The intake form asks for three things: date of birth, clock time, city. There is no field for the animal. The animal comes out of the other three.
That surprises people, because for many of them the animal is the system, or at least the door into it. It is the outermost layer, and underneath it sit the stems and branches.
The scheme is old. It is already on Shang oracle bones, used there mostly for counting days, and it later took over years, months and hours too. 2026 is bingwu: bing, third stem, over wu, seventh branch.
Two strings, offset by one
Ten stems: 甲乙丙丁戊己庚辛壬癸, jia yi bing ding wu ji geng xin ren gui.
Twelve branches: 子丑寅卯辰巳午未申酉戌亥, zi chou yin mao chen si wu wei shen you xu hai.
Two of those collide with words below. The branch yin 寅 is not the yin of yin and yang, and the branch wu 午 is not the stem wu 戊. I give the character where it matters.
The ten stems double as ordinals in modern Chinese. Methane is 甲烷, stem-one gas, with ethane, propane and butane following in order, so a Chinese chemistry student never has to recall how many carbons butane holds. Hepatitis A, B and C are numbered the same way.
They pair by stepping forward together. Jiazi, yichou, bingyin, dingmao. At the tenth step you get guiyou, the stems are spent and xu and hai are still waiting, so the stems start again from jia: jiaxu, yihai. Then the branches run out and restart from zi against bing, giving bingzi. The sixtieth step is guihai; one more and jiazi is back.
Ten times twelve is a hundred and twenty, but only sixty pairs exist; the mixed-polarity half never gets a turn. Odd-numbered stems are yang, even-numbered ones yin, and the branches alternate the same way from zi, so two strings stepping in lock-step means yang always meets yang. There is no jiachou in the table.
A base-sixty counter with no zero
Which year is jiawu? 1894 is. So is 1954. So is 2014. On paper the three are identical, sixty years apart.
Which is why histories rarely print the pair alone. They put a reign title in front: the twentieth year of Guangxu, jiawu. The title locates the year, the pair says which of the sixty slots it fell in. Xinhai, wuxu and gengzi are unambiguous to a Chinese reader because of what happened in those years, not because the characters carry a date.
Sixty steps is one full round, a huajia. Someone turning sixty has come back to the pair they were born under.
The scheme is built for periods and cannot say how long ago. For a number of years you convert to the Gregorian calendar and subtract there; a cycle with no zero has nothing to subtract from. My charting code stores real timestamps and computes the stems and branches only when something needs displaying. More on that in Why a Daoist Priest Writes Code.
What each character carries
Up to here this is only labelling, no different from 1, 2, 3. It becomes usable because every character carries a phase and a polarity as well.
Stems go in pairs: jia and yi wood, bing and ding fire, wu 戊 and ji earth, geng and xin metal, ren and gui water. First of each pair yang, second yin, so jia is yang wood, yi yin wood, down to gui, yin water. Ten characters, ten identities. On what phase means here, and why element was a poor translation, see The Five Phases Are Not Five Substances.
The branches are messier. Main qi runs yin 寅 and mao wood, si 巳 and wu 午 fire, shen and you metal, hai and zi water, with the four left over (chen, xu, chou, wei) all earth at the joints between seasons. Each branch also hides one to three stems: yin 寅 hides jia, bing and wu 戊, chen hides wu 戊, yi and gui, and only zi, mao and you are clean with one each. Those hidden stems are the door into everything downstream: a stem that shows nowhere on the visible row is often lying inside a branch. How much weight each gets is where schools part company; that is in The Useful God and the Taboo God.
There is a spot in the branch polarities I still find unclean. By position, si 巳 is sixth and so yin, wu 午 seventh and so yang. By hidden main qi, si holds bing fire, which is yang, and wu holds ding fire, which is yin. The two accounts point opposite ways, and zi and hai carry the same fault in reverse. The old books file this under a distinction between substance and function; I have read several explanations and none settled it. I chart by position, because that is how I was taught and it has served, but ask me why position should outrank the hidden qi and I can’t tell you. On a chart that matters I run both and look at where they diverge. Most of the time they don’t. When they do I say which one I used and that I’m not sure.
The branches carry three loads
The stems do one job, numbering time. The branches do three.
Months first. Twelve branches for twelve months: the first built on yin 寅, the second on mao, round to the twelfth on chou. Built comes from where the handle of the Dipper points. What matters in practice is that the month boundary is a solar term, not the first of a lunar month. The yin month opens at the instant of lichun, the mao month at jingzhe, timed to the minute. Someone born in the twelfth lunar month but after lichun already carries the next year’s pillar and the new month pillar with it, and nothing on the page looks missing. What becomes of the solar terms south of the equator is in The Twenty-Four Solar Terms Below the Equator.
Hours next. Twelve double-hours in a day. Zi runs eleven at night to one, chou one to three, wu 午 eleven in the morning to one. Noon falls in the middle of the wu hour, which is how wu came to mean midday on its own. Zi straddles midnight, and whether that night’s day pillar counts as today or tomorrow is a real split between schools; my practice and my hesitation are in What a Bazi Chart Can and Cannot Tell You.
Then the animals. Zi rat, chou ox, yin 寅 tiger, mao rabbit, on to hai pig. This layer was made for people who could not read: twelve abstract signs turned into things anyone can picture. The animals are the branches in popular dress, and the dress varies by country: Vietnam has a cat in the mao slot instead of a rabbit. Saying someone is a horse says their birth-year branch is wu 午.
Where it lands: the four pillars
Four pillars means the four moments of birth, year, month, day and hour, each written as a stem over a branch. Eight characters. The year pillar turns at lichun, the month pillar follows the solar terms, and once the hour is fixed the hour stem follows from the day stem. All of it assumes the clock reading has been sorted out: time zone, and daylight saving. Sydney runs it from the first Sunday in October to the first Sunday in April, but only since 2008. Before that it ran from the last Sunday in October to the last Sunday in March, and in the Olympic year it began in August. Queensland and Western Australia don’t observe it now, though both trialled it. On an older birth, look the year up.
The day pillar is the one you cannot derive. You look it up. Days have been counted stem by stem in a run that ignores years, months and the moon and does not restart when a dynasty does, generally held to have gone unbroken since at least the Spring and Autumn period. So you consult an almanac, or write a few lines of code counting forward or back from a known day.
Below the equator
The stems and branches don’t flip. They label time, which belongs to the sky. Two people born at the same instant, one in Sydney and one in Xi’an, get the same eight characters. What swaps is how the solar terms map onto heat and cold; the dividing line is that the stars stay while the earthly trigrams move. That reasoning is in Why “Facing South” Fails in Australia and I won’t redo it here.
Where to start
Recite the sixty pairs in order until you no longer need the table; most people get there faster than they expect. Then the phases and polarities of the ten stems, and the branches with their main qi and hidden stems. Those two tables sit under every step that follows, and if they aren’t solid you spend your time flipping back, which is what makes people quit. Memorise first; the reasoning keeps, and it reads faster once the tables are in your head.