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Five Elements Relation (五行生克)

Determines the Wuxing (五行) relation between two elements — generating (相生, xiangsheng), controlling (相克, xiangke) or same — and returns the full generating and controlling cycles plus the traditional correspondence profile of each element (direction, season, colour, planet, organs, taste, emotion, climate, Hetu numbers, stems, branches, trigrams).

When to use

You need to know how two of Wood, Fire, Earth, Metal and Water relate in the five-element cycles, or the classical correspondences of an element, e.g. when interpreting stems, branches, trigrams or a Bazi chart.

Do not use when: You need relations between specific stems and branches such as 六合 or 三合 (use stem-branch-relations) or trigram attributes (use bagua).

Formula

generating (相生): 木→火→土→金→水→木; controlling (相克): 木克土, 土克水, 水克火, 火克金, 金克木; A generates B if B follows A in the generating cycle, A controls B if B is two steps after A

Correspondences are the standard Han-dynasty tables (五行学说) as summarised in the Wuxing reference; Hetu numbers 水1/6 火2/7 木3/8 金4/9 土5/10. Traditional cultural reference calculation; not a prediction and not medical, legal or financial advice.

Inputs

Parameter	Type	Unit	Required	Description
`element_a`	enum: wood \| fire \| earth \| metal \| water		yes	Element A of the pair (wood/fire/earth/metal/water; Chinese 木火土金水 accepted).
`element_b`	enum: wood \| fire \| earth \| metal \| water		yes	Element B of the pair (wood/fire/earth/metal/water; Chinese 木火土金水 accepted).

Outputs

Output	Type	Description
`relation`	string	Relation of element A to element B in words, with the Chinese formula.
`relation_type`	string	generates, is_generated_by, controls, is_controlled_by or same (from A's point of view).
`relation_cn`	string	Chinese formula, e.g. 木生火, 水克火 or 比和.
`generating_cycle`	string	The full 相生 sequence.
`controlling_cycle`	string	The full 相克 sequence.
`what_a_generates`	string	Element produced by A (its child).
`what_generates_a`	string	Element that produces A (its parent).
`what_a_controls`	string	Element restrained by A.
`what_controls_a`	string	Element that restrains A.
`element_a_profile`	object	Direction, season, colour, planet, yin organ (脏), yang organ (腑), taste, emotion, climate, Hetu numbers, heavenly stems, earthly branches, trigrams and sense organ.
`element_b_profile`	object	The same correspondences for element B.

Example

Wood and Fire: {"element_a":"wood","element_b":"fire"} → {"relation":"Wood generates Fire (木生火)","relation_type":"generates","relation_cn":"木生火","what_a_generates":"Fire (火)","what_a_controls":"Earth (土)","what_controls_a":"Metal (金)","what_generates_a":"Water (水)"}

Water and Fire: {"element_a":"water","element_b":"fire"} → {"relation":"Water controls Fire (水克火)","relation_type":"controls","relation_cn":"水克火","what_a_generates":"Wood (木)","what_generates_a":"Metal (金)"}

GET https://tttkmbb.com/api/v1/calculate/five-elements?element_a=wood&element_b=fire

Machine access

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

Sources

Wikipedia – Wuxing (Chinese philosophy) (reference)
Wikipedia – Bagua (reference)

FAQ

Is the relation symmetric?

No. It is stated from A's point of view: Wood generates Fire, so with A = Fire and B = Wood the type is is_generated_by; likewise controls versus is_controlled_by.

Which organ tables are used?

The classical 脏腑 pairing: Wood liver/gallbladder, Fire heart/small intestine, Earth spleen/stomach, Metal lung/large intestine, Water kidney/bladder. These are cultural correspondences, not medical statements.

Related calculators

Stem and Branch Relations (干支合冲刑害) — Combinations and clashes between specific stems and branches.
Bagua Trigram Lookup (八卦) — Element of each trigram.
Bazi Four Pillars (八字) — Five-element balance of a birth chart.