I Ching Hexagrams: The 64 Symbols of the Book of Changes

What Is a Hexagram?

A hexagram (gua, 卦) is a figure composed of six horizontal lines stacked from bottom to top. Each line is either solid (yang, ⚊) or broken (yin, ⚋). With two possibilities for each of six positions, the total number of unique hexagrams is 2⁶ = 64.

The word "hexagram" comes from Greek (hex = six, gramma = line/figure), but the Chinese term gua carries deeper meaning. It implies a "hanging" or "suspended" image, something that makes the invisible visible. In the earliest commentaries, the hexagrams are described as images (xiang, 象) that the ancient sages observed in nature and recorded as line configurations.

Each hexagram carries a name, a judgment text (attributed to King Wen of Zhou, c. 1100 BCE), and six individual line texts (attributed to his son, the Duke of Zhou). The Confucian tradition later added extensive commentaries known as the Ten Wings, which include the Image (Xiang), the Commentary on the Decision (Tuan), and the Great Treatise (Da Zhuan), among others.

The Eight Trigrams: Foundation of Every Hexagram

Before there were hexagrams, there were trigrams (three-line figures). The eight trigrams represent the fundamental forces of nature:

According to legend, the sage-king Fu Xi (c. 3000 BCE) derived the trigrams from observing the patterns of the natural world: the markings on a tortoise shell, the tracks of birds and animals, the configurations of the stars. The Da Zhuan (Great Treatise) states: "In ancient times, Bao Xi [Fu Xi] ruled the world. He looked upward and contemplated the images in the heavens, looked downward and contemplated the patterns on earth." The eight trigrams provided the building blocks; the 64 hexagrams provided the complete system.

For a full treatment of each trigram, see our guide to the eight trigrams of the I Ching.

How Two Trigrams Become One Hexagram

Every hexagram is formed by placing one trigram on top of another. The lower trigram (lines 1, 2, 3) is called the inner or lower trigram. The upper trigram (lines 4, 5, 6) is called the outer or upper trigram. Since either position can hold any of the eight trigrams, the total number of combinations is 8 x 8 = 64.

The meaning of each hexagram arises from the interaction of its two component trigrams. Hexagram 11 (T'ai / Peace), for example, places Earth (K'un) above Heaven (Ch'ien). The light, rising energy of Heaven moves upward into Earth, while the heavy, descending energy of Earth sinks downward into Heaven. The two forces meet and mingle: this is peace, harmony, and the smooth functioning of all things. By contrast, Hexagram 12 (P'i / Standstill) reverses the arrangement: Heaven above, Earth below. The energies move away from each other. There is no meeting, no communication, no flow.

This principle (that the same two elements produce opposite meanings depending on their arrangement) runs through the entire system. It is the I Ching's way of expressing that context and relationship determine meaning, not the elements in isolation.

The King Wen Sequence: Why the Order Matters

The standard ordering of the 64 hexagrams is attributed to King Wen of Zhou, the founder of the Zhou dynasty, who is said to have arranged them while imprisoned by the last Shang king. This sequence is not random or arbitrary. It follows a pattern based on paired opposition.

The 64 hexagrams are arranged in 32 pairs. In most pairs, the second hexagram is the inversion (the first hexagram turned upside down). Where an inversion produces the same hexagram (as with hexagrams composed entirely of yang or entirely of yin lines), the second member of the pair is instead the complement (every yin line becomes yang and vice versa).

The sequence begins with Hexagram 1 (The Creative, pure yang) and Hexagram 2 (The Receptive, pure yin), establishing the fundamental polarity. It ends with Hexagram 63 (After Completion, where every line is in its "correct" position) and Hexagram 64 (Before Completion, where no line is in its correct position). The message is striking: the I Ching does not end with completion. It ends with incompleteness, signaling that change never stops.

The Xu Gua (Sequence of the Hexagrams), one of the Ten Wings, provides a narrative explanation for why each hexagram follows the one before it: "After the Creative and the Receptive come Difficulty at the Beginning; when things are first born, they are filled with youthful folly..." This running commentary treats the hexagram sequence as a story of human experience unfolding over time.

Upper and Lower Trigrams: The Inner and Outer World

The distinction between the lower and upper trigrams is one of the most important principles in hexagram interpretation. The lower trigram represents the inner world: the personal, the subjective, the situation as experienced from within. The upper trigram represents the outer world: the social, the objective, the situation as it appears from outside.

Alfred Huang, in The Complete I Ching, further associates the lower trigram with the coming force and the upper with the going force. What is below is what is arriving, what is growing; what is above is what is departing, what is receding. This adds a temporal dimension to the spatial one: the lower trigram points toward what is emerging, the upper toward what is fading.

Within each trigram, the three lines also carry positional meaning. Line 1 (bottom of the lower trigram) represents the beginning, the entry point, the situation before action. Line 2 (middle of the lower trigram) is the centre of the inner world and often the most favourable position for a yielding (yin) line. Line 5 (middle of the upper trigram) represents the ruler's position, the place of greatest influence and responsibility. Line 6 (top) represents excess, the point where a situation has gone as far as it can and must reverse.

Nuclear Trigrams: The Hidden Structure

Every hexagram contains two additional trigrams hidden within its structure. These are called nuclear trigrams (hu gua, 互卦). The lower nuclear trigram is formed by lines 2, 3, and 4. The upper nuclear trigram is formed by lines 3, 4, and 5. Together, these nuclear trigrams form a nuclear hexagram: a hexagram within a hexagram.

The nuclear hexagram reveals the inner tendency of the outer situation. It shows what is developing beneath the surface. Hellmut Wilhelm, in Change: Eight Lectures on the I Ching, describes the nuclear hexagram as the "seed situation" that is latent within the visible one. Not all traditional interpreters use nuclear trigrams, but they add a layer of structural depth for those who want to read the hexagram system at multiple levels simultaneously.

For example, Hexagram 3 (Difficulty at the Beginning) has Water over Thunder as its primary trigrams. Its nuclear trigrams are Mountain (lines 2-3-4) and Earth (lines 3-4-5), forming nuclear hexagram 23 (Splitting Apart). This suggests that beneath the surface of the difficult beginning lies a process of necessary dissolution, the clearing away of what cannot sustain itself.

Hexagram Pairs: Inversion and Complementarity

As noted in the King Wen sequence section, hexagrams are arranged in pairs. The two operations that generate pairs are:

Inversion (fan dui, 反對): The hexagram is turned upside down. What was the bottom line becomes the top line. In most cases, this produces a different hexagram. For example, Hexagram 3 (Water over Thunder) inverted becomes Hexagram 4 (Mountain over Water). What was difficulty at the beginning becomes youthful folly, the naivety that follows the initial shock of birth.

Complementarity (pang tong, 旁通): Every line changes to its opposite. Yang becomes yin, yin becomes yang. This operation is used for the eight hexagrams that are symmetrical (they look the same upside down): Hexagrams 1 and 2, 27 and 28, 29 and 30, 61 and 62.

These pairing relationships encode a structural principle: every situation contains its opposite. The I Ching does not recognize any condition as final. Every hexagram implies the existence of its pair, its shadow, its reversal.

The Eight Palaces: Another Way to Organize the 64

The King Wen sequence is not the only way to organize the 64 hexagrams. The Eight Palace system, attributed to the Han dynasty scholar Jing Fang (77-37 BCE), groups the hexagrams into eight families of eight, each family governed by one of the eight trigrams doubled (Hexagram 1, pure Heaven; Hexagram 2, pure Earth; etc.).

Within each palace, the hexagrams are generated by a systematic sequence of line changes starting from the base hexagram. The first change affects line 1, then line 2, then line 3, then line 4, then line 5, then lines 4-3-2-1 return to their original states while new changes cascade. This produces a "family" of eight hexagrams that share an energetic lineage.

The Eight Palace system is particularly important in the Mei Hua (Plum Blossom) school of I Ching divination and in the Wen Wang Gua (King Wen hexagram) method used in traditional Chinese astrology.

Changing Lines and Hexagram Transformation

The hexagram system becomes dynamic through the concept of changing lines. When you consult the I Ching using the three-coin method or the yarrow stalk method, each line you generate has one of four values:

When a hexagram contains changing lines (old yin or old yang), it transforms into a second hexagram. The first hexagram describes the present situation; the second describes what it is becoming. The individual line texts for the changing lines provide specific guidance about the transition.

This mechanism is what makes the I Ching a living system rather than a static reference. A reading with no changing lines describes a settled state. A reading with one changing line points to a specific pressure point. A reading with multiple changing lines describes a situation in rapid flux. The yarrow stalk method, which is older and more mathematically complex than the coin method, produces changing lines less frequently, making each one more weighted. For the full method, see our guide to consulting the I Ching.

All 64 Hexagrams at a Glance

The following table lists all 64 hexagrams in the King Wen sequence with their traditional names (Wilhelm-Baynes translation) and component trigrams:

Note that the names given here follow the Wilhelm-Baynes translation. Other translations use different English renderings. Alfred Huang, for instance, translates Hexagram 1 as "Initiating" rather than "The Creative," and Hexagram 2 as "Responding" rather than "The Receptive." Each translation choice reflects a different interpretive emphasis.

How to Read a Hexagram in Practice

When you cast a hexagram (whether by coins, yarrow stalks, or another method), you read it through several layers:

The Wilhelm-Baynes translation adds the Commentary on the Decision (Tuan) and the Commentary on the Image (Xiang) for each hexagram, providing additional interpretive material. Stephen Karcher's Total I Ching adds oracle keywords and a "Contrasts" section that highlights the hexagram's relationship to its pair.

Jung, Synchronicity, and the Hexagram System

Carl Gustav Jung wrote the foreword to the first English edition of the Wilhelm-Baynes I Ching (1950), and in it he described his own experience of consulting the oracle. Jung's concept of synchronicity (meaningful coincidence that cannot be explained by causal mechanisms) provided the first Western theoretical framework for how the I Ching might work.

Jung proposed that the hexagram drawn at a particular moment is not random but is connected to the psychological state of the questioner through a principle he called the "acausal connecting principle." The hexagram does not cause anything and is not caused by anything. Instead, it participates in the same meaningful pattern as the question and the questioner's situation.

This concept aligned with the I Ching's own philosophy, which holds that every moment has a quality (shi, 時), a specific configuration of energies, and the hexagram reflects that quality. Jung's work gave Western readers permission to take the I Ching seriously as a psychological tool without requiring belief in supernatural causation. For a thorough treatment of Jung's relationship with the I Ching, see our article on I Ching and Carl Jung's synchronicity.

Hexagrams and Binary Mathematics

In 1703, the German mathematician Gottfried Wilhelm Leibniz received a copy of the Fu Xi sequence of hexagrams (a different arrangement from the King Wen sequence, based on a systematic binary progression) from the Jesuit missionary Joachim Bouvet. Leibniz immediately recognized that the hexagram system was structurally identical to the binary number system he had been developing.

In the Fu Xi sequence, if yin (broken line) is assigned the value 0 and yang (solid line) is assigned the value 1, the hexagrams map to binary numbers 0 through 63. Hexagram K'un (all yin) = 000000 = 0. Hexagram Ch'ien (all yang) = 111111 = 63. Every hexagram in between corresponds to a specific binary number when read from bottom to top.

This has led some modern interpreters (notably Terence McKenna with his Timewave Zero theory and Martin Schonberger in The I Ching and the Genetic Code) to propose deeper mathematical connections between the hexagram system and other binary structures in nature, including the 64 codons of the genetic code. These parallels remain speculative but continue to generate scholarly and popular interest.

Hermetic Parallels: The Oracle Tradition Across Cultures

The I Ching stands within a global tradition of oracle systems that use structured symbolic languages to map the dynamics of change. In the Hermetic tradition of the Western world, a similar impulse produced systems like the Tarot, geomancy, and the astrological chart: each one a symbolic framework for reading the quality of a moment or situation.

The Hermetic principle "As above, so below" (attributed to Hermes Trismegistus) finds a direct parallel in the I Ching's upper and lower trigram structure. What is above (the outer trigram, the macrocosm, the situation as it manifests externally) mirrors what is below (the inner trigram, the microcosm, the situation as it is experienced internally). Both traditions hold that the part contains the pattern of the whole.

The Hermetic Synthesis Course examines these cross-cultural parallels in depth, tracing the shared principles that connect Eastern and Western oracle systems.