The 60 Jiazi Cycle: How the Stems and Branches Count the Years

Classical Chinese timekeeping counts in pairs. A Heavenly Stem and an Earthly Branch are written together as one unit — a pillar (柱) — and the two cycles advance side by side, one step each, so that the combinations run out and then begin again. The full sequence is called the Jiazi cycle (甲子), after its first pair, and its length is sixty.

This cycle is the frame that BaZi writes a person's chart on: four pillars, each a stem and a branch, for the year, month, day and hour of birth. It is also how the years themselves are named, which is why a year can be described as, say, a dragon year and a wood year at the same time — two statements about two different halves of the same pair.

1. What the cycle is

Take the ten Stems in their fixed order and the twelve Branches in theirs, and write them out side by side, advancing both at the same speed. The first pair is Jia Zi (甲子), the second Yi Chou (乙丑), the third Bing Yin (丙寅), and so on. The Stem list finishes before the Branch list does, so it starts over while the Branch list is still running, and the two only return to their starting places together after sixty steps.

That single sequence of sixty pairs is the sexagenary cycle, also called the sixty Jiazi. Nothing in it is chosen: the order of the Stems, the order of the Branches and the rule that they advance together generate the whole list.

2. Why ten and twelve give sixty

A first guess would be that ten Stems and twelve Branches can make a hundred and twenty combinations, since every Stem could in principle be paired with every Branch. The cycle contains only sixty, and the reason is polarity.

Both cycles alternate Yang and Yin. The Stems run Yang, Yin, Yang, Yin, and so on; the Branches do the same. Because the two advance together, one step per year, a Stem and a Branch always arrive at the same parity — a Yang Stem pairs only with a Yang Branch, and a Yin Stem only with a Yin Branch. Every Yang-Yang or Yin-Yin pairing is impossible by construction, which halves the list from a hundred and twenty to sixty.

The same result is reached by counting: the Stems repeat every ten steps and the Branches every twelve, so the two are back in their starting alignment at the smallest number of years divisible by both — the least common multiple of ten and twelve, which is sixty.

A useful consequence: a pair tells you its own parity at a glance. Odd-numbered pairs in the table below are Yang-Yang, even-numbered pairs are Yin-Yin, and there is no such thing as a Yang Stem sitting on a Yin Branch. When a chart appears to contain one, one of the two characters has been misread.

3. How a pillar reads

A pillar is written with the Stem above and the Branch below, and each half carries its own information. The Stem names an element and a polarity: Jia (甲) is Yang Wood, Yi (乙) is Yin Wood, Bing (丙) is Yang Fire, and so on through the ten. The Branch names an animal, a season, a direction and a two-hour period of the day: Zi (子) is the Rat, mid-winter, north, and the hours around midnight.

So the pair Jia Chen (甲辰) reads as Yang Wood sitting on the Dragon. The top half says what the energy is — the tall tree, in the case of Jia; the bottom half says where it stands — the Dragon branch, late spring, the south-east. Neither half is a modifier of the other; they are two layers of the same moment.

This is also the structure of a BaZi chart: four pillars, each with a Stem above and a Branch below, for the year, month, day and hour of birth. The Branches are the lower row of the chart, and the hidden Stems inside them add a third layer beneath that.

4. The sixty pairs

The complete cycle, in order. The Stem and Branch columns give the pinyin and the character; the animal is the Branch's zodiac sign, given for convenience because the year pillars are usually spoken of that way. The Lo Shu arrangement and the other standing tables of the knowledge base sit together in the reference tables.

#	Stem	Branch	Animal
1	甲 Jia — Yang Wood	子 Zi	Rat
2	乙 Yi — Yin Wood	丑 Chou	Ox
3	丙 Bing — Yang Fire	寅 Yin	Tiger
4	丁 Ding — Yin Fire	卯 Mao	Rabbit
5	戊 Wu — Yang Earth	辰 Chen	Dragon
6	己 Ji — Yin Earth	巳 Si	Snake
7	庚 Geng — Yang Metal	午 Wu	Horse
8	辛 Xin — Yin Metal	未 Wei	Goat
9	壬 Ren — Yang Water	申 Shen	Monkey
10	癸 Gui — Yin Water	酉 You	Rooster
11	甲 Jia — Yang Wood	戌 Xu	Dog
12	乙 Yi — Yin Wood	亥 Hai	Pig
13	丙 Bing — Yang Fire	子 Zi	Rat
14	丁 Ding — Yin Fire	丑 Chou	Ox
15	戊 Wu — Yang Earth	寅 Yin	Tiger
16	己 Ji — Yin Earth	卯 Mao	Rabbit
17	庚 Geng — Yang Metal	辰 Chen	Dragon
18	辛 Xin — Yin Metal	巳 Si	Snake
19	壬 Ren — Yang Water	午 Wu	Horse
20	癸 Gui — Yin Water	未 Wei	Goat
21	甲 Jia — Yang Wood	申 Shen	Monkey
22	乙 Yi — Yin Wood	酉 You	Rooster
23	丙 Bing — Yang Fire	戌 Xu	Dog
24	丁 Ding — Yin Fire	亥 Hai	Pig
25	戊 Wu — Yang Earth	子 Zi	Rat
26	己 Ji — Yin Earth	丑 Chou	Ox
27	庚 Geng — Yang Metal	寅 Yin	Tiger
28	辛 Xin — Yin Metal	卯 Mao	Rabbit
29	壬 Ren — Yang Water	辰 Chen	Dragon
30	癸 Gui — Yin Water	巳 Si	Snake
31	甲 Jia — Yang Wood	午 Wu	Horse
32	乙 Yi — Yin Wood	未 Wei	Goat
33	丙 Bing — Yang Fire	申 Shen	Monkey
34	丁 Ding — Yin Fire	酉 You	Rooster
35	戊 Wu — Yang Earth	戌 Xu	Dog
36	己 Ji — Yin Earth	亥 Hai	Pig
37	庚 Geng — Yang Metal	子 Zi	Rat
38	辛 Xin — Yin Metal	丑 Chou	Ox
39	壬 Ren — Yang Water	寅 Yin	Tiger
40	癸 Gui — Yin Water	卯 Mao	Rabbit
41	甲 Jia — Yang Wood	辰 Chen	Dragon
42	乙 Yi — Yin Wood	巳 Si	Snake
43	丙 Bing — Yang Fire	午 Wu	Horse
44	丁 Ding — Yin Fire	未 Wei	Goat
45	戊 Wu — Yang Earth	申 Shen	Monkey
46	己 Ji — Yin Earth	酉 You	Rooster
47	庚 Geng — Yang Metal	戌 Xu	Dog
48	辛 Xin — Yin Metal	亥 Hai	Pig
49	壬 Ren — Yang Water	子 Zi	Rat
50	癸 Gui — Yin Water	丑 Chou	Ox
51	甲 Jia — Yang Wood	寅 Yin	Tiger
52	乙 Yi — Yin Wood	卯 Mao	Rabbit
53	丙 Bing — Yang Fire	辰 Chen	Dragon
54	丁 Ding — Yin Fire	巳 Si	Snake
55	戊 Wu — Yang Earth	午 Wu	Horse
56	己 Ji — Yin Earth	未 Wei	Goat
57	庚 Geng — Yang Metal	申 Shen	Monkey
58	辛 Xin — Yin Metal	酉 You	Rooster
59	壬 Ren — Yang Water	戌 Xu	Dog
60	癸 Gui — Yin Water	亥 Hai	Pig

5. Finding the year pillar

The year pillar is fixed in the cycle, not assigned each year by hand. The pair Jia Zi is the first of the sixty, and a year whose pillar is Jia Zi anchors the count: the following year is Yi Chou, the one after that Bing Yin, and the count runs on to pair sixty before returning to Jia Zi. The classical anchor used for the modern era is 1984, a year of Jia Zi.

So any year's pillar is found by counting its distance from a known anchor and taking the remainder on division by sixty. Count whole years between the two, divide that number by sixty, and read the remainder as a position in the table above, with a remainder of zero meaning the sixtieth pair. The same answer is produced by any other known anchor year: the steps advance by one in each list, so the arithmetic is a matter of distance, not of a special starting point.

Two boundaries matter. First, a year's pillar is not the calendar year. The year changes at Li Chun (立春), the solar term in early February, so someone born in the second half of January belongs to the previous year's pillar — a point explained in the Chinese calendar. Second, the lunar New Year is not this boundary either; the spring festival moves through late January and February and can fall on either side of Li Chun.

6. The day, month and hour pillars

The year is the easy one. The other three pillars in a BaZi chart each follow their own rule.

The day pillar is not derived from the year at all. It runs as its own continuous sequence of sixty, counting on without interruption through centuries, so that the day pillar you were born under is a fixed position in a long count that has no relationship to your birth year. That count is what a calculator is for — the anchor and the running total are handled there, and they should not be reconstructed from a year pillar.

The month pillar follows the twelve solar months. The sequence begins with the Tiger month at Li Chun, and each following month begins at the next of the twelve solar terms that open a month, so the month Branch is set by the calendar rather than by the moon. The month Stem comes from the year Stem by a fixed rule, so the year pillar decides which set of twelve month pairs the months of that year are drawn from.

The hour pillar follows the twelve two-hour periods of the day, beginning with the Zi hour around midnight and running through all twelve Branches. Its Stem is derived from the day Stem in the same way: the day pillar fixes the twelve hour pairs that belong to it.

7. Na Yin, the layer above

There is a second, older labelling of the sixty pairs, called Na Yin (納音), "accepted sounds". Where the Stem and Branch each contribute an element of their own, Na Yin assigns a single element name to the pair as a whole — so a pillar can read as Yang Wood on the Stem while Na Yin gives the combination a name of its own.

Na Yin is treated as its own layer of reading, used in some branches of BaZi and in date selection, and it is not simply the sum of the two characters. Its values are a lookup of their own; they are not reproduced here, and a chart should take them from the calculator rather than from a pillar's halves.

8. Why the cycle matters

Three things follow from the cycle directly, and they are the reason it is worth knowing by structure rather than only by calculator.

The year pillar names the year. The animal sign people recognise — the year of the Rat, the year of the Dragon, the year of the Horse — is the Branch half of the year pillar, while the Stem half names the element. A year is spoken of as both at once, and the Grand Duke is read from the year Branch, which is why the Tai Sui sector moves one position every solar year.

The day pillar carries the self. In BaZi the Stem of the day pillar is the Day Master: the character the whole chart is read against, with every other Stem and Branch described by its relationship to that one. The Ten Gods are exactly those relationships, and they cannot be read without first fixing the day pillar.

The cycle sets the rhythm of return. A person's animal year comes round every twelve years, and the full pair — the same Stem and the same Branch together, which is what the Jiazi cycle actually marks — comes round once in sixty. That difference is why the twelve-year return is a social milestone and the sixty-year one is a genuine full circle: only at sixty are both halves of the pillar the same as at birth.

9. Frequently Asked Questions

What is the 60 Jiazi cycle?

It is the sexagenary cycle: the ten Heavenly Stems and the twelve Earthly Branches written in pairs, advancing together one step at a time, which produces a fixed sequence of sixty combinations before the first pair returns. It is used to name years and days, and its pairs are the pillars of a BaZi chart.

Why are there exactly sixty pairs and not a hundred and twenty?

Because both cycles alternate Yang and Yin and the two advance together, so a Stem and a Branch always meet at the same polarity: Yang pairs with Yang and Yin with Yin, and the mixed pairings never occur. That leaves sixty combinations out of the hundred and twenty that ten Stems and twelve Branches could form.

How do I find my Day pillar?

The day pillar comes from a continuous sixty-day count that runs independently of the year, so it cannot be worked back from your birth year by hand. Use a calculator — the BaZi calculator gives all four pillars from your birth date and time, including the Day Master, which is the Stem of the day pillar.

Why does the year pillar change in early February?

Because the year pillar follows the solar year, which begins at Li Chun (立春) around 4 February, not on 1 January and not at the lunar New Year. Births before Li Chun take the previous year's pillar. The Chinese calendar sets out the two new years and why feng shui and BaZi use the solar one.

What is Na Yin?

Na Yin (納音) is a separate naming of the sixty pairs that assigns one element to the pair as a whole, rather than reading the Stem and Branch separately. It is an older layer than the pillar reading itself and is used in some BaZi work and in date selection. Its values are a lookup; they are not shown here.