sexagesimal cycle rule - Chinese years are counted in 60-year cycles.
6. Calculation of rule 1 and 2 must be carried out for the meridian 120 degrees east of Greenwich, roughly corresponds to the east coast of China.