How to calculate your Chinese zodiac sign, element and kua by hand

The Chinese zodiac is the year line of the Chinese calendar, read out loud. Every year has a two-character name, a heavenly stem over an earthly branch, and the branch has carried an animal since at least the second century BC. The step the placemats get wrong comes before any of that: the year does not begin on January 1 but at Chinese New Year, the second new moon after the winter solstice, anywhere from January 21 to February 20. A January birthday almost always belongs to the year before. In 1990 the New Year fell on January 27, so someone born on January 20, 1990 counts as 1989.

There is a second boundary, and the astrologers use it. A bazi chart and a kua number turn the year at Lichun, the start of spring on the solar calendar, around February 4. For a birthday between the two dates the animal differs by rule, which is why calculators sometimes give two answers; the calculator's own section on January and February draws this year's gap, and the year-boundaries dataset has both dates for every year from 1900 to 2100.

Subtract 4 from your Chinese year and divide by 12; the remainder is your place on the wheel, counting from the Rat at 0. The 4 is there because 4 AD was a Rat year, and so was every twelfth year after it, 1984 among them. For 1990: 1990 minus 4 is 1986, and 1986 divided by 12 leaves 6, which is the Horse.

The stem over the branch is one of ten, and there are ten digits, so the last digit of the year fixes the stem and with it the element: 0 or 1 is Metal, 2 or 3 is Water, 4 or 5 is Wood, 6 or 7 is Fire, 8 or 9 is Earth. Even years are yang and odd years yin. 1990 ends in 0, so it was a yang Metal year, and a Metal Horse.

That is why every animal comes in five vintages, one every twelve years: the Wood Horse, the Fire Horse, the Earth Horse, the Metal Horse, the Water Horse. The tradition reads them as five wines from one grape. The Fire Horse is the legend, the sign's own element doubled, and in 1966 the belief that a Fire Horse daughter would burn through a husband cut Japan's birth rate by a quarter for a year, a crater still visible in the census. Each sign's page tells its five vintages in full, and the zodiac elements page lists all sixty pairings with their years.

Three different things get called your element, and readings mix them up constantly. The year's stem gives one (the Metal in Metal Horse); the sign's own branch has a fixed one (the Horse is a Fire sign, every year); and the year's sound, its nayin, has a third. The calculator prints all three and says which is which. None of them is the element a bazi reader means by "you," which comes in the last step.

A year has a branch too, so every sign stands in a fixed relation to it, and the almanacs have named those relations for a thousand years: your own year, the clash directly across the wheel, the six harmonies, the trine allies four places away, the harm and the punishment sets. To read your sign against a year, count the places between the two animals. Six apart is the clash; four apart is the trine. The calculator does this for 2026 and 2027 off the same tables as the 2026 page, and says plainly when the tables record nothing, which for most signs in most years is the honest answer. What offending the year deity means, and what the tradition actually prescribes, is on the Tai Sui page.

Compatibility in the Chinese zodiac is the same geometry. Signs four places apart share a trine and pull the same way; every sign has one secret friend in the six harmonies; the sign directly opposite is the famous clash. The compatibility checker spells out the mechanism behind every pairing, and if you have a second birthday in mind rather than a second sign, does he like me works both animals out across the New Year boundary first.

The same birth year, turned at Lichun rather than at New Year, gives a kua number from one to nine and sorts you into the East or West group of the Eight Mansions school of feng shui. Add the digits of the year until one digit is left. A man subtracts that from 11, a woman adds 4 to it, and either result is reduced to one digit again. There is no kua 5: a man who lands on 5 takes 2, a woman takes 8. For 1990: 1 + 9 + 9 + 0 is 19, then 1 + 9 is 10, then 1. A man born in mid-1990 is 11 minus 1, which is 10, which reduces to 1; a woman is 4 plus 1, which is 5, so 8. That is why the calculator asks whether to read you as a man or a woman, and it is the only line on the leaf that needs to know. The kua calculator gives all eight directions and what to do with them in a room.

The month and the hour have animals of their own, the ones popular astrology calls your inner and secret animals. The months turn on the solar terms, between the 3rd and the 9th of each Western month, starting with the Tiger at Lichun; the hours are twelve double hours, starting with the Rat at 11 pm. Both need the minute in principle, which is why the calculator asks for a birth time and a city.

The year also has a name, one of sixty, jiazi to guihai, and a poetic "received sound" that the Ming almanacs gave each pair of years: metal in the sea, fire on the mountaintop. 1990 was gengwu, the seventh of the sixty. The sexagenary cycle page lists all sixty and finds the name of any date.

Zi Wei Dou Shu, the other great Chinese chart, does not start from the year at all. It starts from your lunar month and your birth hour: count forward from the Tiger palace by the month and back by the hour, and the palace you land on is your Life Palace, the one that shapes the whole chart; count the other way and you have the Body Palace. The calculator names both, and the Zi Wei calculator places the fourteen stars around them.

Your birthday has a second address, the day and month of the lunar calendar it fell on, which is the one a Chinese grandmother keeps and the one that moves on the Western calendar every year. And by the traditional count you were one at birth and a year older every New Year, so the sum is simple: the current Chinese year, minus the Chinese year you were born in, plus one. A 1990 Horse is 37 in the 2026 year, whatever the passport says. The age calculator explains the count and the date it next ticks over.

Your birth day has a stem and a branch of its own, and in a real reading the day stem, not the year animal, is the character that stands for you. It is the one step with no napkin shortcut: the day count runs unbroken through the sixty since antiquity and has to be counted from a known date. The bazi calculator does it, casts all four pillars, names your day master and draws eighty years of them as a life chart, free.