I Ching birth hexagram

How it works

The Zhouyi is a book for divination: a person casts a hexagram, traditionally with yarrow stalks or, from the Tang dynasty on, with three coins, and reads its text. The Plum Blossom method takes its numbers from things instead, and one of its rules takes them from the moment itself: the year, the month, the day and the hour. Chinese calculators apply that rule to the moment of a birth and call the result the lifetime cast (終身卦); the book does not use that name, and the Zhouyi has no birth hexagram of its own. This is the cast EsoTerrier computes.

The rule. Book 1 of the Plum Blossom text says: "年月日為上卦。年月日加時總數為下卦 ... 以八除之 ... 以六除，餘數作動爻". In our translation: the year, month and day make the upper trigram; the year, month and day with the hour added, as one total, make the lower trigram; each is divided by eight; the total is divided by six, and what remains is the moving line. A remainder of 0 counts as 8, or as 6 for the line. The trigrams are numbered in the Earlier Heaven order: 乾 1, 兌 2, 離 3, 震 4, 巽 5, 坎 6, 艮 7, 坤 8.

The numbers come from the lunar calendar. Your birth date is converted to the Chinese lunar calendar. The year counts as its Earthly Branch, from 子 1 to 亥 12, and turns at the lunar new year; the month is the lunar month, a leap month counting as the month it repeats; the day is the lunar day, 1 to 30. The hour is the double hour, from 子 1 (23:00 to 00:59) to 亥 12 (21:00 to 22:59), taken from the local clock time with no correction for the zone or the sun. A birth between 23:00 and 23:59 counts as the 子 hour of the same lunar day, as every Plum Blossom tool counts it. If you do not know your birth time, the noon hour 午 (7) is assumed and the result is marked approximate: the upper trigram does not depend on the hour, but the lower trigram and the moving line do.

A worked example. The sample person in Figure 1 was born on 19 January 1989 at 19:17. On the lunar calendar that is the twelfth day of the twelfth month of a 辰 year, in the 戌 hour. The year counts 5, the month 12, the day 12: 29, which leaves 5 on 8, so 巽 Wind is above. Adding the hour, 11, makes 40, which leaves 0, counted as 8, so 坤 Earth is below. 40 on 6 leaves 4. The birth hexagram is 20 觀 Guān with its fourth line moving; flipping that line gives 12 否 Pǐ, and lines 2 to 5 give the hexagram within, 23 剝 Bō.

What you see. Each hexagram is named by its number, its character, its pinyin with tone marks, and our own English title: "20 觀 Guān · Looking Out". The moving line is read as the one place in the figure that is in motion, and the transformed hexagram as where that motion leads. The texts are our own, written from the Chinese with Legge's public-domain translation of 1882 beside it. The trigrams are shown with their image and family place from the Shuogua, one of the Wings, and with the five phases from the Plum Blossom text's own table, labelled as that table's: a Han assignment, not the Zhouyi's. One further line names the hexagram the Sun stood in at birth on the Human Design wheel, a modern placing of the sixty-four round the zodiac. It is another system's reading, shown as a cross-reference and never as the birth hexagram.

Checked against others. The rule's inputs were checked on 56 timed test births against two calendar libraries, one open-source implementation and the calculators that use the same conventions: they agree on every one. A run over every day from 1940 to 2030 found that our first engine, which summed Gregorian dates, gave the right hexagram for only 13.2 percent of birth hours; it was replaced on 10 October 2026.

Origins and history

The text is about 2,800 years old; the commentaries are centuries younger; the birth cast comes from a book of the Ming period.

The order in which these ideas arrived matters for what the birth hexagram is. The hexagrams and their texts are old; the moral and cosmic reading of them came with the Wings; the numbered trigrams and the circle are Shao Yong's; and the rule that turns a date into a hexagram is in a book compiled four centuries after him and given his name. The Plum Blossom book itself applies the time rule to animals as well as to questions; Chinese calculators made the lifetime cast from it, and Western birth-hexagram tools followed.

The 64 hexagrams

Each hexagram has its own page: its figure and trigrams, the Zhouyi's statement for it with a short quotation from Legge, how the line texts move, the hexagrams it is linked to, and what the birth cast does with it. The received text falls into two parts, hexagrams 1 to 30 and 31 to 64.

Variants and what we leave out

The time rule is applied in more than one way, and the I Ching has other birth hexagrams. We describe them so you can recognise them, and say what we do.

• Gregorian dates. Our first engine summed the Gregorian month and day, as some tools still do; no book teaches it, and it agrees with the lunar rule about one time in eight. Replaced. One calculator's separate "solar" mode sums the full year number; recorded, not offered.
• The year at the start of spring. Some calculators turn the year at Lì Chūn, about 4 February, as BaZi does; the rule as printed and most tools turn it at the lunar new year. The two differ only for births in the weeks between. We use the lunar new year, which matches the lunar month and day.
• The year's stem instead of its branch. One author's variant for the lifetime cast; the text and every calculator use the branch.
• No birth time. The Chinese tools refuse; one Western tool assumes noon and says so, as we do. Our first engine used an invented formula without the hour; it is gone.
• The rest of the Plum Blossom book. It also casts from a number of objects, a sound, a written character or a direction, and reads a cast by setting the two trigrams against each other as 體 (the body, the trigram without the moving line) and 用 (its use, the trigram with it), through the five phases. Those belong to a consultation, a question asked at a moment, and we do not compute them.
• Yarrow stalks and coins. The classical oracle casts each line, so a hexagram can have anywhere from none to six moving lines, and the two methods give the line kinds different odds. The time cast always gives exactly one. A cast you make yourself would be a different feature.
• The 河洛理數 birth hexagram. A late Ming manual turns the eight characters of a birth into River Chart and Luo Writing numbers and builds two trigrams from them, by the year's polarity and the person's sex, and reads the lines as periods of life. It needs the BaZi pillars and a sex, and we do not offer it; it is one reason we never present the lifetime cast as the only Chinese birth hexagram.
• Six-line divination. Jing Fang's school assigns stems, branches and family roles to the lines, the method most Chinese divination software runs; an expert layer we do not show.
• The solar-degree hexagram. Human Design (1987) and Gene Keys take the hexagram the Sun stood in on a wheel that is Shao Yong's circle turned to start hexagram 41 at 2° Aquarius. Our chart names it in one labelled line.
• The Han calendars. Twelve "sovereign" hexagrams mark the lunar months, from 復 (24) at the winter solstice to 乾 (1) and from 姤 (44) to 坤 (2); a table of sixty marks the days. They give a hexagram of a month or day, not of a person. Each hexagram page names its month where it has one.
• Other "birth hexagram" calculators. Four-pillar schemes, odd and even sums of the stems and branches, numerology on the digits of the date: recorded in our research, not used.
• The Mawangdui order and names. Scholarship, not a display option: we use the received numbers and characters, as every tradition does.

Myths and disputed claims

What is said about the I Ching and the birth hexagram, who says it, and what the record shows. The label is ours.

• A birth hexagram is a classical practice of the I Ching, three thousand years old.

  false

  Who says it: Western birth-hexagram calculators, the old page writer's file, and our own first public page.

  What the record shows: Neither the Zhouyi nor the Ten Wings nor the Han and Song commentaries defines one. Birth hexagrams come from late imperial manuals: the Plum Blossom text's time rule, applied by calculators to people, and the 河洛理數 of 1632. So we name the method and its date, and do not present it as the only one.

• The hexagrams are humanity's oldest binary code, and Leibniz confirmed it in 1703.

  false

  Who says it: Popular pages, the old page writer's file and our first public page.

  What the record shows: Leibniz had worked out binary arithmetic by 1679. What Bouvet sent him in 1701 was Shao Yong's 11th-century arrangement, which does count from 0 to 63; the Zhouyi's own order does not. Whether the arrangement is binary at all is still argued (Ryan 1996, Maitre 2025), and modern computing does not descend from it.

• The Earlier Heaven arrangement of the trigrams and hexagrams is ancient and comes from Fuxi.

  false

  Who says it: The Song diagram tradition itself, which labelled the diagrams Fuxi's, and most popular pages.

  What the record shows: It first appears with Shao Yong in the 11th century; his school traced it to the Daoist Chen Tuan (died 989), and Zhu Xi printed it in 1188. No earlier source has it.

• Fuxi drew the eight trigrams after looking up at the sky and down at the earth.

  told as lore

  Who says it: The Xici, the Hanshu and every traditional account.

  What the record shows: A founding story, first written in the Xici in the Warring States period. Fuxi is a culture hero; nothing about the trigrams can be dated to him.

• King Wen wrote the hexagram texts in prison at Youli, and his son the Duke of Zhou wrote the line texts.

  told as lore

  Who says it: Sima Qian's Shiji (about 91 BCE), then the orthodox tradition from the Han on.

  What the record shows: The Shiji says only that King Wen 'is said to have' expanded the eight trigrams to sixty-four. The four-author scheme is Han. Scholars date the text to the late 9th century BCE, more than a century after him.

• Confucius wrote the Ten Wings.

  false

  Who says it: The Shiji, the Hanshu and imperial orthodoxy until the Qing.

  What the record shows: Ouyang Xiu wrote about 1050 that the Xici and the rest are 'not the sage's work, and not one person's words'. Modern scholarship dates the Wings from the Warring States to the early Han, by unknown hands.

• The received order of the hexagrams was fixed by King Wen and is the book's original order.

  told as lore

  Who says it: The tradition, and the order's own name.

  What the record shows: Its age and author are unknown. The Mawangdui silk copy of 168 BCE uses a different order built from the trigrams. We number by it because every tradition does.

• The I Ching is over three thousand years old.

  disputed

  Who says it: Most popular pages and our old page.

  What the record shows: The hexagram and line texts are dated to the last quarter of the 9th century BCE, about 2,800 years ago. Older roots are inferred, not documented.

• Shao Yong invented the Plum Blossom method after watching two sparrows fight on a plum branch.

  told as lore

  Who says it: The book's own opening story, our first public page and most sites on the method.

  What the record shows: The story is the book's. The book repeats a verse from Zhu Xi (1188), carries a preface dated to a year that never existed and names a Ming minister among its transmitters; the first author to mention it lived from 1485 to 1563. The method is attributed to Shao Yong.

• Shao Yong was the sole proponent of the image-and-number school.

  false

  Who says it: The old page writer's file and our first public page.

  What the record shows: The school runs from the Han (Meng Xi, Jing Fang) through Chen Tuan and Zhou Dunyi to Zhu Xi. Shao Yong was its most famous Song exponent, not its only one.

• The birth hexagram is a personality blueprint, and the hexagram it becomes is where a person is evolving to.

  unverified

  Who says it: The old page writer's file, our first public page and Western birth-hexagram sites.

  What the record shows: A modern reading with no source in the tradition and no evidence. We present the hexagram in the book's own terms: a situation, its moving line, what it becomes.

• The lower trigram is the subconscious and the upper the conscious self.

  unverified

  Who says it: The old page writer's file and our old page.

  What the record shows: The Wings do call the lower trigram inner and the upper outer. The psychology is modern and unsourced; we keep inner and outer and drop it.

• The time method makes casting with coins or yarrow stalks obsolete.

  false

  Who says it: The old page writer's file and our first public page.

  What the record shows: Casting remains the tradition's main practice. The Plum Blossom method is one later school, and its own book also casts from objects, sounds and written characters.

• The oracle works by synchronicity.

  unverified

  Who says it: C. G. Jung's foreword to the English Wilhelm translation (1949), and most Western introductions since.

  What the record shows: A hypothesis Jung offered in place of causality. No test of it exists; we say that he proposed it, and no more.

• The sixty-four hexagrams correspond to the sixty-four codons of DNA.

  unverified

  Who says it: Martin Schönberger (1973) and many web pages.

  What the record shows: Both sets have sixty-four members because both are built from a small alphabet in groups. Nothing beyond the count has been shown to match.

• The ring of hexagrams round the zodiac used by Human Design is a traditional I Ching teaching.

  false

  Who says it: 'I Ching astrology' sites that show the wheel without its origin.

  What the record shows: It is Shao Yong's circle, rotated by Ra Uru Hu in 1987 to 1989 so that hexagram 41 starts at 2° Aquarius. No Chinese source we found puts the hexagrams on degrees of the zodiac.

• The sixty-four English titles of the Wilhelm/Baynes translation are free to use as a set.

  disputed

  Who says it: Common practice among I Ching apps and sites, and our own engine before October 2026.

  What the record shows: A single title is a short phrase, but the set belongs to a translation registered in 1950 and renewed in 1977. We use our own titles, of which some plain ones coincide with theirs, and name theirs only one at a time, labelled.

• Our calculation applied true solar time and gave the exact six-bit string of a birth with zero margin for error.

  false

  Who says it: EsoTerrier's own page before 10 October 2026.

  What the record shows: No solar-time correction was ever applied, and the engine then summed Gregorian numbers, which gave the wrong hexagram for about nine births in ten. It now uses the lunar date the method requires.

Stories and lore

These are told as the tradition tells them.

Fuxi looks up and down. The Xici tells how the ancient ruler Baoxi, that is Fuxi, "looked up and contemplated the images in the heavens, looked down and contemplated the patterns on the earth", studied the markings of birds and beasts, and made the eight trigrams. The same Wing names the River Chart and the Luo Writing as models the sages followed; the dotted diagrams that carry those names appear only in the Song.

King Wen in prison. Sima Qian writes that the last Shang king imprisoned the Western Earl at Youli, and that there, "it is said", he expanded the eight trigrams into sixty-four. Later tradition has him writing the hexagram texts in his cell and his son, the Duke of Zhou, the line texts: a Han scheme.

The broken bindings. The Shiji also says that Confucius in old age loved the Changes and read his bamboo copy until its leather bindings broke three times. The Analects has him ask for a few more years to study the Changes at fifty, in a sentence whose key character another early text read as "also", which removes the book from it.

The recluse of Luoyang. Shao Yong refused office and lived at Luoyang in a house he called the Nest of Peace and Joy; he fitted all history into cycles of 129,600 years, and taught that one should observe things from the standpoint of things. Already in the Song he had a name for foreknowledge, and the Song History adds that people later credited him with predictions made after the event, which he "probably did not make".

The plum blossom and the sparrows. The book's first case: in a 辰 year, on the seventeenth day of the twelfth month, in the 申 hour, Master Kangjie, that is Shao Yong, was looking at plum blossom and saw two sparrows fighting over a branch and falling to the ground. He counted 5 for the year, 12 and 17 for the month and day, 34 in all: 兌 above. With 9 for the hour he had 43: 離 below. 43 on 6 left 1, the first line, so 49 革 Gé became 31 咸 Xián. And he told, the book says, how the next evening a girl picking blossom would be chased off by the gardener and fall. The method is attributed to him; the book was compiled long after his death, and the story is its legend.

Bouvet's letter. In February 1701 Leibniz explained his binary numbers to the Jesuit Joachim Bouvet in Beijing. Bouvet wrote back on 4 November 1701 that the figures of Fuxi were the same thing, and enclosed a woodcut of Shao Yong's circle and square. The letter reached Hanover in April 1703.

Jung's casts. Writing his foreword in Zurich in 1949, Jung asked the oracle what it thought of being introduced to the West, drew hexagram 50, the Cauldron, and then 29, and framed it all in his idea of synchronicity.

Wilhelm and Lao Naixuan. Richard Wilhelm, a missionary in Qingdao, translated the book with the scholar Lao Naixuan, leaning on the Song readings of Cheng Yi and Zhu Xi. His German of 1924, through Baynes and Jung, became the I Ching of the English-speaking world.

Evidence and criticism

What the text was. Since Shaughnessy's dissertation of 1983 and Kunst's of 1985, scholars read the Zhouyi as a Western Zhou divination record, compiled in the late 9th century BCE, without a moral philosophy of its own; the moral and cosmic reading came with the Wings. Rutt's translation of 1996 reads it that way, without the later commentary.

The manuscripts. The Mawangdui copy shows a different order and variant names; the Fuyang copy shows the text used with stock divination formulas; the Shanghai strips show a stable text with marks no one has explained. Together they show a book in use and still varying in the 3rd and 2nd centuries BCE.

The attributions. Ouyang Xiu rejected Confucius' authorship of the Wings in the 11th century, Qing scholars and modern sinologists finished the work, and reference works now treat the four sages as legend.

Shao Yong's name on the Plum Blossom book. The book repeats Zhu Xi's trigram verse, written in 1188 or later; its preface is dated to a year that did not exist; it names a Ming minister among its transmitters; the first author to mention it is Ming. The Song History's life of Shao Yong does not list it, and the Qing imperial catalogue does not list it at all. The method is his in name.

The binary question. Leibniz had binary arithmetic by 1679 and saw in 1703 that Shao Yong's arrangement matches it. Ryan finds no binary number system in China and argues that Shao Yong grasped the doubling without the arithmetic; Maitre argues the diagram is binary in form though built the other way round. Both agree it is Shao Yong's arrangement, not an ancient code.

The birth hexagram. No study tests the lifetime cast, and none is likely to: it has 64 hexagrams times 6 lines as outcomes, fixed by the calendar, so everyone born in the same lunar day and double hour shares one. Experienced readers on the Clarity forum are divided on it, and the site's founder doubts that it adds anything to asking the oracle in the ordinary way.

Arguments within the tradition. The Wings' moral reading against the diviners' use; the Han image-and-number schools against Wang Bi's reading by meaning; Zhu Xi's return to the book as an oracle anyone could consult; the Qing cataloguers' distrust of number books under Shao Yong's name; and today, practitioners' arguments over the start of the year and the stem against the branch.

What we can check. Only that we apply the rule as written, and as independent tools apply it: 56 of 56 timed test births agree. That is a check of the arithmetic.

Rights and names. The Chinese text, the Plum Blossom book, Legge's translation of 1882 and Wilhelm's German are public domain, so we quote them, briefly and credited. The English of Wilhelm and Baynes is in copyright: registered in 1950 and renewed in 1977. Single titles are short phrases, which copyright does not protect, but the sixty-four as a set belong to that translation, so our titles are our own and theirs appear one at a time, labelled: for hexagram 1, "Wilhelm/Baynes: The Creative". Our earlier pages gave their titles as the translation, and those pages are gone. The names of the hexagram characters in the Unicode standard follow those titles closely; we use only the characters. Human Design and Gene Keys are named as other systems, with their notices below.

Terms

Hexagram (卦)

A figure of six lines, each whole (yang) or broken (yin), read from the bottom up. There are sixty-four, each with a name and a text in the Zhouyi.

Trigram

A figure of three lines; there are eight. Every hexagram is a lower trigram, called inner, under an upper one, called outer. Named here 乾 Qián Heaven, 兌 Duì Lake, 離 Lí Fire, 震 Zhèn Thunder, 巽 Xùn Wind, 坎 Kǎn Water, 艮 Gèn Mountain, 坤 Kūn Earth.

Earlier Heaven order (先天)

Shao Yong's numbering of the trigrams, 乾 1, 兌 2, 離 3, 震 4, 巽 5, 坎 6, 艮 7, 坤 8, traditionally credited to Fuxi. The Plum Blossom method counts by it.

King Wen order

The received order of the sixty-four hexagrams, by which they are numbered 1 to 64. Its age and author are unknown; the name is the tradition's.

Line names

Lines are counted 1 to 6 from the bottom. The text names each by its place and nature: 初九 for a yang first line, 六二 for a yin second line, nine standing for yang and six for yin.

Moving line (動爻)

The line in motion. In a Plum Blossom time cast there is exactly one; it flips to give the transformed hexagram.

Transformed hexagram (變卦, 之卦)

The hexagram the figure becomes when its moving line flips: where the motion leads.

Nuclear hexagram (互卦)

The hexagram within: lines 2, 3 and 4 as its lower trigram and 3, 4 and 5 as its upper.

Inverse and opposite

The inverse (綜卦) is the figure turned upside down; the opposite (錯卦) has every line flipped.

King Wen pair

The hexagram each one is paired with in the received order: 1 with 2, 3 with 4 and so on. The pair is the inverse for 56 hexagrams and the opposite for the 8 that read the same upside down.

Judgment, Image, line text

The hexagram statement (卦辭), the Wings' one-sentence reading of the two trigrams (大象, the Great Image), and the statement for each line (爻辭).

Ten Wings (十翼)

The commentaries bound with the Zhouyi: the Tuan, the Xiang and the Xici in two parts each, the Wenyan, Shuogua, Xugua and Zagua. Written by later hands, though tradition credited Confucius.

Plum Blossom method (梅花易數)

A way of casting a hexagram from numbers, the time of day among them, set out in a book compiled in the Ming period under Shao Yong's name.

Lifetime cast (終身卦)

The calculators' name for the Plum Blossom time rule applied to a birth. The book itself does not use the term.

Birth hexagram

Our name for the result. We do not call it natal, a word that reads as astrology, nor attach King Wen's name to it, as some websites do: the King Wen number is only the numbering.

Double hour (時辰)

One of the twelve two-hour periods named by the Earthly Branches, from 子 (23:00 to 00:59) to 亥 (21:00 to 22:59).