Months are moons, so twelve of them fall short
A lunation is a little over 29.5 days, so twelve of them come to roughly 354 days. A tropical year is about 365.2422 days. Left alone, a purely lunar calendar walks backwards through the seasons by eleven days a year, which is what the Islamic calendar does and what the Chinese calendar refuses to do.
Each Chinese month begins on the day of a new moon, evaluated in Beijing time. Whole days matter here, not instants: a new moon just before midnight and one just after start months a day apart, and in borderline years that single day moves the animal for everyone born in the gap.
The December solstice anchors the year
The anchor is not the new year at all. It is month 11, defined as the month containing the December solstice — in practice, the month whose first day is the last new-moon day on or before the solstice day. Month 1, and with it the new year, is normally the second new moon after that solstice.
That rule is what produces the familiar 21 January to 20 February window. Within this site's range the earliest new year is January 21, 1966 and the latest February 20, 1985, a spread of about a month, and the date moves by roughly eleven days earlier each year until a leap month throws it forward again.
Leap months, and the major solar terms that find them
The sun's ecliptic longitude is divided into twenty-four solar terms; the twelve at multiples of 30 degrees are the major terms, the zhongqi. Each ordinary month should contain exactly one of them. When thirteen new moons fall between one month 11 and the next, one month contains none, and that month is the leap month.
A leap month has no number of its own. It repeats the number of the month before it, so a year can hold two fourth months. Leap years run 383 to 385 days against 353 to 355 for ordinary ones — in this range the shortest lunar year is 353 days and the longest 385. If the leap month falls before month 1, the new year is pushed to the third new moon after the solstice instead of the second, which is the whole reason the boundary cannot be tabulated by eye.
Stems, branches, and why the cycle is sixty
Each year carries two labels. The branch is one of twelve animals; the stem is one of ten, pairing the five elements with a yang and a yin form. The two counters advance together, and because ten and twelve share a factor of two, only half the possible combinations occur: sixty, not a hundred and twenty.
So an element and an animal meet once every sixty years rather than every twelve. A Wood Dragon year returns after a lifetime, and the sixtieth birthday — the return to one's own pillar — is marked precisely because it takes that long. The element is not decoration on top of the animal; it is the half of the label that makes the cycle long.
Why so many tables are wrong
Most zodiac lookups split the animals at midnight on 1 January. That is right for about eleven months of any year and wrong for the five to seven weeks at its head, which is on the order of one birthday in eight. The error is not subtle: it does not shift a reading slightly, it names a different animal.
Recent years with a leap month include 2001, 2004, 2006, 2009, 2012, and each of them runs more than 380 days. Any table that assumes a fixed length, or a fixed start, disagrees with the calendar it claims to be reporting. The year pages on this site compute both ends from the ephemeris instead.
Questions people ask about this
Why does the Chinese new year move?
Because it is tied to a new moon, and twelve lunar months fall about eleven days short of a solar year. A leap month resets the drift every two or three years.
What is a leap month?
An extra month inserted when thirteen new moons fall between one month 11 and the next. It is the first month containing no major solar term, and it repeats the previous month's number.
How long is a Chinese year?
353 to 355 days without a leap month, 383 to 385 with one. The animal covers the whole span, however long it runs.
Why sixty years rather than twelve?
Ten stems and twelve branches advance in step and realign only after sixty steps, so an element and an animal pair up once in sixty years.