Chinese Calendar Algorithm - Year 1901 to 2100 - v4.14, by Dr. Herong Yang
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:
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:
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