Chinese calendar

The Chinese calendar is a lunisolar calendar formed by combining a purely lunar calendar with a solar calendar.

The following rules for the Chinese Calendar (I believe) are equivalent to the rules as given by Helmer Alaksen. http://www.math.nus.edu.sg/aslaksen/calendar/chinese.shtml

These rules make use of the Tropical Zodiac familiar to Westerners. This must not be confused with the actual constellations corresponding to the 12 signs.

(1) The months are lunar months, such that the first day (beginning midnight) of each month is the day of the astronomical new moon.

(2) Each year has 12 regular months, which are numbered in sequence (1 to 12). A year may also have an intercalary month, which may come after any regular month. It has the same number as the preceding regular month, but is designated intercalary.

(3) The Chinese solar year (sui) is divided into 12 parts that are equivalent to the sun signs of the tropical zodiac.

(4) Intercalary months are arranged so that, the sun always enters Capricorn on the 11th regular month (month 11) of a year.

(5) If there are 12 months between two successive occurrences of month 11, one of these 12 months must be an intercalary month and it is the first of these 12 months during which the sun remains within the same zodiac sign throughout.

(6) The times of the astronomical new moons and the sun entering a zodiac sign are determined by the Purple Mountain Observatory in Chinese Time.

Usually, the number of a regular month is determined by which sign the sun is in at the start of the month:

Month  Zodiac Sign at Start
11     Sagittarius (by rule 4)
12     Capricorn
 1     Aquarius
 2     Pisces
 3     Aries
 4     Taurus
 5     Gemini
 6     Cancer
 7     Leo
 8     Virgo
 9     Libra
10     Scorpio

Some astronomers believed this correspondence to be always true, but there are exceptions. An exception occurred in 1985, after the sun had entered Capricorn and then Aquarius in month 11, causing the Chinese new year to occur on 20 February 1985 in Pisces rather than Aquarius.

The problem here is that there is a month in which the sun enters two signs of the zodiac. I'll refer to such a month as a dual-entry month. If a given month is a dual-entry month or has a dual-entry month before it and no earlier than the preceeding month 11, the above correspondence may fail, otherwise it holds.

The years are named by a 12-year cycle of animals and a 5-year cycle of elements combining to form a 60-year cycle, known as a jiazi (from "wood rat," the name of the first year of the standard cycle). Some figures of speech use "jiazi" to mean "a full lifespan;" one who has lived more than a jiazi is obviously blessed. (Cf. the Biblical "three-score years and ten.")

The months of the years may also be given names from the animal cycle.

This sequence is traditionally assigned according to a legend:

One day, the twelve animals fought over the precedence of the animals in the cycle of years in the calendar. The Chinese gods held a contest to see which should be first: they all lined up on the bank of a river, and were given the simple task of getting to the opposite shore. Depending on arrival, the first to get there would get the first year, and the order would depend upon how fast they finished.

three versions

So all the animals lined up on the river bank and they all jumped in. The rat snuck up and climbed on the ox's back. Just as the ox came ashore, the rat jumped off and finished the race first. The lazy pig came to the far shore last. And so the rat got the first year named after him, the ox got the second year, and the pig ended up as the last.
According to Chinese legend, the twelve animals quarreled one day as to who was to head the cycle of years. The gods were asked to decide and they held a contest: whoever was to reach the opposite bank of the river would be first, and the rest of the animals would receive their years according to their finish.
All the twelve animals gathered at the river bank and jumped in. Unknown to the ox, the rat had jumped upon his back. As the ox was about to jump ashore, the rat jumped off the ox's back, and won the race. The pig, who was very lazy, ended up last. That is why the rat is the first year of the animal cycle, the ox second, and the pig last animal in the year cycle.

See Chinese zodiac for more details.