# Ming Gua Calculator (命卦 / Eight Mansions)

> Computes the personal trigram (命卦, minggua) and Kua number from the birth year and sex by the Luoshu year-star method, assigns the East Four / West Four group (东四命 dongsiming / 西四命 xisiming) and lists the four favourable and four unfavourable directions of the Eight Mansions (八宅, bazhai) school.

- Calculator id: `ming-gua` · Category: I Ching & Five Elements (`yijing`) · Tool name: `calculate_ming_gua`
- Canonical page: https://tttkmbb.com/yijing/ming-gua · This document: https://tttkmbb.com/yijing/ming-gua.md · JSON definition: https://tttkmbb.com/yijing/ming-gua.json

## Purpose

Computes the personal trigram (命卦, minggua) and Kua number from the birth year and sex by the Luoshu year-star method, assigns the East Four / West Four group (东四命 dongsiming / 西四命 xisiming) and lists the four favourable and four unfavourable directions of the Eight Mansions (八宅, bazhai) school.

**Use when:** You need someone's Kua number, Ming Gua trigram or Eight Mansions directions from a birth date, with the year boundary at 立春 (default) or Chinese New Year.

**Do not use when:** You need the annual Flying Star of a year (use nine-star-feng-shui), the zodiac animal (use chinese-zodiac) or a full Bazi chart (use bazi-four-pillars).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `birth_date` | date |  | required | Gregorian birth date (civil date in China Standard Time), 1900–2100. |
| `sex` | enum: male \| female |  | required | Sex used by the traditional formula (male and female formulas differ). |
| `boundary` | enum: lichun \| lunar_new_year |  | optional, default "lichun" | Where the Chinese year changes for birthdays in January–February: 立春 (about 4 February, the feng shui convention) or Chinese New Year. |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `gua` | string |  | Personal trigram with pinyin, symbol and nature. |
| `gua_number` | integer |  | Luoshu number of the trigram: 1 坎, 2 坤, 3 震, 4 巽, 6 乾, 7 兑, 8 艮, 9 离 (5 is replaced by 2 for men and 8 for women). |
| `group` | string |  | East Four (东四命: 坎 离 震 巽) or West Four (西四命: 乾 坤 艮 兑). |
| `element` | string |  | Five-element attribution of the trigram. |
| `favorable_directions` | object |  | sheng_qi (生气), tian_yi (天医), yan_nian (延年), fu_wei (伏位) → compass direction. |
| `unfavorable_directions` | object |  | jue_ming (绝命), wu_gui (五鬼), liu_sha (六煞), huo_hai (祸害) → compass direction. |
| `stars_legend` | string |  | Meaning of the eight wandering stars (八游星). |
| `year_used` | integer |  | Chinese year the birth date falls in under the chosen boundary. |
| `year_star` | string |  | Luoshu star of the birth year (1864 = 一白, descending one per year). |
| `disclaimer` | string |  | Cultural-reference statement. |

## Formula

`year_star k = 1 − ((year − 1864) mod 9), wrapped into 1–9; male gua = k (5 → 2 坤); female gua = 15 − k reduced into 1–9 (5 → 8 艮); trigram by Luoshu number; directions from the Eight Mansions table`

Equivalent to the popular rules male = (10 − yy) mod 9 for 19xx / (9 − yy) mod 9 for 20xx and female = (yy + 5) mod 9 / (yy + 6) mod 9 with 0 read as 9. The year changes at 立春 by default. Traditional cultural reference calculation; not a prediction and not medical, legal or financial advice.

## Data Sources

- Wikipedia – Feng shui (Eight Mansions, 八宅) — https://en.wikipedia.org/wiki/Feng_shui (reference, retrieved 2026-09-24)
- Wikipedia – Lo Shu Square — https://en.wikipedia.org/wiki/Lo_Shu_Square (reference, retrieved 2026-09-24)
- Wikipedia – Bagua — https://en.wikipedia.org/wiki/Bagua (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/ming-gua?birth_date=…&sex=…`
- `POST https://tttkmbb.com/api/v1/calculate/ming-gua` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/ming-gua · OpenAPI operationId `calculate_ming_gua` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "ming-gua", "inputs": {…}}`

## Example

- Female born 1990-06-01: inputs `{"birth_date":"1990-06-01","sex":"female"}` → `{"gua":"艮 Gen ☶ (Mountain)","gua_number":8,"group":"West Four (西四命)","element":"Earth (土)","favorable_directions":{"sheng_qi":"Southwest (SW, 西南)","tian_yi":"Northwest (NW, 西北)","yan_nian":"West (W, 西)","fu_wei":"Northeast (NE, 东北)"},"unfavorable_directions":{"jue_ming":"Southeast (SE, 东南)","wu_gui":"North (N, 北)","liu_sha":"East (E, 东)","huo_hai":"South (S, 南)"},"year_used":1990,"year_star":"1 一白 (Yi Bai, White)"}`
- Male born 2000-06-01: inputs `{"birth_date":"2000-06-01","sex":"male"}` → `{"gua":"离 Li ☲ (Fire)","gua_number":9,"group":"East Four (东四命)","favorable_directions":{"sheng_qi":"East (E, 东)","tian_yi":"Southeast (SE, 东南)","yan_nian":"North (N, 北)","fu_wei":"South (S, 南)"},"unfavorable_directions":{"jue_ming":"Northwest (NW, 西北)","wu_gui":"West (W, 西)","liu_sha":"Southwest (SW, 西南)","huo_hai":"Northeast (NE, 东北)"},"year_star":"9 九紫 (Jiu Zi, Purple)"}`

```
GET https://tttkmbb.com/api/v1/calculate/ming-gua?birth_date=1990-06-01&sex=female
```

## Limitations

You need the annual Flying Star of a year (use nine-star-feng-shui), the zodiac animal (use chinese-zodiac) or a full Bazi chart (use bazi-four-pillars). Equivalent to the popular rules male = (10 − yy) mod 9 for 19xx / (9 − yy) mod 9 for 20xx and female = (yy + 5) mod 9 / (yy + 6) mod 9 with 0 read as 9. The year changes at 立春 by default. Traditional cultural reference calculation; not a prediction and not medical, legal or financial advice. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Which year applies to a January or early-February birthday?**

Feng shui schools use the solar year starting at 立春 (about 4 February); someone born on 1990-01-20 is therefore counted in 1989. Choose boundary = lunar_new_year to use Chinese New Year instead.

**What happens when the formula gives 5?**

There is no trigram 5 (the Luoshu centre), so tradition assigns men to 坤 (2) and women to 艮 (8).

## Related

- [Bagua Trigram Lookup (八卦)](https://tttkmbb.com/yijing/bagua.md) — Attributes of the resulting trigram.
- [Luoshu Square (洛书)](https://tttkmbb.com/yijing/luoshu-square.md) — The square whose numbers define the Kua numbers.
- [Chinese Zodiac Calculator (生肖)](https://tttkmbb.com/lunar/chinese-zodiac.md) — Zodiac animal and stem-branch of the same birth year.