The sexagenary cycle: sixty names that count the years, the days and you

Ten against twelve. The stems and the branches step forward together, one notch each, so jia sits on zi, then yi on chou, bing on yin, and so on down the line. Because both move at once, a stem in an odd position only ever meets a branch in an odd position: jia will pair with zi, yin, chen, wu, shen and xu, and never in sixty lifetimes with chou. Half the grid of 120 possible pairs is never visited, and after sixty steps jia lands on zi again. That is the whole mechanism. Everything else on this page is what people have done with it.

In the table, the element and polarity are the stem's, the animal is the branch's, and the sound is the nayin the pair shares with its neighbor, explained at the end of the page. The two years against each name are the ones in the last two full cycles, 1924 to 1983 and 1984 to 2043, on the Lichun rule the chart uses; if you were born in January or early February, the year-boundaries page has both dates for your year.

The same sixty words run four separate clocks, and the clocks do not agree about when to turn over. The Hong Kong Observatory's note on the system puts the history plainly: the years and the days have carried these names "for two to three thousand years," while the months and the hours were once named by branch alone, and "people started to make stems of the months after the stem of the year, and stems of the hours after the stem of the day." So the year turns at Lichun, the start of spring, around February 4; the month turns at one of twelve solar terms rather than at a new moon; the day rolls on regardless of anything, which gets its own section below; and the hour takes its branch from the clock and its stem from the day, by the five-rats rule on the shichen page. A bazi chart is one reading off each clock at the moment of birth, which is why the same date can sit in two different months, and why a birth at 23:30 is a different chart on different calculators.

Once you can read the names, a slice of modern Chinese history reads differently. The war with Japan of 1894 is the jiawu war; the failed reforms of 1898 are the wuxu reforms; the Boxer year of 1900 is gengzi; and the revolution that ended the empire in 1911 is, in every Chinese textbook, the xinhai revolution. Nobody chose those as nicknames; a Chinese textbook simply has no other name for the years, and the four printed here are checked against our calculator's year table every time this page is built. The names also explain the birthday. Sixty years after you were born the year is called by the same two characters as the year of your birth, for the first time since; the tradition calls that birthday the huajia, and the reason it is called that is waiting in the section on sounds.

Jiazi is a plain name, two syllables, and the sixty once had grander ones. The Erya, the oldest surviving Chinese glossary (compiled somewhere between the Warring States and the early Han, so before about 150 BC), has a chapter on the heavens with two short lists in it. One is headed "The Year's Yang" and runs: when the Great Year is in jia, it is called yanfeng; in yi, zhanmeng; in bing, rouzhao; and so on through the ten stems. The other is headed "The Year's Names" and does the same for the twelve branches, starting not from zi but from yin: when the Great Year is in yin, the year is called shetige. Put the two lists together and a jiazi year is a yanfeng kundun year, which nobody has said aloud in a very long time.

Where the words come from nobody knows, and the glossary does not say; they may be transcriptions of something that was not Chinese. What the Han did know is what they were for. The Huainanzi, a compendium presented to the throne in 139 BC, goes through the twelve in the same order and attaches each to a planet: when the Great Yin is in yin, it says, the year's name is shetige, and "its male counterpart is the Year Star," which is Jupiter; then it lists the lunar lodges Jupiter occupies that year and the month in which it rises before dawn. The Great Year of the Erya is an invisible marker running opposite Jupiter, a shadow planet that moves through the twelve stations at exactly one a year. The names were Jupiter's names.

That is also, almost certainly, why they died. The Huainanzi says the Year Star "completes its circuit in twelve years." It does not, quite: Jupiter's real period is 11.86 years, so a counter that steps one station a year falls a full station behind the planet roughly every 86 years, and sooner or later someone has to choose between the sky and the count. You can watch the choice not yet made in the Shiji. When Emperor Wu reformed the calendar in 104 BC, Sima Qian records the edict that launched it: the year is to be named yanfeng shetige, the month biju, the day is jiazi, and midnight of the new moon falls on the winter solstice. Yanfeng shetige is jiayin. Run the count in use today back to 104 BC and you get dingchou. The two series are not the same series, and the Shiji's own table of the years that followed spells several of the stem names differently from the Erya and puts two of them, zhaoyang and shangzhang, on different stems altogether, which tells you the grand names were never as settled as the plain ones. Zhang He, in a 2020 study of the cycle, gives the dating that follows from all this: in the oracle-bone inscriptions the pairs "are mostly used to reckon days, and, at least since the Han dynasty, years." The day count is the ancient thing. The year count, the one your zodiac animal rides on, is a Han arrangement that took over Jupiter's job and kept its arithmetic.

The Erya adds one line under its lists that is worth carrying away. "Zai means year," it says: "the Xia said sui, the Shang said si, the Zhou said nian." Three dynasties, three words for the thing the sixty names count, and the one that won, nian, is the one in xinnian, new year, today.

Of the four clocks, the day is the one to trust, because it is the one nobody has ever adjusted. The Hong Kong Observatory's printed calendar for December 2025 gives the 31st the name jiaxu. Its calendar for January 2026 gives the 1st yihai, the next name in the list. Nothing happened at midnight except the fireworks. Our engine agrees with the Observatory on both dates, and this page checks that it does before it will build. The day count does not know about January, or Chinese New Year, or Lichun; it has been adding one since long before any of those boundaries existed, and it has never once gone back to jiazi to start over.

How long is never? The Spring and Autumn Annals, the court chronicle of the state of Lu, opens its third year (720 BC) with an entry that reads, in full: "Third year, spring, the royal second month, jisi day, the sun was eaten." Take the Observatory's yihai for January 1, 2026, count back to February 22, 720 BC in the Julian calendar, and you have gone 1,002,546 days. Divide by sixty, take the remainder, step back that far along the list, and the name you land on is jisi. NASA's canon of historical eclipses lists a total eclipse of the sun on exactly that date. One million days, and the count is still on the same beat as a scribe in Lu with a knife and a strip of bamboo.

Behind Lu the trail runs on into the bones. The Shang diviners at Anyang, around 1200 BC, dated every question they put to the ancestors with a day name; in the translations Columbia's Sources of Chinese Tradition prints, a diviner cracks his shell "on yiwei (day 32)," and Zhang He finds a complete run of all sixty "neatly aligned" in the inscriptions. Whether the same count runs unbroken from Anyang to Lu is harder to check, because the centuries between leave too few dated records to test against the sky. From Lu to this morning, it holds.

This is also the reason a birth year cannot tell you your day master, however many websites imply it can. The year pillar is one clock and the day pillar is another; two people born a year apart to the day are 365 or 366 names apart, which is five or six steps along the list. Your birthday next year carries a different day name from this year's, and sixty years on, when the year's name comes back, the day's does not, because sixty years is 21,900-odd days and not a multiple of sixty. The day pillar has to be counted, from an anchor, through every day in between. The finder above does the counting; the calculator does it and then reads the result.

Every two names share a sound. Jiazi and yichou are both "metal in the sea"; bingyin and dingmao are "fire in the furnace"; and so on down the sixty in pairs, thirty images in all, each one of the five elements dressed as a thing. The scheme is called nayin, "received sounds," and the name is not a metaphor. Wan Minying's Sanming Tonghui of 1578, the Ming encyclopedia of fate-reading, opens its chapter on them by citing Shen Kuo's eleventh-century Mengxi Bitan: the sixty nayin "are based on the sixty pitch-pipes, taking each in turn as the tonic." The method, it goes on, is the one the pipes use to generate one another: "marry within the same class, and beget at the eighth," so jiazi takes yichou as its wife and produces renshen eight steps down. And why does the list begin with metal, when every other five-element list begins with wood or water? "Of the five phases, only metal cast into a vessel gives a ringing sound; that is why the received sounds put metal first." The sixty names are, at bottom, the note a bell makes when struck.

Then the manual explains what the images are for, and the explanation is the best thing in the chapter. The Yellow Emperor, it says, "divided the jiazi by weight and matched them into sixty, and called them the flowered jiazi." That word, hua, flower, is the one in huajia, the sixtieth birthday: your sixtieth is your flowered cycle. The twelve stations of the branches, the text goes on, are a human life. At zi and chou "yin and yang first conceive; the person is in the womb." At yin and mao they begin to grow. At chen and si they are "like a person of thirty or forty, with a footing in the world." At wu and wei they are "a person of fifty or sixty, and whether they are rich or poor, high or low, can be known." At shen and you the harvest is in, and at xu and hai "the person should rest." Which is why jiazi and yichou, at the first station, are metal in the sea: "the breath is still wrapped up; it has a name and no form, like a person in the mother's belly." Renshen and guiyou, at the metal stations shen and you with water stems over them, are the sword edge: "the White Emperor holds sway; hardness comes of a hundred temperings; a red light shoots at the Dipper and the Ox, a white blade set in frost and snow." And renxu and guihai, at the very end, are the great sea, which "takes in the hundred rivers, boundless." The list is a life, from the womb to the ocean.

What our calculator does with the sounds is nothing, and it is worth saying so. The day-master method it implements, the one that descends from the Song Yuanhai Ziping, weighs stems and hidden stems and does not score nayin; the sounds belong to the older way of reading a chart, by the year pillar and its sound, which is why an older relative may tell you they are "a fire in the furnace" rather than "a yin Wood day master," and why the Ming manual spends thirty sections on them. The finder above prints the sound of your year and of your day as identity, the way a surname is identity. The reading starts somewhere else.