Chinese calendar

The rules of the Chinese calendar

1. The moment of every new moon and every solar term is calculated in Chinese standard time, UTC+8 (120° east).
2. A Chinese day runs from midnight to midnight in that time.
3. The day of the new moon is the first day of a month.
4. The month containing the winter solstice (Dongzhi) is always month 11.
5. If there are thirteen months from one month 11 to the next, the first month without a major solar term (zhongqi) is the leap month.
6. Month 1 is the second month after month 11 (leap months not counted); the first day of month 1 is Chinese New Year.

These are the core rules of the Chinese standard GB/T 33661-2017, as Yuk Tung Liu summarises and translates them. We have not been able to read the text of the standard itself.

The leap month

Twelve lunar months are shorter than a solar year. About every third year a Chinese year therefore gets a thirteenth month. The major-term rule decides which: the first month without a zhongqi takes the number of the month before it, marked as leap.

The rule is old: the Hanshu already says that a new moon without a major term is a leap month. Since the reform of 1645 the calendar uses true rather than mean solar terms; as a result a month can have two major terms, and a month without a major term can still not be a leap month.

The year 2033

In 2033 the simple rule "the first month without a major term is the leap month" gives the wrong answer. In the eight months around the end of 2033 there are three months without a major term and two months with two major terms. By the correct rule only the month that begins on 22 December 2033 is a leap month, and it is a second month 11.

That is not only on this page: the Hong Kong Observatory's table for 2033 has month 11 twice (on 22 November and 22 December), and Yuk Tung Liu works it out in his example. Our calculation gives the same and is tested separately for 2033.

Checked against the Hong Kong Observatory

We compared every day from 1901 to 2100 (73,048 days) with the conversion tables of the Hong Kong Observatory: the start of the months, the leap months and the dates of the solar terms.

From 1929 everything matches, except for three cases where a new moon or solar term falls within a minute of midnight in Beijing: the Dahan of 20 January 1979 (7 seconds before midnight) and the new moons of September 2057 and August 2097. Before 1929 the Hong Kong Observatory used Beijing local time; in eight years (1912, 1913, 1914, 1916, 1917, 1920, 1927 and 1928) a single day then differs from our calculation in UTC+8.

What we do not know

• We have not been able to read the text of the standard GB/T 33661-2017; the rules above come from Yuk Tung Liu's summary.
• For the years before 1929 this page does not follow Beijing local time; sources may differ by a day there.
• New moons and solar terms are calculated with Astronomy Engine. The standard demands an accuracy of one second; Yuk Tung Liu finds that requirement puzzling, because the distant future cannot be calculated so precisely.
• The statement about 2033 rests on the Hong Kong Observatory's table and on Yuk Tung Liu's example; we could not read Aslaksen's study (2010).
• We have not checked whether common almanacs always agree with the standard.

Sources

• Hong Kong Observatory, Gregorian-Lunar Calendar Conversion Tables 1901 to 2100 and The 24 Solar Terms (hko.gov.hk).
• Yuk Tung Liu, 農曆編算法則 (Rules for computing the Chinese calendar) and the worked examples (ytliu0.github.io/ChineseCalendar).
• GB/T 33661-2017, 农历的编算和颁行 (Calculation and promulgation of the Chinese calendar): only the register record of the standard (openstd.samr.gov.cn).
• Hanshu, juan 21 (律曆志), on the leap month: 「朔不得中，是謂閏月」 (zh.wikisource).
• Astronomy Engine (MIT licence) for the positions of Sun and Moon.