Lo Shu Grid

What this long-form adds to the Lo Shu calculator

The calculator above does one thing: it counts how many times each digit from 1 to 9 appears in your birth date. The copy above it explains that count, and this site's article on missing numbers in the Lo Shu grid walks through how digits go in, what missing and repeated mean, the six planes and the arrows. This section does not repeat those. It looks at the grid as a piece of arithmetic across real calendars: what a date can and cannot put into it, how the century shapes it, how common each gap and each plane actually is across seventy-six years of birth dates, which other calculators read the same count, and where they read it differently. All figures come from running this app's engine.

The square behind the display order

This site's numerology rules fix the display order as 4 9 2 across the top, 3 5 7 through the middle and 8 1 6 along the bottom, and note that every row, column and diagonal of that arrangement adds up to 15. It is easy to check: 4 + 9 + 2, 3 + 5 + 7 and 8 + 1 + 6 are the rows; 4 + 3 + 8, 9 + 5 + 1 and 2 + 7 + 6 the columns; 4 + 5 + 6 and 2 + 5 + 8 the diagonals. Eight lines, each totalling 15, with 5 at the centre of four of them.

That property belongs to the layout, not to your count. The grid's cells hold how many times a digit appears; the 15 is about the digits' labels. Nothing in the engine adds up cell values or checks anything against 15. The order matters for one practical reason: the six planes the profile engine checks are the three rows and three columns of this exact arrangement, so if the digits were laid out differently, different digits would share a plane. The two diagonals, 4-5-6 and 2-5-8, are part of the magic square but are not planes in this engine.

What a birth date can put into the grid

A date supplies at most eight digits: up to two for the day, up to two for the month and four for the year. Zeros are dropped, so the real number counted is often smaller. A few consequences follow directly from how calendars are written.

• The month can only add the digits 1 to 9 on its own, or 1 and 0, 1 and 1, or 1 and 2 for October, November and December. So a late-year birth always adds at least one 1.
• The day adds one or two digits; days 10, 20 and 30 add a single non-zero digit because the zero is dropped.
• The year adds the most, and the same digits for everyone born in that year. 1994 contributes 1, 9, 9 and 4 to every grid cast for that year.
• The fewest digits any date in the range below contributes is three - 1 January 2000 gives 1, 1 and 2. The most is eight, for a date such as 28 December 1999 with no zeros anywhere.

Because so much comes from the year, many different dates produce the same grid. Across the 18,262 dates from 1950 to 1999 the engine produced only 1,745 distinct grids, and across the 9,497 dates from 2000 to 2025 only 1,023. On average, then, about ten birth dates share any given grid. The calculator's own copy gives one pair, 14 August and 18 April 1994; there are many more.

What the day, the month and the year each contribute

It helps to see the three parts of the date separately, because they behave very differently. The month is the most predictable: January to September each add their own single digit, October adds a 1 (the zero is dropped), November adds two 1s and December adds a 1 and a 2. So any birth in the last quarter of the year has at least one 1 in its grid from the month alone, and a November birth has two.

The day is next. Days 1 to 9 add one digit. Days 10, 20 and 30 also add only one, a 1, 2 or 3. Days 11 to 19 always add a 1 plus a second digit, days 21 to 29 always add a 2 plus a second digit, and day 31 adds a 3 and a 1. That is part of why 1s and 2s dominate grids: thirteen of the thirty-one possible days put at least one 1 into the grid and twelve put a 2 in, before the month or year has added anything.

The year contributes the same four digits to everyone born in it - 1, 9, 9 and 4 for 1994, which is why both 1 and 9 are already dominant on the sample's grid before the day and month are counted, and 1 and 9 again for every 1900s year. A year in the 2000s contributes a 2 and then, until 2010, only one more non-zero digit at most: 2005 gives just 2 and 5. Twins born on the same day share the whole grid, and siblings born in the same year share every digit the year contributes.

Two days apart: the turn of the century

The century's weight is easiest to see across the night of 31 December 1999. The engine gives 31 December 1999 three 1s, one 2, one 3 and three 9s - missing 4, 5, 6, 7 and 8, with no plane complete and none absent. One day later, 1 January 2000 gives two 1s and one 2, and nothing else - missing seven digits, with the Emotional and Thought planes both absent.

Nothing about two people born a day apart justifies a reading that different, and the grid does not pretend otherwise: it is honestly reporting that one date is written with eight non-zero digits and the next with three. It is a useful example to keep in mind whenever a grid looks unusually full or unusually empty. Check first how many non-zero digits the date has; that alone explains most of what you see.

The century, measured

The calculator's limits already say that the century fills cells for everyone born in it. Running the engine over every date shows how strongly. The table gives the share of dates in each period on which each digit is missing.

For a twentieth-century birth a missing 1 or 9 is impossible, and for a birth from 2000 onward a missing 2 is impossible. Less obvious is the swing in the other digits. In the 1900s, 5 to 8 are each missing on about three dates in five; for the 2000s, with two zeros in the year until 2010 and one after, the date supplies fewer digits and 5 to 9 are each missing on about three dates in four. A gap at 6 or 7 is ordinary in either century. A gap at 1 is something only a twenty-first-century birth can show, and even then on about one date in five.

Decade by decade

Splitting the same run by decade shows the third digit of the year at work. In every decade, the decade's own digit is never missing - nobody born in the 1970s lacks a 7 - while the other middle digits are each missing on about three dates in four.

The 1990s stand out among twentieth-century decades because the decade digit is 9, which the century already supplies, so the decade adds nothing new and the average number of empty cells rises from about 4.1 to 4.9. The 2000s are the emptiest decade in the range, because years 2000 to 2009 contain two zeros. If you compare your grid with a sibling's or a parent's, much of the difference will be explained by this table before any reading begins.

How many cells are usually empty

No date in either period fills every cell, and none fills eight of them; the fullest grids leave two digits out. The typical twentieth-century grid in this range has four or five empty cells, and the typical grid from 2000 onward has five or six. If your grid is missing five digits you are in the largest group of all. Reading a long list of gaps as unusual would be a misreading of the arithmetic.

The extremes, and what produces them

The fullest grids in the range belong to dates whose day, month and year between them spread across many digits. The first such dates the run found were in 1953: 26 April 1953, for instance, has every digit except 7 and 8. At the other end, the emptiest grids are dates written almost entirely in 2s and 0s. 22 February 2022 gives six 2s and nothing else - eight empty cells - and the same is true, with fewer 2s, of 2 February 2000 and 2 February 2002.

The highest count any single cell reached in the run was 6 - six 1s on dates like 11 November 1981 and 11 November 2011, six 2s on 22 February 2022. Five or more of one digit happened on 196 dates in the whole period. The engine treats all of these the same way it treats a count of 2: the digit is dominant. Nothing in this calculator distinguishes a count of 6 from a count of 2, and the pattern detectors on the other grid calculators, which only ask whether a cell is filled, do not either.

Repeated digits across the population

The same run counts how often each digit is dominant - written twice or more. Across all 27,759 dates from 1950 to 2025, a 1 is dominant on 56.8% of dates, a 2 on 30.8% and a 9 on 27.2%. Every other digit is dominant on roughly 2.5% to 5.6% of dates, with 3 and 4 the rarest. The reason is again the calendar: 1 arrives from 1900s years, from days 10 to 19 and from three of the twelve months; 2 from 2000s years and days in the 20s; 9 from 1900s years. A dominant 1 is the single most common feature of a grid in this period, which is worth remembering before reading it as a personal emphasis.

How often each plane is complete or absent

The planes table itself is in the article linked above and in this site's numerology rules. What neither gives is how often each outcome happens. Across every date from 1950 to 2025:

Two of these are almost settled by the century. The Mental plane holds both 9 and 2, so every 1900s year fills it with a 9 and every 2000s year with a 2 - in this range it is never absent. The Will plane holds 9 and 1, which twentieth-century years supply together, so it is complete on more than a quarter of dates and absent on very few. At the other end, the Thought and Emotional planes contain 3 and 4, the two digits most often missing, so they are frequently empty and rarely complete. A complete Thought plane, at about one date in eighty, is the rarest outcome in the table.

A few grids read in full

The numerology profile runs the planes and the Arrows of Pythagoras on the same count. These are its results for four dates, so you can see how the parts fit together.

• 14 August 1994 (the page's sample): missing 2, 3, 5, 6, 7; dominant 1, 4, 9. No complete plane; Emotional and Action absent. No arrow complete in the Tao layout.
• 17 April 1990 (the article's example): missing 2, 3, 5, 6, 8; dominant 1, 9. No complete or absent plane. One arrow, 1-4-7.
• 27 December 1965: missing only 3, 4 and 8; dominant 1 and 2. Will and Action complete, Thought absent. One arrow, 1-5-9.
• 29 June 1978: missing 3, 4 and 5; dominant 9. Practical and Action complete, no absent plane. One arrow, 7-8-9.

Notice that a complete plane and a complete arrow are different tests on different layouts. 27 December 1965 completes the Will plane (9, 5, 1, a column in the Lo Shu order) and also the Tao arrow 1-5-9 (a diagonal in his order) - the same three digits happen to form a line in both. 29 June 1978 completes the Practical plane (8, 1, 6) but its arrow is 7-8-9, which is not a Lo Shu row or column at all.

Comparing two grids in one family

Putting two grids side by side is the most common thing people do after running this calculator once. Take the page sample, 14 August 1994, and the article's example, 17 April 1990. Both years begin 1, 9, 9, so both grids already hold a 1 and two 9s before the day and month are read. The sample then adds 1, 4, 8 and 4; the other adds 1, 7, 4 and 0. The result is that the two grids agree that 1 and 9 each appear twice and that 4 is present (twice in the sample, once in the other), and differ in only one filled cell each: the sample has an 8 and no 7, the other has a 7 and no 8. Their shared gaps are 2, 3, 5 and 6.

That one-cell difference is enough to change the planes. The sample, missing 7 as well as 3 and 5, has an empty Emotional plane; the 1990 date has a 7 there and so has no absent plane at all. It is also enough to change the Arrows of Pythagoras, where 1, 4 and 7 form a line for the 1990 date. Small differences in the count can flip a reading that is built on whole lines, which is a good reason to look at the count first and the labels second.

One digit, three positions

This app draws its grids in three different layouts, from three different books; the Vedic one also casts its own digits rather than reading this count. Where a digit sits decides which other digits count as its neighbours, so it is worth seeing them side by side.

Only 5 shares a position in two layouts (the centre, in Lo Shu and Tao), and 3 and 9 share theirs between the Vedic layout and Tao's. Everything else moves. A pair of digits that sit side by side in one layout can be on opposite corners in another, which is why the Vedic and Sepharial calculators find combinations this page never mentions. The count you see here is the input for the Sepharial calculator, while the Vedic one casts its own grid; the readings differ because the geometry, and for the Vedic Grid the digits, differ.

Every calculator that reads this count

• Vedic Grid - the one exception: it does not read this count but casts its own grid the way Advanced Vedic Numerology does (PDF p.13), from the day, the month and the last two digits of the year with the Moolank and Bhagyank added, then lists the arrows, conjunctions, aspects, angulars and trines present in its 3 1 9 / 6 7 5 / 2 8 4 layout. For the sample it finds eight.
• Sepharial Grid - the same layout and the same count, read with the combination text of Numerology Masters Notes. For the sample it finds six. Its source casts the grid differently from this page, which that calculator's long-form explains.
• Health Tendencies - takes only the list of missing digits from this count and reports the body areas one source associates with each gap, with no diagnosis.
• Numerology Profile - the full profile, with the missing and dominant lists, the planes and the arrows. It needs a name.
• The signed-in Life Blueprint mentions your missing numbers by name when it lays numerology beside your chart.

All of them call the same function on the same date, so they cannot disagree about which digits are present. On the signed-in Numerology page, the health card is handed the profile's own missing-number list rather than recomputing it, precisely so the card and the grid beside it can never drift apart.

What the count does not include

Some numerology methods add derived numbers into the grid - a reduced day, the total of the date, sometimes the Mulank or Bhagyank. This engine does not. Only the digits written in the date go in. That is why your Mulank can be missing from your own grid, which this site's rules call correct rather than a bug: 17 April 1990 has a Mulank of 8 (1 + 7) and no 8 anywhere in the date. Readers who have cast a grid by hand using a method that adds reductions will see more filled cells there than here. Neither is an error of arithmetic; they are different recipes, and this page follows the plain-count one documented in section 4 of the rules.

Checking your grid by hand

1. 1.Write the day, the month and the four-digit year as plain numbers, with no leading zeros - for example 27, 12, 1965.
2. 2.List every digit: 2, 7, 1, 2, 1, 9, 6, 5.
3. 3.Drop any zeros.
4. 4.Tally: 1 twice, 2 twice, 5 once, 6 once, 7 once, 9 once; 3, 4 and 8 not at all.
5. 5.Place the tallies in the 4 9 2 / 3 5 7 / 8 1 6 order. The cells for 3, 4 and 8 - the whole Thought column - are empty.

If the page and your tally disagree, the cause is almost always a dropped digit of the year or a zero counted by mistake. The calculator reads the calendar date exactly as entered, with no time zone involved, so it cannot shift the day.

Common misreadings of a grid

• Treating a gap as rare. Four to six empty cells is the norm, and gaps at 3 and 4 are each present on around seven dates in ten.
• Treating a dominant 1 as a personal emphasis. It is the most common feature of any grid in this period, present on more than half of all dates.
• Reading the cells as scores. A cell holds a count of how often a digit is written. Three 9s is not three times as much of anything to this engine; it is reported as dominant, exactly like two.
• Assuming the sum of 15 means something about you. The magic-square property belongs to the digit labels in the layout. Your counts are never added up.
• Mixing layouts. A line that is complete in the Tao arrangement or the Vedic arrangement is not a line in the Lo Shu order, and the reverse. Each calculator states its own layout.
• Counting zeros, or the century twice. Zeros never count, and the year's four digits are counted once each, like every other digit.
• Adding derived numbers by habit. If you were taught to put the Mulank or the date's total into the grid, your hand-cast grid will differ from this one. This engine counts only what is written.

Limits worth keeping in view

The grid is the most mechanical thing in this site's numerology, and that is its strength: anyone can check it. Its weakness is the same fact seen from the other side. Most of what it shows is decided by the century and the shape of the calendar, a tenth of dates share their grid with nine others, and the most common features - a dominant 1, a missing 3 or 4, an absent Thought plane - are common precisely because of how dates are written. Any reading layered on top inherits those facts. The calculators that read the grid say which source they follow, and this page's job is only to make the count itself clear.

For the wider approach to sources and uncertainty across the site, see the methodology; for the core numbers that sit beside the grid, the free numerology tool and the Numerology feature.

More questions about the Lo Shu grid

Is it unusual to have five or six empty cells?

No. For births from 1950 to 1999 the most common number of empty cells is four (42.8% of dates), then five; for births from 2000 to 2025 it is five (44.6%), then six. No date in the whole range fills more than seven cells.

Why can a 1900s birth never be missing 1 or 9?

Because every year from 1900 to 1999 begins with 1 and 9, and the grid counts the year's digits. In the same way, every year from 2000 to 2099 contains a 2.

Does a digit written five times mean more than one written twice?

Not to this engine. Both are reported as dominant. The pattern detectors on the Vedic and Sepharial pages only check whether a cell is filled. The Vedic source's own text mentions repetition in a few combinations, but only as prose.

Why are the diagonals not planes?

The profile engine's plane table lists the three rows and three columns of the Lo Shu order and nothing else. The diagonals, 4-5-6 and 2-5-8, still add to 15 in the magic square, but the engine does not report them.

How many people share my grid?

On average about ten birth dates per grid in the period run: 1,745 distinct grids for 18,262 dates in 1950-1999, and 1,023 for 9,497 dates in 2000-2025. Dates with the same digits in a different order always match.

Which plane is most often complete?

The Will plane (9, 5, 1), on 27.8% of dates from 1950 to 2025, largely because 1900s years supply both 1 and 9. The Thought plane (4, 3, 8) is the least often complete, at 1.2%.

Why does the Sepharial page show a different grid in its book example?

Its source casts the grid with reduced numbers and without the century, while this page and the Sepharial calculator use this plain count; only the Vedic Grid calculator casts its own grid, the way its own book does. The Sepharial long-form shows the difference on the book's own example date.

Why do 1990s births have more empty cells than 1980s births?

Because the decade digit of a 1990s year is 9, which the century already supplies. A 1980s year adds an 8 that the century does not, so it fills one more cell for everyone born in that decade. The run gives an average of 4.88 empty cells for the 1990s against 4.14 for the 1980s.

Do twins always share a grid?

Twins born on the same calendar day do, because birth time is never read. Twins born either side of midnight have different days and can have different grids; the engine reads the date exactly as entered.

Will my grid ever change?

No. It is fixed by the date of birth. Nothing in the engine reads today's date. Numerology numbers that move with time are the personal cycles, not the grid.