Learn · Numbers · 14 min read · Updated September 2026

Numbers, floors and doors

What the tradition counts and what it merely fears. The River Chart and the Lo Shu, odd numbers as yang and even as yin, the nine on the emperor’s door and the nails that told a rank; the four that sounds like death and the eight that sounds like wealth, the floors that towers leave out and what a number fetches at sale; the fourth of the month; and why a classical reading never asks your house number.

Oriented W 270°

Metal

Fig. 01 Brushed silver. Metal is the element of the west, and the chart gives it the numbers four and nine.

Two kinds of number run through feng shui and they are always confused. The first is the tradition’s own: the ten numbers of the River Chart and the nine of the Lo Shu, odd for yang and even for yin, each pair tied to a direction and an element, and nine as the fullest of them, written on the emperor’s gates in gilt. The second is a pun: four sounds like death and eight like wealth, so towers leave out their fourth floors and a house numbered eight sells for more. The first is in the classics and decides nothing about your address. The second is in the market and decides a little. This essay draws both, and says which is which.

The River Chart and the numbers of the elements

Fig. 01 The River Chart, He Tu, drawn as the Song philosophers printed it and turned so that north is at the top, as every plan on this site is. The ten numbers stand in five pairs at the five places: one and six at the north, which are Water; two and seven at the south, Fire; three and eight at the east, Wood; four and nine at the west, Metal; five and ten at the centre, Earth. The odd numbers are white dots and yang, the even black and yin, and each pair sets a small number inside and its partner, five more, outside. This is where the Five Elements got their numbers and the compass schools their pairing of numbers with directions; the Lo Shu, its companion square, is drawn on its own page. The chart is a Song reconstruction, first printed in the eleventh century and set at the front of Zhu Xi’s commentary on the Changes in 1177; the Great Commentary’s line that “the River gave forth the Chart and the Luo the Writing” is a thousand years older and describes nothing. The numbers one to five are called the generating numbers and six to ten the completing ones.

The Great Commentary to the Book of Changes, the Xici, says that the Yellow River gave forth a chart and the Luo gave forth a writing, and that the sages took them as models. It does not say what either looked like, and for a thousand years nobody drew them. The dot diagrams the tradition now calls the River Chart, He Tu, and the Luo Writing, the Lo Shu, appear in the early eleventh century, in a book by Liu Mu on the numbers of the Changes; they pass through Shao Yong’s number cosmology, and Zhu Xi set them at the front of his commentary on the Changes in 1177, with the names as they have stood since. Cammann traced the two diagrams from the Han to the Song and found the square of three known to the Han as a calendar device and a talisman, and the dot pictures a Song invention that gave old numbers a new face.

The chart drawn above is the ten numbers in five pairs at the five places. One and six stand at the north and are Water; two and seven at the south, Fire; three and eight at the east, Wood; four and nine at the west, Metal; five and ten at the centre, Earth. The numbers one to five are the generating numbers, sheng shu, and each with five added is its completing number, cheng shu; the odd numbers are drawn as white dots and are yang, the even as black and yin, so that every place holds one of each. This is where the Five Elements got their numbers, and it is the frame the Compass schools use when they pair a number with a direction: the water methods of the San He school count the chart’s pairs, the Eight Mansions count the Lo Shu, and the flying stars are the nine numbers of the Lo Shu walked round the palaces in the Lo Shu’s own order. Needham gave the two diagrams a section of his history of Chinese mathematics and read them as what they are: a number lore, sober about odd and even and ingenious about the magic square, that never became arithmetic.

Tradition · Odd, even and nine

The tradition’s arithmetic of luck begins and ends with parity. Odd numbers are yang and heaven’s, even numbers yin and earth’s; the Xici counts the numbers of heaven as one, three, five, seven and nine and of earth as two, four, six, eight and ten. Nine is the greatest of the yang numbers and its square the fullest, which is why the emperor’s number is nine and his gates carry eighty-one nails a leaf. The line of the Changes from which the throne took its title, the fifth line of the first hexagram, “the flying dragon in the heavens”, is the ninth kind of line in the fifth place, and the sovereign is the “nine-five”. None of this concerns a house number. It concerns which numbers are heaven’s, and a tradition that liked to build in odd bays, three, five, seven and nine, for the same reason.

Nine, and what was written on a door

Fig. 02 The door nails by rank, four pairs of leaves in elevation. The Qing regulations fixed the count of the gilt bosses on a great door as a mark of the household’s station: nine rows of nine on each leaf of the emperor’s gates, eighty-one, nine being the greatest yang number and its square the fullest; nine by seven for a prince of the first rank; seven by seven for a duke and the ranks near him; five by five for the lords below; and none at all on the door of a commoner, however rich, whose leaves were plain and, by the same rules, not red. The nails are the one place the tradition’s numbers were written on the outside of a house, and they were written by law rather than by the compass. The leaves are vermilion, the bosses gilt, the knocker rings at the middle of each leaf in the place of a nail; the grids are as the sumptuary rules of the Collected Statutes of the Qing give them. Counting the nails on a surviving gate in Beijing still tells the rank of whoever built it.

The one place the tradition’s numbers were written on the outside of a house was its door, and they were written by law. The Qing statutes fixed the count of the gilt bosses, men ding, on a great door by the rank of whoever lived behind it: nine rows of nine on each leaf of the emperor’s gates, nine by seven for a prince of the first rank, seven by seven for a duke and the ranks near him, five by five for the lords below, and none on the door of a commoner, whose leaves were also forbidden to be red. Knapp’s survey of the old dwellings gives the sumptuary rules with the rest of them, the bays a merchant might build and the colours he might not paint, and a walk along the gates of Beijing still reads them: count the nails and the household is known. The Forbidden City has nine written all over it, in the nails, the nine-dragon screen, the flights of steps, and the legend that it holds nine thousand nine hundred and ninety-nine rooms and a half, one short of heaven’s ten thousand.

This is the tradition’s number lore at its most exact, and it is about station, not fortune. The nails did not bring the prince luck; they said what he was, and the same statutes that gave him sixty-three of them forbade the man next door any. The site draws it because the paperbacks’ talk of a lucky house number has borrowed the tradition’s prestige for something the tradition never did, and the gates are the evidence of what it did instead.

The four and the eight

The lore of the lucky number is younger, and it is not a lore of numbers at all but of sounds. In Mandarin sì, four, is a tone away from sǐ, death; bā, eight, rhymes with fā, to prosper, and does so more closely in Cantonese, where baat and faat are nearly one word; jiǔ, nine, sounds like jiǔ, long-lasting, and liù, six, like liú, to flow, whence the wish that everything go “six-six smoothly”. Cantonese hears whole phrases in the compounds: fourteen is sap sei, which is “sure to die”, twenty-four is “easy to die”, twenty-eight “easy to prosper”. The Beijing Olympics opened at eight minutes past eight in the evening on the eighth day of the eighth month of 2008, and nobody in the country needed it explained. Japan hears its own puns, shi for four and death, ku for nine and suffering, so that its hospitals leave out rooms four and nine as the West leaves out the thirteenth floor; the beyond China essay follows the tradition there.

Fig. 03 What the homophones do to a building. A: the lift panel of a tower of forty floors that numbers them as Hong Kong and much of the Chinese-speaking world do, leaving out every floor with a four in it, because four sounds like death, and the thirteenth for the Western tenants; the fortieth floor’s button reads fifty-six, and sixteen numbers are missing. B: what a number is worth when a house is sold, from the Vancouver study of Fortin, Hill and Huang: in the neighbourhoods where many buyers were Chinese, a house whose address ended in four sold for about two per cent less than the same house would have, and one ending in eight for about two and a half per cent more; elsewhere in the city the numbers made no difference. The effect is real and it is a market’s, not a building’s. The lift panel is a composite of the numbering used in Hong Kong towers, where the top floor of a building of fewer than fifty storeys can be numbered in the eighties; Vancouver’s council required consecutive numbering in new buildings in 2015. The bars are the study’s central estimates and the figures are rounded.

A tower numbers its floors for the buyers it expects, and in Hong Kong and much of the Chinese-speaking world it leaves out every floor with a four in it and, for the Western tenants, the thirteenth. The panel drawn above is a composite of the practice: forty floors, fourteen numbers missing, the top button reading fifty-six. It is not an exaggeration. A tower on Conduit Road in Hong Kong completed in 2009 has forty-six storeys and a top floor numbered eighty-eight, having skipped the fours, the thirteenth and the forties entire, and its penthouse sold on the number. The pun is a market before it is a belief, and the market can be measured.

What a number costs

Evidence · The price of a digit

Four studies have put a figure on it. Bourassa and Peng found in Auckland in 1999 that houses with lucky numbers sold at a premium in the suburbs where Chinese buyers were many and at none elsewhere. Chau, Ma and Ho found in Hong Kong in 2001 that flats on floors with an eight fetched more, and more in a rising market than a falling one, which is what a fashion does and a fundamental does not. Fortin, Hill and Huang, with Vancouver sales, found an address ending in four sold for about 2.2 per cent less and one ending in eight for about 2.5 per cent more, in the neighbourhoods where the buyers were largely Chinese, and nothing in the rest of the city; the bars in the drawing are theirs. Shum, Sun and Wu found the same shape in transaction data from a mainland city, with the flats’ size, floor and view held constant. The effect is real, it is a few per cent, it lives where the buyers do, and it is a premium paid by the next buyer, not a property of the house.

What the classics never ask

Misconception · Your house number decides your luck

The paperbacks add the digits of an address to a single number and read it like a horoscope. The method is Western numerology of the nineteenth century wearing Chinese dress. The classical manuals, all of them older than the house number, which reached European cities in the eighteenth and nineteenth centuries and Chinese ones with the treaty ports, never mention an address; the Book of Burial counts nothing, and the compass texts count directions. The Chinese lore that does exist is homophonic, a matter of what a digit sounds like in a particular dialect, which is why a four is worse in Cantonese than in Mandarin and worse in Hong Kong than in Shanghai. A number that means death in one language and nothing in the next is not a property of the house.

The site’s own use of numbers is the tradition’s. The Lo Shu numbers on the bagua and in the flying-star charts are directions and periods, not fortunes: the eight star was the timely one from 2004 to 2023 because the Lo Shu’s cycle put it there, and the nine is timely from 2024, and neither has anything to do with the digit on a door. The Eight Mansions kua number is a birth-year count that sorts people into two groups, and its arithmetic is the Lo Shu’s with five left out. When a number appears on this site it is a bearing, a period, a count of bays, a distance in centimetres, or the reading on a meter; a reader who finds it doing anything else has found a paperback, not the tradition.

The numbers, in practice

Count directions, not digits. The one and six, three and eight of the chart are the north and the east; use them as the compass schools do, for where a thing goes, never for whether a house is lucky.
Read the door for what it says. Nine by nine is an emperor, seven by seven a duke, none a commoner; the numbers on a classical house are rank, and the front door guide gives the rest of the door.
Treat your address as the market treats it. In a neighbourhood that pays for an eight, price it in; in one that does not, ignore it. Nothing in the classics turns on the number on your gate.
Know which pun is yours. Four is death in Cantonese and Mandarin and in Japanese, thirteen is the West’s, and a lift panel tells you who the building was sold to.
Keep the odd bays. If the tradition has a number for a house it is an odd one: three, five, seven or nine bays, an odd count of steps, a centre that is a bay and not a column. That is yang, and it is the whole of the rule.
Leave the digit-adding to the paperbacks. A single number from an address is numerology in translation; the misconceptions essay keeps its company.