Chinese Zodiac Calculator

There is no table behind this calculator and no almanac lookup. The branch is a remainder: subtract 4 from the year and take the remainder on division by 12, because 4 CE was a Rat year and the cycle has run unbroken since. For 1990 that leaves 6, and counting the Rat as position zero, position 6 is the Horse.

The element is the same operation on a different modulus. Ten heavenly stems pair with the 12 branches, so (year − 4) mod 10 picks the stem; each of the five phases covers two consecutive stems, one yang and one yin. For 1990 the stem index is 6, which makes it Metal and yang — a Metal yang Horse. Two divisions, and the whole naming falls out. This is the part of Chinese astrology that is genuinely arithmetic, and it is worth separating from the parts that are not.

The one thing the arithmetic cannot do is tell you where your year starts. A Chinese year runs from one lunar new year to the next, and that opening moves with the Moon: it falls somewhere between 21 January and 20 February, never outside. This page will not print a date for any particular year, because a moving instant published as a fixed date is wrong for most of the years a reader will try. What follows from the window is practical and exact: a birthday after 20 February is unambiguous, since that is the latest the opening can fall, and a birthday before 21 January belongs to the previous animal for certain. In between, the actual date for that year decides. This site's own data shows the cost of getting it wrong: of the well-known names listed on the twelve animal pages, five carry a corrected Chinese year rather than their Gregorian one, and every one of those corrections moves the year back by exactly one, which is what a birthday earlier in the calendar year than that year's opening does.

Everything a reader needs to check the result card is in this one table. The polarity column is worth pausing on: it does not vary. A branch does not alternate between yang and yin from one of its years to the next, and the reason is parity — every even-numbered branch here is yang and every odd-numbered one is yin, so Ox years are yin in 1901 and in all the others. That was checked rather than copied: every year of the 1900–2100 span was assigned to its branch and the polarities collected, and each of the 12 branches returned exactly one.

The fixed-element column is not an even split, which is the first surprise in the table: Earth carries 4 of the 12 branches while the remaining four phases take two each. Five phases do not divide twelve, so an uneven distribution is forced; which phase gets the extra branches is not, and it is assigned by tradition rather than derived. That is why FIXED_ELEMENT is one of the few tables in the Chinese data on this site that is tabulated instead of computed.

The trine column carries an element name that looks arbitrary until you see the rule. Rat, Dragon and Monkey are Water, Earth and Metal animals respectively, yet the group is named Water. The element belongs to the group's cardinal branch — the four at every third position, Rat, Rabbit, Horse and Rooster — and exactly one of those falls in each trine, which is a consequence of the trines being spaced four apart and is proved in this file rather than assumed. So the four trine elements are Water, Metal, Fire and Wood, all distinct, and Earth names no trine at all — and it is the same phase that holds the most branches, so the busiest element in the column to its left is the one absent from this one. Only four animals — Rat, Rabbit, Horse and Rooster — have a fixed element equal to their own trine's, and they are the cardinal branches themselves.

Those two columns are worth reading together. Trine alone sorts the 12 branches into 4 groups and fixed element alone into 5, so each on its own collapses several animals together; taken as a pair they produce 12 distinct combinations, which is one per branch, so the two classifications together separate all of them. That is the practical reason both columns are in the table: neither is redundant.

The branches are not only a cycle of years. They also cut the day into 12 double hours of two hours each, which is where the hour column in the table above comes from, and it is the part of the system a birth time is needed for. The 12 spans were checked end-to-start around the whole ring: each one begins where the last ends and the last closes back onto the first, covering 24 hours with no gap and no overlap.

The interesting consequence is where the ring starts. Exactly one of the 12 spans ends at a smaller number than it begins — the Rat hour, 23:00–01:00 — so it is the one that crosses midnight. That is not a rounding artefact: the first branch takes the two hours straddling the turn of the clock, which is why the Chinese day is usually said to change at the start of that span rather than at midnight, and why a birth in the small hours can belong to the previous day's branch.

This is the closest Chinese parallel to the Vedic hora, which likewise hands each stretch of the day to a ruler. The two do not line up, and it is worth being precise about why. The hora cuts the day into 24 parts rather than 12 and rotates seven planetary rulers through them, so the divisions are half as long and there are twice as many of them; and the hora day opens at sunrise, which moves through the year, rather than at a fixed hour of the clock. A reader who knows one system cannot read the other off it. The hora calculator works the Vedic side out for a given day and place.

12 animals make 66 unordered pairs. The classical relations name 34 of them and leave 32 unnamed — nearly half the grid has no traditional relation at all, which is the single most useful fact on this page and the one every filled-in compatibility chart hides. A chart with a verdict in all 66 cells has supplied 32 of them from somewhere other than the tradition it cites.

The relations themselves are positional, which is why they can be counted rather than looked up. San he, the trine, joins the branches four places apart, giving 12 pairs across four groups of three. Liu he, the six unions, pairs the branches whose positions sum to one step past the start of the cycle, giving 6 fixed partnerships. Liu chong, the clash, is the branch directly opposite, 6 pairs across the diameter of the ring. And 12 pairs sit three places apart, the relation popular lists disagree about most, which is why this site names it as secondary rather than giving it the weight of the other three.

Two cells in that grid carry two labels at once, and they are the reason a list of “best matches” can never be the whole answer. Pig with Tiger and Monkey with Snake are each a fixed liu he partnership and also three branches apart, so the tradition gives them a union and a friction in the same breath. Popular charts resolve that by picking whichever label suits the tone of the page. This one prints both and leaves the reading to be argued.

That collision also shows up as an uneven count of partners. 8 of the 12 animals have 6 named partners; the other 4 — Tiger, Snake, Monkey and Pig — have 5, because for them two of the relations land on the same animal instead of on two different ones. Across the whole grid the 34 named pairs carry 36 labels between them, and 2 are the surplus the double-labelled cells account for.

One thing this grid is not is a forecast, and the distinction matters more here than anywhere else on the page. A trine or a clash is a statement about two positions on a ring of 12, and everything read into it beyond that — that the trine gets on well, that the clash argues — is a traditional gloss laid over the geometry rather than something the geometry contains. Where this site does carry such a gloss, as it does for each of the four trines on the animal pages, it is offered as the traditional character ascribed to that group and not as a claim about the people born in it. The grid above is the part that can be checked.

The result card shows an element, and it is the element of the year's heavenly stem. The branch table above also shows an element for each animal, and it is a different one: the animal's own, assigned permanently by tradition. Both are called “your element” in ordinary writing about the Chinese zodiac, which is why a reader can come away with two answers and no way to reconcile them.

Counting settles what their relationship is. Across a full sexagenary run there are 60 animal-and-stem combinations, five per animal rather than ten, because ten and 12 share a factor and a branch therefore only ever meets stems of its own polarity. Those five cover the five phases once each, so the year's stem element equals the animal's fixed element in 12 of the 60 combinations — exactly one year in five for any given animal. Those 12 are the combinations where the two answers agree; in the other 48 they differ, and both are correct about different things.

The five phases are also not a list of substances. They are defined by what they do to one another, in two cycles: sheng, generating, steps one place on — Wood feeds Fire, Fire feeds Earth, Earth feeds Metal, Metal feeds Water, Water feeds Wood — and the chain closes where it began. Ke, controlling, steps two places on instead, which is why Wood controls Earth rather than Fire. The order the phases are listed in on this site is that generating cycle rather than an alphabetical one, which is what lets both relations be computed from a position instead of tabulated; the chain was walked at build time to confirm it visits all five, closes, and is written in that order.