Tool · Reference
Heavenly Stems and Earthly Branches (干支)
Every BaZi chart is written in two alphabets: ten heavenly stems 天干 and twelve earthly branches 地支. Combined, they produce exactly sixty pairs — the 干支 — which is why the traditional cycle repeats every sixty years. Enter a birth date to see which pairs yours produced, and what each one is called.
The short version
A stem is what shows on the surface; a branch is its root. A pillar is a stem sitting above a branch, and the pair has a name of its own — the 60 甲子 names, whose 纳音 reading is older than the rest of the system.
The stems and branches are not symbols to be decoded one at a time. They are a counting system: a way of naming years, months, days and hours on a cycle that never depends on when you started counting.
Your four 干支 pairs
Free · no sign-up
One pair for the year, month, day and hour of birth. The date alone is enough for the first three; the hour pillar needs a birth time.
How it’s calculated
- 1
Name the day
The day pillar advances exactly one pair per calendar day with no gaps, which makes it the most reliable part of the chart — a continuous count that has been kept for well over a millennium.
- 2
Name the year and month
The year pillar advances at the exact astronomical moment of 立春. The month pillar advances at each of the twelve 节 — the “sectional” solar terms — which is why it does not change on the 1st of the month.
- 3
Name the hour
The twelve branches each cover two hours, so the hour branch is fixed by the time of day. The hour stem is then derived from the day stem by a fixed rule, the 五鼠遁.
The full rule set — every convention, in order, with the engine field names — is published on the methodology page.
What a heavenly stem is
There are ten stems: 甲 乙 丙 丁 戊 己 庚 辛 壬 癸. Each one is a fixed element in a fixed polarity — 甲 is yang wood, 乙 is yin wood, 丙 is yang fire, and so on down the list. There is no ambiguity and no interpretation in the mapping.
In a chart the stem is the visible character, the outward one. It pairs with exactly one branch to form a pillar. Stems are also what the ten gods are computed from: your day master is a stem, and every other stem is classified against it.
What an earthly branch is
There are twelve branches: 子 丑 寅 卯 辰 巳 午 未 申 酉 戌 亥. Each carries an element, an animal, a two-hour period of the day, and a season. The animals you already know from the so-called Chinese zodiac — that zodiac is simply the year branch, read as an animal.
What makes branches structurally different from stems is that they are not single characters. Each branch hides one to three stems inside it, known as the hidden stems, 藏干. 子 hides only 癸; 寅 hides 甲, 丙 and 戊. This is the single most commonly skipped part of BaZi, and skipping it makes element counts and ten-god tables incomplete.
Why the cycle is sixty and not 120
Ten stems and twelve branches could theoretically pair in 120 ways. Only 60 of those actually occur. The reason is arithmetic: 10 and 12 share a factor of 2, so the stem sequence and the branch sequence stay in step with each other and only half the combinations ever line up. After 60 steps both sequences return to their starting point.
That is the origin of the sixty-year cycle, 六十甲子. Years, months, days and hours are all numbered on it. 1984 opened a cycle with 甲子; the next 甲子 year is 2044. Because the day cycle runs continuously, the day pillar of any date can be computed by counting forward from any known anchor — which is exactly what the engine does, and what the self-test checks against published almanac data.
纳音 — the older layer, still in use
Each of the sixty pairs also carries a name from a separate system called 纳音 náyīn: 甲子 and 乙丑 are both 海中金 “gold in the sea”, 丙寅 and 丁卯 are both 炉中火 “fire in the furnace”, and so on. The sixty pairs are grouped in twos, giving thirty 纳音 names.
纳音 predates the four-pillar method and works on different principles, which is why its names sometimes seem unrelated to the elements of the characters in the pair. It is not used to compute anything in this engine — but it is part of what people mean when they say a person’s “year of birth” in traditional terms, so the full table is below.
Two calendars, two different answers
The most confusing thing about 干支 for newcomers is that China has two new years. The lunar new year, 春节, falls on the new moon nearest the start of spring. The BaZi year boundary, 立春, falls at the exact astronomical moment the sun reaches 315° of solar longitude, which is usually around 3–5 February.
For most of the year the two agree. For births in the gap between them — a week or two, depending on the year — they do not, and the popular zodiac animal and the BaZi year pillar name different animals. Neither is wrong; they are answering different questions. This site always shows the year pillar, because that is the one the chart is built on. The tool above tells you when the two disagree for your own date.
A worked example
The same worked case used throughout the site, so you can cross-check one page against another: 4 February 1990, 10:00, Taipei. Note that the year pillar and the popular zodiac disagree here — and the reason is the subject of the last section above.
Input
- Date
- 4 Feb 1990
- Time
- 10:00
- Place
- Taipei, Taiwan
- Time zone
- Asia/Taipei
Nearest 节
Next: 立春, 4 Feb 1990 10:14Birth at 10:00 — 14 minutes before the year boundary.
Year 年
己巳
Jǐ Sì
- Stem
- 己 · 土
- Branch
- 巳 · Snake
- 纳音
- 大林木
Month 月
丁丑
Dīng Chǒu
- Stem
- 丁 · 火
- Branch
- 丑 · Ox
- 纳音
- 涧下水
Day 日
庚子
Gēng Zǐ
- Stem
- 庚 · 金
- Branch
- 子 · Rat
- 纳音
- 壁上土
Hour 时
辛巳
Xīn Sì
- Stem
- 辛 · 金
- Branch
- 巳 · Snake
- 纳音
- 白蜡金
The fourteen-minute year, and the snake who is called a horse
立春 fell at 10:14 that morning and the birth is at 10:00, so the year pillar is 己巳 — a Snake year. The popular zodiac calls this birth a Horse, because the lunar new year had already passed on 27 January and the animal is taken from the lunar year. Both statements come from the same birth data and both are correct in their own system. A calculator that quietly mixes them will look consistent and be wrong; one that names both, as this page does, looks inconsistent and is right.
Engine v1.1.0 · these eight characters, this tally — reproduce them any time from the same input.
The ten heavenly stems 天干
Ten characters, each one a fixed element in a fixed polarity. The stems are what a chart shows on its surface.
- 甲Jiǎ
Wood · Yang
- 乙Yǐ
Wood · Yin
- 丙Bǐng
Fire · Yang
- 丁Dīng
Fire · Yin
- 戊Wù
Earth · Yang
- 己Jǐ
Earth · Yin
- 庚Gēng
Metal · Yang
- 辛Xīn
Metal · Yin
- 壬Rén
Water · Yang
- 癸Guǐ
Water · Yin
The twelve earthly branches 地支
Twelve characters, each carrying an element, an animal, a two-hour period of the day — and, crucially, one to three hidden stems.
- 子ZǐRat水23:00–01:00癸
- 丑ChǒuOx土01:00–03:00己 癸 辛
- 寅YínTiger木03:00–05:00甲 丙 戊
- 卯MǎoRabbit木05:00–07:00乙
- 辰ChénDragon土07:00–09:00戊 乙 癸
- 巳SìSnake火09:00–11:00丙 庚 戊
- 午WǔHorse火11:00–13:00丁 己
- 未WèiGoat土13:00–15:00己 丁 乙
- 申ShēnMonkey金15:00–17:00庚 壬 戊
- 酉YǒuRooster金17:00–19:00辛
- 戌XūDog土19:00–21:00戊 辛 丁
- 亥HàiPig水21:00–23:00壬 甲
The sixty pairs 六十甲子
Ten stems and twelve branches only combine in sixty ways, because 10 and 12 share a factor of 2 — only half of the 120 theoretical pairs ever occur, and the cycle restarts after sixty. 1984 was a 甲子 year; the next is 2044. The four pillars of the worked example on this page are outlined.
- 甲子海中金pair 1 of 60
- 乙丑海中金pair 2 of 60
- 丙寅炉中火pair 3 of 60
- 丁卯炉中火pair 4 of 60
- 戊辰大林木pair 5 of 60
- 己巳大林木pair 6 of 60
- 庚午路旁土pair 7 of 60
- 辛未路旁土pair 8 of 60
- 壬申剑锋金pair 9 of 60
- 癸酉剑锋金pair 10 of 60
- 甲戌山头火pair 11 of 60
- 乙亥山头火pair 12 of 60
- 丙子涧下水pair 13 of 60
- 丁丑涧下水pair 14 of 60
- 戊寅城头土pair 15 of 60
- 己卯城头土pair 16 of 60
- 庚辰白蜡金pair 17 of 60
- 辛巳白蜡金pair 18 of 60
- 壬午杨柳木pair 19 of 60
- 癸未杨柳木pair 20 of 60
- 甲申泉中水pair 21 of 60
- 乙酉泉中水pair 22 of 60
- 丙戌屋上土pair 23 of 60
- 丁亥屋上土pair 24 of 60
- 戊子霹雳火pair 25 of 60
- 己丑霹雳火pair 26 of 60
- 庚寅松柏木pair 27 of 60
- 辛卯松柏木pair 28 of 60
- 壬辰长流水pair 29 of 60
- 癸巳长流水pair 30 of 60
- 甲午砂中金pair 31 of 60
- 乙未砂中金pair 32 of 60
- 丙申山下火pair 33 of 60
- 丁酉山下火pair 34 of 60
- 戊戌平地木pair 35 of 60
- 己亥平地木pair 36 of 60
- 庚子壁上土pair 37 of 60
- 辛丑壁上土pair 38 of 60
- 壬寅金箔金pair 39 of 60
- 癸卯金箔金pair 40 of 60
- 甲辰覆灯火pair 41 of 60
- 乙巳覆灯火pair 42 of 60
- 丙午天河水pair 43 of 60
- 丁未天河水pair 44 of 60
- 戊申大驿土pair 45 of 60
- 己酉大驿土pair 46 of 60
- 庚戌钗钏金pair 47 of 60
- 辛亥钗钏金pair 48 of 60
- 壬子桑柘木pair 49 of 60
- 癸丑桑柘木pair 50 of 60
- 甲寅大溪水pair 51 of 60
- 乙卯大溪水pair 52 of 60
- 丙辰沙中土pair 53 of 60
- 丁巳沙中土pair 54 of 60
- 戊午天上火pair 55 of 60
- 己未天上火pair 56 of 60
- 庚申石榴木pair 57 of 60
- 辛酉石榴木pair 58 of 60
- 壬戌大海水pair 59 of 60
- 癸亥大海水pair 60 of 60
How branches interact: 冲合刑害
Beyond their own elements, branches relate to each other. These are the six classical relation types, and they are why two charts with the same elements can still read very differently. Every chart the calculator produces is checked against these tables, and the result shows which ones fired.
Six clashes 六冲相对的两个支
The branch directly opposite on the twelve-cycle dial. Read as the strongest structural tension.
- 子午
- 丑未
- 寅申
- 卯酉
- 辰戌
- 巳亥
Six combinations 六合两两相合
Pairs that bind and, in practice, transform toward the element shown.
- 子丑 · 土
- 寅亥 · 木
- 卯戌 · 火
- 辰酉 · 金
- 巳申 · 水
- 午未 · 土
Six harms 六害相穿
Quieter friction than a clash, but it repeats — usually read as something that keeps returning.
- 子未
- 丑午
- 寅巳
- 卯辰
- 申亥
- 酉戌
Punishments 相刑互刑与自刑
Three mutual patterns plus four branches that punish themselves when they repeat.
- 寅巳
- 巳申
- 申寅
- 丑戌
- 戌未
- 未丑
- 子卯
- 辰辰
- 午午
- 酉酉
- 亥亥
Three-harmonies 三合三支成一局
Three branches spread around the dial that pool into one element. Only a complete trio counts.
- 申子辰 · 水
- 亥卯未 · 木
- 寅午戌 · 火
- 巳酉丑 · 金
Directional meetings 三会三支成一方
Three consecutive branches of one season — the strongest formation of an element in the system.
- 寅卯辰 · 木 · East
- 巳午未 · 火 · South
- 申酉戌 · 金 · West
- 亥子丑 · 水 · North
Two things worth saying plainly. First, the relation types overlap on purpose: 寅 and 巳 are a harm and a punishment, and 巳 and 申 are a combination and a punishment — classical practice reads both, so we report both rather than picking one. Second, none of these is good or bad news by itself. A clash is a source of motion, not misfortune; a combination is a binding, not a blessing. What they mean depends on the day master and the season, which is a separate step from detecting them.
Questions
- How do I find my 干支?
- Enter your birth date above. The day pillar needs only the date; the year and month pillars also need only the date, because they are anchored to solar terms rather than to the clock. The hour pillar is the only one that requires a birth time.
- Why does my year pillar change in February instead of on 1 January?
- Because the BaZi year is a solar year, not a calendar year. It begins at 立春, the exact moment the sun reaches 315° of solar longitude — normally 3–5 February. The timezone and year you were born in are irrelevant to this; the engine uses the astronomical moment, to the minute.
- What are hidden stems and why do they matter?
- Each earthly branch contains one to three heavenly stems. 子 contains only 癸, while 寅 contains 甲, 丙 and 戊. Ignoring them understates an element tally and drops ten gods out of the chart entirely — so any calculator that only counts the eight visible characters is giving you a partial picture.
- Why is the cycle 60 years long and not 120?
- Because ten and twelve share a common factor of two. The stem and branch sequences stay in step, so only 60 of the 120 possible pairs ever occur, and the sequence returns to 甲子 after 60 steps.
- What is 纳音 and do I need it?
- 纳音 is a separate naming system from an older tradition that groups the sixty pairs into thirty poetic names, such as 海中金 “gold in the sea”. It is not used in the computations on this site, but it is widely referenced, so the full table is published above.
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BaziPattern provides AI-generated readings for entertainment and cultural exploration purposes only. Readings are not predictions, or medical, legal, or financial advice.