I Ching Hexagram Calculator (Three-Coin Method)
The I Ching, or Book of Changes, is one of the oldest books in the world. Toss three virtual coins six times to build a hexagram, or enter the results of real coins you tossed yourself.
For entertainment and self-reflection: The I Ching is a classic of Chinese literature and philosophy; the casting here uses your browser’s random number generator and the readings are short summaries for reflection. Nothing on this page is a prediction, and it is not financial, medical, psychological or legal advice. Use it as a prompt for thought, not as a basis for decisions.
Cast a hexagram
Enter tosses from real coins
For each line, from the bottom (line 1) up, add the coins: heads = 3, tails = 2. Each line totals 6, 7, 8 or 9.
How the three-coin method works
An I Ching hexagram is a stack of six lines, each either solid (yang) or broken (yin). It is built from the bottom up, one line per throw. With the three-coin method you toss three coins together and add them: heads count 3 and tails count 2. The total is always 6, 7, 8 or 9:
| Total | Coins | Line | Chance |
|---|---|---|---|
| 6 | three tails | old yin: broken, changing | 1 in 8 |
| 7 | two tails, one head | young yang: solid, stable | 3 in 8 |
| 8 | two heads, one tail | young yin: broken, stable | 3 in 8 |
| 9 | three heads | old yang: solid, changing | 1 in 8 |
After six throws you have your primary hexagram. Lines that came up 6 or 9 are called changing or moving lines. They are thought to be at a turning point, about to become their opposite. If you have any, flip each one (a changing yin becomes yang, a changing yang becomes yin) to get a second figure, often called the relating or changed hexagram. Traditionally the first figure describes the present situation and the second shows where it is heading. If no lines change, the reading rests on the first hexagram alone.
Each hexagram is also two trigrams, three-line figures linked with natural images: Heaven, Earth, Thunder, Water, Mountain, Wind, Fire and Lake. The lower trigram (lines 1 to 3) is read as the inner or earlier part of the situation and the upper trigram (lines 4 to 6) as the outer or later part. Eight trigrams combined in every possible way give 8 × 8 = 64 hexagrams.
This calculator follows the received King Wen sequence, the order used in almost every edition of the book, so hexagram 1 is the Creative and hexagram 64 is Before Completion. The virtual coins use your browser’s cryptographic random number generator, so every toss has exactly the traditional odds. If you prefer to toss real coins, open "Enter tosses from real coins" and type the six totals.
Worked example
Suppose the six throws, from bottom to top, total 7, 8, 9, 7, 8, 8. That gives the lines solid, broken, solid, solid, broken, broken. The lower three (solid, broken, solid) form Fire; the upper three (solid, broken, broken, reading upward) form Thunder. Thunder over Fire is hexagram 55, Feng, Abundance, an image of a peak of fullness, like the sun at noon.
Line 3 came up 9, an old yang, so it changes. Turning that solid line into a broken one makes the lower trigram Thunder as well, giving Thunder over Thunder: hexagram 51, Zhen, Shock. A reader might take that as "a full, bright period, with something startling coming that will test your composure". The calculator does this arithmetic for you and shows both hexagrams.
A short history of the Book of Changes
The core of the I Ching, known as the Zhouyi (Changes of Zhou), took shape in the Western Zhou dynasty in China, roughly three thousand years ago. It consists of the 64 hexagrams, a brief "judgement" for each, and a short statement for each line. Scholars think it grew out of divination practices in which a question would be put and an answer drawn by a random procedure. Over the following centuries, commentaries known as the Ten Wings were added. Tradition credits them to Confucius; modern scholars date them to the late Warring States and early Han periods and see them as the work of several hands. With the Ten Wings, the book became a work of philosophy as well as divination, and in the Han dynasty it was made one of the Confucian classics.
The oldest method of casting uses fifty yarrow stalks divided and counted in a lengthy procedure. The three-coin method is a later, quicker substitute and has been widely used for many centuries. Its odds are slightly different: with yarrow stalks a changing yang line is three times as likely as a changing yin line, while with coins both have a 1 in 8 chance.
The book has had a long life outside China too. The German philosopher Gottfried Wilhelm Leibniz, in a paper of 1703 on binary arithmetic, noted that an ordering of the hexagrams he had received from a Jesuit correspondent in China matched counting in binary. James Legge’s English translation of 1882 made the text widely available to English readers, and Richard Wilhelm’s German translation of 1924, later put into English with a foreword by Carl Jung, became a counterculture favourite in the 1960s. Archaeology has added new evidence: a manuscript found at Mawangdui in 1973, from the second century BCE, preserves the text in a different hexagram order.
Using the I Ching for reflection
Many modern readers use the I Ching less as an oracle and more as a structured way of thinking. The hexagram texts are full of images about timing, restraint, cooperation, difficulty and renewal. A random draw puts one of these images in front of you and invites you to ask how it might apply. Some practical tips:
- Ask open questions. "What should I understand about this situation?" tends to work better than "Will I get the job?". The book speaks in images, not yes or no.
- Write it down. Note the date, the question, the hexagram and your first reaction. Looking back weeks later is often the most interesting part.
- Read the trigrams. Even without a book, the pair of images (Water over Mountain, Wind over Lake) can be a useful prompt.
- Do not keep re-casting. Hexagram 4 itself advises against asking the same question again and again. If an answer does not fit, sit with it rather than fishing for a better one.
- Keep decisions grounded. Use the reflection to clarify what you think, then make real decisions on real information.
All 64 hexagrams
The table lists every hexagram in King Wen order with its traditional name, a common English title and its trigrams (upper over lower). The short summaries shown with your result are our own paraphrases, informed by Legge’s public-domain translation.
| # | Name | Trigrams | |
|---|---|---|---|
| 1 | ䷀ | Qian — The Creative | Heaven over Heaven |
| 2 | ䷁ | Kun — The Receptive | Earth over Earth |
| 3 | ䷂ | Zhun — Difficulty at the Beginning | Water over Thunder |
| 4 | ䷃ | Meng — Youthful Inexperience | Mountain over Water |
| 5 | ䷄ | Xu — Waiting | Water over Heaven |
| 6 | ䷅ | Song — Conflict | Heaven over Water |
| 7 | ䷆ | Shi — The Army | Earth over Water |
| 8 | ䷇ | Bi — Holding Together | Water over Earth |
| 9 | ䷈ | Xiao Chu — Small Taming | Wind over Heaven |
| 10 | ䷉ | Lü — Treading Carefully | Heaven over Lake |
| 11 | ䷊ | Tai — Peace | Earth over Heaven |
| 12 | ䷋ | Pi — Standstill | Heaven over Earth |
| 13 | ䷌ | Tong Ren — Fellowship | Heaven over Fire |
| 14 | ䷍ | Da You — Great Possession | Fire over Heaven |
| 15 | ䷎ | Qian — Modesty | Earth over Mountain |
| 16 | ䷏ | Yu — Enthusiasm | Thunder over Earth |
| 17 | ䷐ | Sui — Following | Lake over Thunder |
| 18 | ䷑ | Gu — Repairing What Is Spoiled | Mountain over Wind |
| 19 | ䷒ | Lin — Approach | Earth over Lake |
| 20 | ䷓ | Guan — Contemplation | Wind over Earth |
| 21 | ䷔ | Shi He — Biting Through | Fire over Thunder |
| 22 | ䷕ | Bi — Grace | Mountain over Fire |
| 23 | ䷖ | Bo — Splitting Apart | Mountain over Earth |
| 24 | ䷗ | Fu — Return | Earth over Thunder |
| 25 | ䷘ | Wu Wang — Innocence | Heaven over Thunder |
| 26 | ䷙ | Da Chu — Great Taming | Mountain over Heaven |
| 27 | ䷚ | Yi — Nourishment | Mountain over Thunder |
| 28 | ䷛ | Da Guo — Great Excess | Lake over Wind |
| 29 | ䷜ | Kan — The Abyss | Water over Water |
| 30 | ䷝ | Li — Clarity | Fire over Fire |
| 31 | ䷞ | Xian — Attraction | Lake over Mountain |
| 32 | ䷟ | Heng — Duration | Thunder over Wind |
| 33 | ䷠ | Dun — Retreat | Heaven over Mountain |
| 34 | ䷡ | Da Zhuang — Great Power | Thunder over Heaven |
| 35 | ䷢ | Jin — Progress | Fire over Earth |
| 36 | ䷣ | Ming Yi — Darkening of the Light | Earth over Fire |
| 37 | ䷤ | Jia Ren — The Family | Wind over Fire |
| 38 | ䷥ | Kui — Opposition | Fire over Lake |
| 39 | ䷦ | Jian — Obstruction | Water over Mountain |
| 40 | ䷧ | Xie — Deliverance | Thunder over Water |
| 41 | ䷨ | Sun — Decrease | Mountain over Lake |
| 42 | ䷩ | Yi — Increase | Wind over Thunder |
| 43 | ䷪ | Guai — Breakthrough | Lake over Heaven |
| 44 | ䷫ | Gou — Coming to Meet | Heaven over Wind |
| 45 | ䷬ | Cui — Gathering Together | Lake over Earth |
| 46 | ䷭ | Sheng — Pushing Upward | Earth over Wind |
| 47 | ䷮ | Kun — Exhaustion | Lake over Water |
| 48 | ䷯ | Jing — The Well | Water over Wind |
| 49 | ䷰ | Ge — Revolution | Lake over Fire |
| 50 | ䷱ | Ding — The Cauldron | Fire over Wind |
| 51 | ䷲ | Zhen — Shock | Thunder over Thunder |
| 52 | ䷳ | Gen — Keeping Still | Mountain over Mountain |
| 53 | ䷴ | Jian — Gradual Development | Wind over Mountain |
| 54 | ䷵ | Gui Mei — The Marrying Maiden | Thunder over Lake |
| 55 | ䷶ | Feng — Abundance | Thunder over Fire |
| 56 | ䷷ | Lü — The Traveller | Fire over Mountain |
| 57 | ䷸ | Xun — The Gentle | Wind over Wind |
| 58 | ䷹ | Dui — Joy | Lake over Lake |
| 59 | ䷺ | Huan — Dispersion | Wind over Water |
| 60 | ䷻ | Jie — Limitation | Water over Lake |
| 61 | ䷼ | Zhong Fu — Inner Truth | Wind over Lake |
| 62 | ䷽ | Xiao Guo — Small Excess | Thunder over Mountain |
| 63 | ䷾ | Ji Ji — After Completion | Water over Fire |
| 64 | ䷿ | Wei Ji — Before Completion | Fire over Water |
Frequently asked questions
How does the I Ching coin method work?
Toss three coins six times. Count heads as 3 and tails as 2, and add each throw to get 6, 7, 8 or 9. Odd totals give solid lines and even totals give broken lines, built from the bottom up. Totals of 6 and 9 are changing lines.
What are changing lines?
Lines that come up 6 (old yin) or 9 (old yang). They are seen as being at a turning point. Flipping them gives a second hexagram that traditionally shows where the situation is heading.
What if I get no changing lines?
Then there is only one hexagram, and the reading rests on its main text. With three coins this happens about 18% of the time, since each line has a 3 in 4 chance of being stable.
Is the yarrow stalk method different?
Yes. It is older and slower, and its odds differ: with yarrow stalks a changing yang line comes up three times as often as a changing yin line, while with coins both have a 1 in 8 chance.
How old is the I Ching?
The core text dates from the Western Zhou dynasty, roughly three thousand years ago. The philosophical commentaries called the Ten Wings were added several centuries later.
Are the virtual coins truly random?
They use your browser’s cryptographic random number generator, which gives each coin an even 50/50 chance. Nothing is stored or sent anywhere.
Can the I Ching predict the future?
There is no scientific evidence that it can. Many people value it as a classic text and as a tool for reflection, which is how this page presents it.
Sources and further reading
- Legge, J. (trans.) The Yi King, Sacred Books of the East vol. 16, Oxford, 1882 (public domain).
- Wilhelm, R. and Baynes, C. F. (trans.) The I Ching or Book of Changes, Pantheon Books (Bollingen Series XIX), 1950; 3rd ed. Princeton University Press, 1967.
- Shaughnessy, E. L. I Ching: The Classic of Changes (Mawangdui text), Ballantine, 1997.
- Smith, R. J. The I Ching: A Biography, Princeton University Press, 2012.
- Leibniz, G. W. "Explication de l’arithmétique binaire", 1703.
- Wikipedia: "I Ching" and "I Ching divination".
By Stanley King · About 8calc · Last reviewed October 2026