24 Mountains & Degree Table
The full circle-to-mountain mapping the engine computes from — every one of the 24 Mountains（二十四山，Èrshísì shān；繁體 二十四山）, its exact 15° span, and the zones that decide whether a chart is a lower-trigram chart or a replacement chart.
Reference table · collated against the repository rule tables · static page, no scripts, no data collection.
What the 24 Mountains are
A compass circle is 360°. The 24 Mountains（二十四山；繁體 二十四山）divide it into 24 named sectors of exactly 15° each. Each sector carries one character: the twelve Earthly Branches（十二地支）, eight of the ten Heavenly Stems（八干 — the two center stems 戊 and 己 are excluded）, and the four corner trigrams（四維：乾 qián、坤 kūn、艮 gèn、巽 xùn）. The texts call this combined set the "eight stems and four dimensions"（八干四維）. Three adjacent mountains form one of the eight palaces（卦宮）, so the ring is eight palaces × three mountains, and every third boundary line falls on a palace edge at 22.5° + 45°k.
The ring lives on the Earth plate, Correct Needle（地盤正針，dìpán zhèngzhēn）of the luopan — the one ring that every plate type, of every school, agrees on. See the companion page Luopan Compass Layers for where this ring sits among the others.
The four hard rules
1. Each mountain is exactly 15°. 360° ÷ 24 = 15°. No exceptions, no school variation — this is arithmetic.
2. Lower trigram（下卦 xiàguà；繁體 下卦）= the mountain's center ± 4.5°, a 9°-wide band. A reading inside this central 9° produces an ordinary lower-trigram flying-star chart.
3. Replacement（替卦 tìguà；繁體 替卦）= the remaining 3° on each side. A reading in the outer 3° of a mountain — still inside the mountain, but outside the central 9° — triggers the replacement-star chart. The texts justify the figure as "four and a half degrees each way, nine in all"（左右四度半共九度）, with the remaining 6° split 3°/3°.
4. Every boundary line ends in .5 — specifically in 2.5 or 7.5. Start and end of each mountain, and the 4.5°/3° sub-boundaries inside it, all fall on multiples of 7.5°. A boundary value ending in any other digit is a transcription error.
The complete degree table
All 24 rows, verbatim. Angles are compass bearings clockwise from true north 0°. The lower-trigram band and the two replacement zones always sum to the mountain's full 15°: 3° + 9° + 3°.
| Palace（卦宮） | Mountain（山） | Start ° | Center ° | End ° | Lower trigram 9° | Replacement 3° each side | Yuan long（元龍） |
|---|---|---|---|---|---|---|---|
| Kan 坎 | Ren 壬 | 337.5 | 345 | 352.5 | 340.5–349.5 | 337.5–340.5 / 349.5–352.5 | Earth 地 |
| Kan 坎 | Zi 子 | 352.5 | 0 | 7.5 | 355.5–4.5 | 352.5–355.5 / 4.5–7.5 | Heaven 天 |
| Kan 坎 | Gui 癸 | 7.5 | 15 | 22.5 | 10.5–19.5 | 7.5–10.5 / 19.5–22.5 | Human 人 |
| Gen 艮 | Chou 丑 | 22.5 | 30 | 37.5 | 25.5–34.5 | 22.5–25.5 / 34.5–37.5 | Earth 地 |
| Gen 艮 | Gen 艮 | 37.5 | 45 | 52.5 | 40.5–49.5 | 37.5–40.5 / 49.5–52.5 | Heaven 天 |
| Gen 艮 | Yin 寅 | 52.5 | 60 | 67.5 | 55.5–64.5 | 52.5–55.5 / 64.5–67.5 | Human 人 |
| Zhen 震 | Jia 甲 | 67.5 | 75 | 82.5 | 70.5–79.5 | 67.5–70.5 / 79.5–82.5 | Earth 地 |
| Zhen 震 | Mao 卯 | 82.5 | 90 | 97.5 | 85.5–94.5 | 82.5–85.5 / 94.5–97.5 | Heaven 天 |
| Zhen 震 | Yi 乙 | 97.5 | 105 | 112.5 | 100.5–109.5 | 97.5–100.5 / 109.5–112.5 | Human 人 |
| Xun 巽 | Chen 辰 | 112.5 | 120 | 127.5 | 115.5–124.5 | 112.5–115.5 / 124.5–127.5 | Earth 地 |
| Xun 巽 | Xun 巽 | 127.5 | 135 | 142.5 | 130.5–139.5 | 127.5–130.5 / 139.5–142.5 | Heaven 天 |
| Xun 巽 | Si 巳 | 142.5 | 150 | 157.5 | 145.5–154.5 | 142.5–145.5 / 154.5–157.5 | Human 人 |
| Li 離 | Bing 丙 | 157.5 | 165 | 172.5 | 160.5–169.5 | 157.5–160.5 / 169.5–172.5 | Earth 地 |
| Li 離 | Wu 午 | 172.5 | 180 | 187.5 | 175.5–184.5 | 172.5–175.5 / 184.5–187.5 | Heaven 天 |
| Li 離 | Ding 丁 | 187.5 | 195 | 202.5 | 190.5–199.5 | 187.5–190.5 / 199.5–202.5 | Human 人 |
| Kun 坤 | Wei 未 | 202.5 | 210 | 217.5 | 205.5–214.5 | 202.5–205.5 / 214.5–217.5 | Earth 地 |
| Kun 坤 | Kun 坤 | 217.5 | 225 | 232.5 | 220.5–229.5 | 217.5–220.5 / 229.5–232.5 | Heaven 天 |
| Kun 坤 | Shen 申 | 232.5 | 240 | 247.5 | 235.5–244.5 | 232.5–235.5 / 244.5–247.5 | Human 人 |
| Dui 兌 | Geng 庚 | 247.5 | 255 | 262.5 | 250.5–259.5 | 247.5–250.5 / 259.5–262.5 | Earth 地 |
| Dui 兌 | You 酉 | 262.5 | 270 | 277.5 | 265.5–274.5 | 262.5–265.5 / 274.5–277.5 | Heaven 天 |
| Dui 兌 | Xin 辛 | 277.5 | 285 | 292.5 | 280.5–289.5 | 277.5–280.5 / 289.5–292.5 | Human 人 |
| Qian 乾 | Xu 戌 | 292.5 | 300 | 307.5 | 295.5–304.5 | 292.5–295.5 / 304.5–307.5 | Earth 地 |
| Qian 乾 | Qian 乾 | 307.5 | 315 | 322.5 | 310.5–319.5 | 307.5–310.5 / 319.5–322.5 | Heaven 天 |
| Qian 乾 | Hai 亥 | 322.5 | 330 | 337.5 | 325.5–334.5 | 322.5–325.5 / 334.5–337.5 | Human 人 |
A note on Zi（子 zǐ）, the row that crosses north: its span is written 352.5° → 7.5° through 0°. Angles wrap at 360°, so "355.5–4.5" means 355.5° through 0° to 4.5°.
The three yuan-long classes
Each palace's three mountains carry one of three yuan-long（元龍 yuánlóng）classes, and the table column records it: within each palace, the middle mountain is Heaven Yuan Long（天元龍）, the mountain clockwise before it is Human Yuan Long（人元龍）, and the mountain clockwise after it is Earth Yuan Long（地元龍）. The class matters twice over: it decides which mountain's yin-yang governs the direction of the flying stars, and it decides the lodging palace when the star 5 enters the center. This is why the table tracks it per mountain rather than per palace.
The Eight Fierce Lines at palace boundaries
Where a reading crosses a palace edge — not merely a mountain edge — the tradition keeps a specific warning: the Eight Fierce Lines of the Cross-Palace Needle Rhyme（出卦八凶針度歌，chūguà bā xiōng zhēndù gē；繁體 出卦八凶針度歌）. Eight boundary midpoints are named, each contributing two lines, sixteen in all.
Reverse-engineering the rhyme against the degree table shows the geometry exactly: every one of the sixteen lines is precisely 3° on either side of its mountain-boundary midpoint — that is, each fierce line is the shared edge between one mountain's lower-trigram band and the neighboring mountain's replacement zone. The rhyme, whatever its provenance, encodes the same 3°/9° partition as the table above.
| Boundary midpoint | Midpoint bearing | The two fierce lines |
|---|---|---|
| Jia–Yin 甲寅 | 67.5° | 64.5° / 70.5° |
| Bing–Si 丙巳 | 157.5° | 154.5° / 160.5° |
| Geng–Shen 庚申 | 247.5° | 244.5° / 250.5° |
| Ren–Hai 壬亥 | 337.5° | 334.5° / 340.5° |
| Chou–Gui 丑癸 | 7.5° | 4.5° / 10.5° |
| Chen–Yi 辰乙 | 127.5° | 124.5° / 130.5° |
| Wei–Ding 未丁 | 217.5° | 214.5° / 220.5° |
| Xu–Xin 戌辛 | 307.5° | 304.5° / 310.5° |
Two cautions accompany it. First, two different thresholds must not be conflated: the cross-palace boundary is ±3° measured from the mountain-boundary midpoint（卦界 = 22.5° + 45°k）, while the lower-trigram / replacement boundary is ±4.5° measured from the mountain's centerline — different baselines, different meanings, and only the former turns a leaning into a cross-palace one. Second, whether the sixteen lines should fire as automatic warnings by default is treated as a school-difference rule pending practitioner review — see the School Dispute Register for how such rules are handled, and for the related lower-trigram/replacement threshold entry.
How a reading uses this table
The engine's procedure is the classical one, made mechanical:
- Take the measured bearing θ of the facing, look it up in the table to get the facing mountain（向山）; the sitting mountain（坐山）is 180° opposite — facing = sitting + 180° (mod 360).
- Stand inside the building looking out through the main door: what is behind you is the sitting side, what is in front is the facing side.
- Check which zone of the mountain θ falls in: the central 9° → lower-trigram chart; either outer 3° → replacement chart, with the cross-palace check from the Eight Fierce Lines applied first.
- Carry the mountain's yuan-long class into the star-flying and replacement-star steps.
Because every boundary in the table ends in 2.5 or 7.5, a measurement can only land on a boundary by prior agreement about rounding — the table itself never places a boundary elsewhere. What the table cannot cure is measurement error in θ itself; the companion page Luopan Compass Layers covers how the engine handles magnetic declination（磁偏角）and why the seam-needle offset is not a declination correction.
Sources: collated against the repository rule tables (GB/T conventions for bearing notation and decimal degrees; degree values cross-checked line-by-line against the collated authoritative table). No page-view or popularity claims are made anywhere on this site.