[{"data":1,"prerenderedAt":248},["ShallowReactive",2],{"article:ming-gua-calculation:en":3,"article-topic:eight-mansions-feng-shui:en":143,"related-articles:en:eight-mansions-feng-shui:ming-gua-calculation:":237},{"slug":4,"title":5,"description":6,"category":7,"topicSlug":8,"legacyPath":9,"authorId":10,"publishedAt":11,"updatedAt":12,"noindex":13,"summary":14,"sections":15,"references":108,"relatedTools":125,"seo":126,"contentImage":129},"ming-gua-calculation","Ming Gua: The Formula, and the Three Places It Breaks","Ming gua in one modular step: 2 minus the year for men, the year plus 4 for women, mod 9. The two-digit shorthand fails in all 100 years after 1999, and the fold at five doubles one gua.","Feng Shui","eight-mansions-feng-shui","\u002Fpages\u002Farticles\u002Fminggua-jisuan-fangfa.html","zhang-hao","2026-01-29","2026-11-01",false,"The formula is a single modular step that needs no century correction. Every disagreement between published tables comes from a convention: an expired two-digit shorthand, a fold at five that gives one gua double weight, and a year boundary at 立春 that sits about seven days from the lunar new year.",[16,21,69,75,81,88,93,102],{"heading":17,"body":18},"A feng shui number you can check before you use it",[19,20],"Ming gua takes two inputs, the year a person was born and their sex, and returns one of eight values. That is unusual in this field: the step is fully specified, so the same year put through two published tables should give the same trigram. When two tables disagree, and they do, the disagreement is never mysterious. It comes from one of three conventions, and each of the three can be isolated and tested on its own.","That makes the calculation worth doing carefully even if you never use the answer. If the simplest step in Eight Mansions cannot be reproduced, the elaborate steps built on top of it inherit the problem.",{"heading":22,"body":23,"table":27},"The whole formula is one modular step",[24,25,26],"Reduce the birth year modulo 9, then apply a fixed offset: for a man, subtract the year from 2; for a woman, add 4. Read a remainder of 0 as 9. That is the entire rule, and it works across the century boundary without adjustment.","Most books state it as a digit sum instead, which is the same arithmetic in a different costume. A number and its digit sum have the same remainder modulo 9, so summing the digits of the year, reducing to a single digit d, then computing 11 minus d for a man and 4 plus d for a woman gives an identical result. If the answer exceeds 9, subtract 9 once more.","Seven years are enough to see that the two forms agree, and to see what the output looks like before the five is handled.",{"headers":28,"rows":35},[29,30,31,32,33,34],"Birth year","Digits, reduced","Man: 11 − d","Man's gua","Woman: d + 4","Woman's gua",[36,43,50,53,59,62,67],[37,38,39,40,41,42],"1982","20 → 2","9","9 Li","6","6 Qian",[44,45,46,47,48,49],"1984","22 → 4","7","7 Dui","8","8 Gen",[51,52,41,42,39,40],"1985","23 → 5",[54,55,56,57,58,49],"1999","28 → 1","1","1 Kan","5 → 8",[60,61,39,40,41,42],"2000","2",[63,46,64,65,61,66],"2005","4","4 Xun","2 Kun",[68,39,61,66,64,65],"2025",{"heading":70,"body":71},"The shorthand that stopped working in 2000",[72,73,74],"A shorter version circulates widely: take the last two digits of the year, subtract them from 100 for a man, subtract 4 from them for a woman, and divide by 9. It reproduces every result in the table above, because for years beginning 19 it is the same arithmetic. It also fails completely for years beginning 20, and it fails silently, returning a trigram that looks perfectly valid.","Take 2005. The shorthand gives 100 minus 5, which is 95, whose remainder modulo 9 is 5, which folds to 2 Kun. The digit method gives 4 Xun. Checked across 2000 to 2099, the shorthand disagrees with the digit method in all one hundred years, in the same direction, for both sexes.","The reason is that 100 leaves a remainder of 1 modulo 9, so each century shifts the constant by one. Dropping the century digits is only safe while the century you dropped happens to cancel. The repair is either to subtract from 99 instead of 100 for the 2000s, or to stop using the shorthand and sum the digits.",{"heading":76,"body":77},"Five is not a trigram, and it is not rare",[78,79,80],"The eight palaces sit around a centre that has no direction, so the number 5 has no trigram to attach to. The classical convention folds it: a man reads 5 as 2 Kun, a woman reads 5 as 8 Gen. Over the two hundred years from 1900 to 2099 the raw result is 5 in 22 of the male years and 23 of the female years, which is one person in nine.","Folding doubles the weight of the trigram it lands on. Kun falls to 44 of those 200 male years, twice as often as any other gua, and Gen falls to 45 of the female years. A table that lists eight rows hides this: the rows are not equally likely.","There is a second convention, less common, that swaps the two folds, sending men to Gen and women to Kun. Both folds are West Group, so the group does not change and a careless reader will not notice. The directions do change. Kun's Sheng Qi is northeast, Gen's is southwest, so for the one person in nine who hits 5 the two conventions point them at opposite corners of the same group.",{"heading":82,"body":83},"The year boundary is 立春, and it costs about two percent of birthdays",[84,85,86,87],"The year the formula wants is not the Gregorian year on a birth certificate and not the lunar year either. It is the solar year that begins at 立春, when the sun reaches 315 degrees of ecliptic longitude, which falls on 3 to 5 February.","The gap between 立春 and the first day of the lunar year is small but not zero. Between 1950 and 2050 the median gap is 7 days, the range is 0 to 16, and 立春 comes second in 46 of those 101 years. Anyone born inside that window gets a different gua depending on which boundary the table uses.","2026 is a wide year. 立春 falls on 4 February and the lunar new year on 17 February, thirteen days later. A boy born on 10 February 2026 is past 立春, so he belongs to 2026 and reads 1 Kan, East Group. A table that waits for the lunar new year puts him in 2025 and reads 2 Kun, West Group. Thirteen days of disagreement produce a different group and a different set of four directions.","The size of the exposure is easy to state. The ambiguous window averages 7.45 days, about two percent of a year, so roughly one birth in forty-nine sits inside it. Ignoring the boundary altogether is worse: 1 January to 立春 is 34 days, about nine percent of all birthdays, and every one of those is assigned to the wrong year.",{"heading":89,"body":90},"What the eight outputs actually cover",[91,92],"Because the fold pushes every 5 into the West Group, the two groups are not the same size. Four trigrams are East Group and four are West Group, but the folded weight lands on the West side for both sexes, so West Group takes five ninths of all people, about 55.6 percent. Counted over 1900 to 2099 the measured share is 55 percent of male years and 56 percent of female years.","The sequence also repeats every nine years, which is why the same gua keeps appearing across unrelated generations. Nine consecutive male years cover eight distinct values with exactly one repeat and no 5 at all: 1984 through 1992 read 7, 6, 2, 4, 3, 2, 1, 9, 8. Two men born nine years apart therefore carry the same number, and the number says nothing about which decade they grew up in.",{"heading":94,"body":95,"bullets":96},"Checking your own number in a minute","The steps below reproduce the table, and the last step is a cross-check that catches an arithmetic slip:",[97,98,99,100,101],"Write the four-digit birth year. If the birthday falls before 立春, which is 3 to 5 February, use the previous year.","Sum the four digits, then sum again until one digit remains. Call it d.","A man computes 11 minus d; a woman computes 4 plus d. If the result is above 9, subtract 9.","If the result is 5, a man reads 2 Kun and a woman reads 8 Gen.","Cross-check with the modular form: a man computes 2 minus the year, a woman computes the year plus 4, take the remainder after dividing by 9, and read a remainder of 0 as 9. Both routes must land on the same trigram.",{"heading":103,"body":104},"What the number cannot do",[105,106,107],"Ming gua is one of two tables in Eight Mansions, not the whole system. The other table belongs to the building, generated from its facing direction, and the reading is a comparison between the two. A person's number on its own says which directions suit them; it does not say whether the house has any of them available.","It also does not rank people, predict income, or overlap with the favourable elements read from a full birth chart. Those are separate calculations with separate inputs, and a person can easily have a gua that points one way and a chart that favours another. When they conflict, the gua is the narrower claim: it concerns orientation, and orientation is usually the cheapest thing in a room to change.","The failure mode worth remembering is the quiet one. A wrong year boundary, a shorthand that expired in 1999, or a swapped fold each produce a valid-looking trigram with no error message. The only defence is to compute the number twice, by two routes, and see whether they agree.",[109,117],{"id":110,"kind":111,"title":112,"detail":113,"publisher":114,"url":115,"accessedAt":116},"huangdiZhaijing","traditional","Huangdi Zhaijing (黄帝宅经)","Historical context for traditional residential orientation and spatial vocabulary. Modern recommendations are judged against real conditions.","Wikisource digital text","https:\u002F\u002Fzh.wikisource.org\u002Fwiki\u002F%E9%BB%83%E5%B8%9D%E5%AE%85%E7%B6%93","2026-07-14",{"id":118,"kind":119,"title":120,"detail":121,"publisher":122,"url":123,"accessedAt":124},"noaaSolarCalculator","practical","NOAA Solar Calculator","Used to check local solar noon and the equation of time, which is the part the true-solar-time correction adds to or subtracts from clock time.","NOAA Global Monitoring Laboratory","https:\u002F\u002Fgml.noaa.gov\u002Fgrad\u002Fsolcalc\u002F","2026-10-16",[],{"title":5,"description":127,"path":128},"How a ming gua is calculated, why the two-digit shorthand fails after 1999, what happens to a result of five, and where the birth year actually starts.","\u002Farticles\u002Fming-gua-calculation",{"src":130,"srcByLocale":131,"alt":133,"altByLocale":134,"captionByLocale":137,"width":141,"height":142},"\u002Fimg\u002Farticles\u002Fming-gua-calculation.svg",{"tw":132},"\u002Fimg\u002Farticles\u002Fming-gua-calculation-tw.svg","Four rows comparing the ming gua rule with what each convention costs: the modular step that holds in every century, the two-digit shorthand that fails after 1999, the fold at five, and the year boundary at 立春.",{"zh":135,"tw":136},"命卦规则与三处约定代价的四行对照：跨世纪都成立的取模式、2000 年后失效的两位简写、得五的折法，以及立春年份边界。","命卦規則與三處約定代價的四行對照：跨世紀都成立的取模式、2000 年後失效的兩位簡寫、得五的折法，以及立春年份邊界。",{"en":138,"zh":139,"tw":140},"The rule itself is one modular step and needs no century correction. Every failure is at the level of convention: a shorthand that expires in 1999, a fold at five, and a year that starts at 立春.","规则本身只有一个取模，跨世纪不用修正；出问题的都在约定层：1999 年就过期的简写、得五的折法，以及从立春起算的年份。","規則本身只有一個取模，跨世紀不用修正；出問題的都在約定層：1999 年就過期的簡寫、得五的折法，以及從立春起算的年份。",1280,960,{"topic":144,"articles":174,"tools":236},{"slug":8,"title":145,"eyebrow":146,"description":147,"relatedTools":148,"articleIdeas":149,"seo":154,"sections":158},"Eight Mansions Feng Shui","Ba Zhai feng shui","A working guide to Eight Mansions (Ba Zhai) feng shui: the personal ming gua, the house gua taken from a measured sitting direction, the eight-star table that joins them, and the three places the tradition actually reads.",[],[150,151,152,153],"Ming Gua Calculation","Four Auspicious Directions","Bed Placement by Eight Mansions","Room Selection by Personal Gua",{"title":155,"description":156,"path":157},"Eight Mansions Feng Shui Guide","Learn Eight Mansions feng shui: ming gua calculation, eight directions, favorable sectors, and practical home layout applications.","\u002Ftopics\u002Feight-mansions-feng-shui",[159,162,165,168,171],{"heading":160,"body":161},"What it is: two numbers, one table","Eight Mansions (Ba Zhai, 八宅) is the smallest complete system in feng shui. It needs two trigrams and nothing else. The gua of the person — the ming gua — is derived from the birth year and gender, with the year adjusted if the birthday falls before that year’s lunar new year. The gua of the house comes from its sitting direction, measured with a compass rather than assumed. Put the two side by side and the tradition hands back a fixed table: eight directions, each with a star already attached. There is no chart to draw, no period to look up, no star to fly. That smallness is the point, and it is also why the system gets claimed for far more than it does.",{"heading":163,"body":164},"The eight directions and what each one is for","The table always produces the same eight names. Four are read as favourable — Sheng Qi (生气), Tian Yi (天医), Yan Nian (延年), Fu Wei (伏位). Four are read as unfavourable — Jue Ming (绝命), Wu Gui (五鬼), Liu Sha (六煞), Huo Hai (祸害). Which direction receives which name depends entirely on the gua you started from, and the assignment is fixed by the Da You Nian song (大游年歌), a mnemonic that generates the whole table from a line of verse. Nothing in that process looks at your house, your health, or your year. It is arithmetic on a birth year and a compass bearing. Read the eight names as a vocabulary for ranking directions, and the system stops pretending to know things it was never built to know.",{"heading":166,"body":167},"East group or west group: which one are you","The eight gua split into two sets. Kan 1, Li 9, Zhen 3 and Xun 4 form the east group; Kun 2, Dui 7, Qian 6 and Gen 8 form the west group. An east-group person’s four favourable directions are the east-group directions, and the same holds on the west side. From that comes a claim you will hear often: east-group people should live in east-group houses. The underlying rule is real, but the veto is not. In a city flat you rarely choose the sitting direction, and a household of four frequently contains both groups. What the rule can honestly do is rank the rooms inside the house you already have.",{"heading":169,"body":170},"The three places that matter: door, bedroom, stove","Classical Ba Zhai is not a room-by-room audit. It reads three points — the door (门), the main bedroom (主) and the stove (灶) — and asks whether each sits in a favourable or unfavourable direction for the people who use it. The reason is historical. In the houses the system was built for, those three points were where household life actually happened, and surveying every square metre would have been wasted effort. Modern homes have more rooms and different routines, so keep the three-point habit as a way of setting priorities, then add the two or three rooms you genuinely spend hours in, and treat the rest as optional.",{"heading":172,"body":173},"When it doesn't help","Three limits are worth stating plainly. First, it ignores form: the road outside, the shape of the plot, a bedroom with no window. A favourable direction on a bad room is still a bad room. Second, it has no time dimension — unlike the flying star systems, Ba Zhai does not shift with the period or the year, so it cannot say anything about when. Third, the compass reading is the weak link: a phone compass, a steel door frame or a five-degree error can push a direction into the next sector and rename every entry in the table. Use Eight Mansions as a tie-breaker between layouts that already work, never as the reason to accept a layout that does not.",[175,178,189,200,212,225],{"slug":4,"title":5,"description":6,"category":7,"topicSlug":8,"legacyPath":9,"authorId":10,"publishedAt":11,"updatedAt":12,"summary":14,"relatedTools":176,"seo":177},[],{"title":5,"description":127,"path":128},{"slug":179,"title":180,"description":181,"category":7,"topicSlug":8,"legacyPath":182,"authorId":10,"publishedAt":183,"updatedAt":184,"summary":185,"relatedTools":186,"seo":187},"four-auspicious-directions","Four Auspicious Directions in Eight Mansions: The Verse and the Table","How the Da You Nian song turns one line of verse into eight directions: the reading order, a table for all eight gua, the rank order of the four favourable names, and what the table cannot decide.","\u002Fpages\u002Farticles\u002Fsiji-xiangfang-jiangjie.html","2026-01-31","2026-10-29","The four favourable directions are generated rather than chosen. One verse, read around the eight palaces from your own trigram, produces the whole table — and the same table ranks the four, so you know which to drop first.",[],{"title":180,"description":181,"path":188},"\u002Farticles\u002Ffour-auspicious-directions",{"slug":190,"title":191,"description":192,"category":7,"topicSlug":8,"legacyPath":193,"authorId":10,"publishedAt":194,"updatedAt":12,"summary":195,"relatedTools":196,"seo":197},"bed-placement-eight-mansions","Bed Placement: The Wall Comes First, the Direction Second","Bed placement in Eight Mansions is two decisions: which wall can take a headboard, then which favourable direction that wall gives. A worked example shows the conflict no table resolves.","\u002Fpages\u002Farticles\u002Fbazhai-chuangwei-buju.html","2026-02-02","A solid headboard, a view of the door and no window overhead decide where the bed goes. The direction follows the headboard, so one wall can give two answers, and when two people share the bed their tables cross with no exchange rate between them.",[],{"title":191,"description":198,"path":199},"How Eight Mansions bed placement works once the wall is fixed: the four favourable directions, the position rules that come first, and a worked example with two people.","\u002Farticles\u002Fbed-placement-eight-mansions",{"slug":201,"title":202,"description":203,"category":7,"topicSlug":8,"legacyPath":204,"authorId":10,"publishedAt":205,"updatedAt":206,"summary":207,"relatedTools":208,"seo":209},"room-selection-personal-gua","Room Selection by Personal Gua: Eight Mansions Guide","Compare room options using the traditional personal gua and house gua framework while accounting for daylight, ventilation, noise, access, area, and each household member's needs.","\u002Fpages\u002Farticles\u002Fbazhai-fangjian-xuanze.html","2026-02-04","2026-10-17","Treat personal gua as one optional traditional preference, not a verdict on who should use a room. Compare practical conditions and household needs before making a choice.",[],{"title":202,"description":210,"path":211},"Learn how personal gua is used as one traditional room-selection reference alongside practical household requirements.","\u002Farticles\u002Froom-selection-personal-gua",{"slug":213,"title":214,"description":215,"category":7,"topicSlug":8,"legacyPath":216,"authorId":10,"publishedAt":184,"updatedAt":184,"summary":217,"relatedTools":218,"seo":220},"how-to-measure-house-facing-direction","How to Measure Which Way Your Home Faces","Three methods for the one input every direction-based method needs: a phone compass, a noon shadow, and the building's own plan. Each fails in a different way, and the cheapest one fails most often indoors.","","Sitting and facing are 180 degrees apart, so a home needs one measurement, not two. Eight sectors tolerate 22.5 degrees of error and twenty-four mountains tolerate 7.5, which decides whether a phone is enough. The page gives the four-reading test for a contaminated indoor compass, the solar-noon table for five cities, the plan method that ignores magnetism, and a worked case where 13 degrees flips the sector.",[219],"feng-shui-luo-pan",{"title":221,"description":222,"path":223,"type":224},"How to Measure Your Home's Facing Direction","Measure the facing direction of a flat with a phone compass, a noon shadow, or the building plan. Includes the four-reading contamination test, solar noon times, and where 13 degrees changes the sector.","\u002Farticles\u002Fhow-to-measure-house-facing-direction","article",{"slug":226,"title":227,"description":228,"category":7,"topicSlug":8,"legacyPath":216,"authorId":10,"publishedAt":229,"updatedAt":229,"summary":230,"relatedTools":231,"seo":232},"bagua-map-placement","Bagua Map Placement: Which Wall, and Which North","The bagua map is pinned to the front door in one version and to the compass in another. What a sector contains, how much floor the centre gets, and where the two stop overlapping.","2026-10-31","Two maps share the same nine trigram names and disagree about what they are pinned to. The compass version gives each trigram 45 degrees, which is exactly three of the luopan's 24 mountains, and leaves the centre with no angular width at all. The door-aligned version divides the plan into nine equal cells, so the centre holds 11.1 per cent of the floor. Rotate one against the other and the overlap is arithmetic: at 30 degrees the two southeast corners share a third of the same patch, at 45 they share nothing. On an L-shaped plan the nine cells stop being ninths, and a five-degree instrument error leaves a fifth of all headings undecided.",[219],{"title":233,"description":234,"path":235,"type":224},"Bagua Map: Two Versions, Two Anchors","Two bagua maps share the same nine names and disagree about the anchor. Sector widths, a centre with no width, and the rotation at which they stop overlapping.","\u002Farticles\u002Fbagua-map-placement",[],{"articles":238},[239,242,245],{"slug":179,"title":180,"description":181,"category":7,"topicSlug":8,"legacyPath":182,"authorId":10,"publishedAt":183,"updatedAt":184,"summary":185,"relatedTools":240,"seo":241},[],{"title":180,"description":181,"path":188},{"slug":190,"title":191,"description":192,"category":7,"topicSlug":8,"legacyPath":193,"authorId":10,"publishedAt":194,"updatedAt":12,"summary":195,"relatedTools":243,"seo":244},[],{"title":191,"description":198,"path":199},{"slug":201,"title":202,"description":203,"category":7,"topicSlug":8,"legacyPath":204,"authorId":10,"publishedAt":205,"updatedAt":206,"summary":207,"relatedTools":246,"seo":247},[],{"title":202,"description":210,"path":211},1793614151925]