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I Ching Hexagram Lookup (六十四卦)

Identifies one of the 64 hexagrams (六十四卦, liushisi gua) from its King Wen number, name, two trigrams or line digits and returns its lines, trigrams, nuclear (互卦, hugua), inverse (综卦, zonggua) and opposite (错卦, cuogua) hexagrams, its Jing Fang palace (京房八宫, Jingfang bagong) with 世/应 (shi/ying) lines, and the received judgment text (卦辞, guaci).

King Wen number (optional)Hexagram number 1–64 in the King Wen sequence (1 = 乾, 64 = 未济). Give exactly one of king_wen_number, name, lines or the trigram pair. Name (optional)Chinese name (屯, 水雷屯, 乾为天; traditional forms accepted), pinyin (zhun; ambiguous pinyin such as qian or bi is rejected with the candidates) or Wilhelm/Baynes title (Difficulty at the Beginning). Upper trigram (optional)Upper (outer) trigram, in any form accepted by bagua (坎, kan, water, ☵, 010). Must be given together with lower_trigram. Lower trigram (optional)Lower (inner) trigram, in any form accepted by bagua. Lines (bottom→top) (optional)Six digits from line 1 (bottom) to line 6 (top): 1/0 for yang/yin, or 6/7/8/9 (老阴/少阳/少阴/老阳) as produced by yarrow or coin casting.

When to use

You need to identify or describe a hexagram, convert between its number, name, trigram pair and line pattern, or find its derived hexagrams and palace position.

Do not use when: You have moving lines and need the changed hexagram and reading rule (use hexagram-change), or you need to cast a hexagram from a date or numbers (use meihua-yishu).

Formula

lower trigram = lines 1–3, upper trigram = lines 4–6; nuclear = lines 2,3,4 + 3,4,5; inverse = reversed line order; opposite = each line flipped; binary_value = Σ line_i · 2^(i−1); 应 = 世 ± 3

King Wen order, names and lines from the received text; English titles from Wilhelm/Baynes (1950). Palaces follow the Jing Fang (京房) system: flip lines 1–5 of the palace hexagram in turn, flip line 4 back for 游魂 and restore the lower trigram for 归魂. Traditional cultural reference calculation; not a prediction and not medical, legal or financial advice.

Inputs

Parameter	Type	Required	Description
`king_wen_number`	integer	no	Hexagram number 1–64 in the King Wen sequence (1 = 乾, 64 = 未济). Give exactly one of king_wen_number, name, lines or the trigram pair. Range: ≥ 1, ≤ 64
`name`	string	no	Chinese name (屯, 水雷屯, 乾为天; traditional forms accepted), pinyin (zhun; ambiguous pinyin such as qian or bi is rejected with the candidates) or Wilhelm/Baynes title (Difficulty at the Beginning).
`upper_trigram`	string	no	Upper (outer) trigram, in any form accepted by bagua (坎, kan, water, ☵, 010). Must be given together with lower_trigram.
`lower_trigram`	string	no	Lower (inner) trigram, in any form accepted by bagua.
`lines`	string	no	Six digits from line 1 (bottom) to line 6 (top): 1/0 for yang/yin, or 6/7/8/9 (老阴/少阳/少阴/老阳) as produced by yarrow or coin casting.

Outputs

Output	Type	Description
`number`	integer	Position 1–64 in the King Wen sequence.
`name_cn`	string	Simplified Chinese name.
`full_name_cn`	string	Traditional descriptive name with the trigram images, e.g. 水雷屯 or 乾为天.
`pinyin`	string	Hanyu pinyin of the name.
`english`	string	Wilhelm/Baynes title.
`symbol`	string	Unicode hexagram symbol (U+4DC0 + number − 1).
`lines`	string	Six digits from line 1 to line 6; 1 = yang, 0 = yin.
`lines_text`	string	Traditional line titles from bottom to top, e.g. 初九六二 … 上六.
`upper_trigram`	string	Outer trigram (lines 4–6) with pinyin, symbol and nature.
`lower_trigram`	string	Inner trigram (lines 1–3) with pinyin, symbol and nature.
`nuclear_hexagram`	string	Hexagram formed by lines 2-3-4 (lower) and 3-4-5 (upper).
`inverse_hexagram`	string	The hexagram turned upside down (lines reversed).
`opposite_hexagram`	string	All six lines flipped yin↔yang.
`palace`	string	Jing Fang (京房) palace the hexagram belongs to, with its element.
`palace_position`	string	本宫 / 一世 … 五世 / 游魂 / 归魂 position within the palace.
`shi_line`	integer	Position (1–6) of the 世 line: 6 for the palace hexagram, 1–5 for generations 1–5, 4 for 游魂, 3 for 归魂.
`ying_line`	integer	Position of the 应 line, three lines away from 世.
`judgment_text`	string	Received classical judgment text of the 周易 (Zhouyi), simplified characters.
`sequence_pair`	string	Partner hexagram in the King Wen pairing (2n−1, 2n): its inverse, or its opposite for the eight symmetric hexagrams.
`binary_value`	integer	Integer of the six bits with the top line as the most significant bit (乾 = 63, 坤 = 0).
`notes`	string	Conventions used.

Example

Hexagram 1 乾: {"king_wen_number":1} → {"name_cn":"乾","symbol":"䷀","lines":"111111","nuclear_hexagram":"1 乾 Qian (The Creative) ䷀","inverse_hexagram":"1 乾 Qian (The Creative) ䷀","opposite_hexagram":"2 坤 Kun (The Receptive) ䷁","palace":"乾宫 (Qian palace, Metal)","palace_position":"本宫卦 (Bengong, palace hexagram)","shi_line":6,"ying_line":3,"binary_value":63}

Lines 100010 (屯): {"lines":"100010"} → {"number":3,"name_cn":"屯","full_name_cn":"水雷屯","upper_trigram":"坎 Kan ☵ (Water)","lower_trigram":"震 Zhen ☳ (Thunder)","nuclear_hexagram":"23 剥 Bo (Splitting Apart) ䷖","inverse_hexagram":"4 蒙 Meng (Youthful Folly) ䷃","opposite_hexagram":"50 鼎 Ding (The Cauldron) ䷱","palace":"坎宫 (Kan palace, Water)","palace_position":"二世卦 (Ershi, second generation)","shi_line":2,"ying_line":5,"sequence_pair":"4 蒙 Meng (Youthful Folly) ䷃","binary_value":17}

GET https://tttkmbb.com/api/v1/calculate/hexagram-lookup?king_wen_number=1

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/hexagram-lookup (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/hexagram-lookup · Markdown: https://tttkmbb.com/yijing/hexagram-lookup.md · JSON definition: https://tttkmbb.com/yijing/hexagram-lookup.json
MCP: server https://tttkmbb.com/mcp, tool lookup_iching_hexagram
OpenAPI operationId: lookup_iching_hexagram
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – List of hexagrams of the I Ching (reference)
Wikipedia – King Wen sequence (reference)
Wilhelm R. & Baynes C. F. (1950) The I Ching or Book of Changes, Bollingen Series XIX, Princeton University Press (textbook)

FAQ

In which order are the six digits?

Bottom to top: the first digit is line 1 (初), the sixth is line 6 (上), the order in which a hexagram is built when casting. Digits 6/7/8/9 are read as old yin / young yang / young yin / old yang, so 6 and 8 are yin and 7 and 9 are yang.

What are the nuclear, inverse and opposite hexagrams?

The nuclear hexagram (互卦) uses lines 2-3-4 as its lower and 3-4-5 as its upper trigram; the inverse (综卦) is the hexagram read upside down; the opposite (错卦) flips every line. The King Wen sequence pairs each hexagram with its inverse, or with its opposite when the inverse is itself.

What do 世 and 应 mean?

In the Jing Fang palace system each hexagram has a self line (世爻) whose position depends on its generation within the palace (6, 1–5, 4 for 游魂, 3 for 归魂) and a response line (应爻) three positions away; Liu Yao charts use them.

Related calculators

Hexagram Change Calculator (变卦) — Apply moving lines to get the changed hexagram and the reading rule.
Bagua Trigram Lookup (八卦) — Attributes of the two component trigrams.
Liu Yao Hexagram Chart (六爻) — Six-line (六爻) chart with 世/应 and palace for divination records.