Lo Shu Grid by Date of Birth: Missing Numbers Counted

A Lo Shu grid is a three-by-three square with a box for each number from 1 to 9. To fill it from a date of birth, write each digit of the date into its box. A 0 has no box and is dropped, and any box left empty is a “missing number”. An eight-digit date can never fill all nine boxes. On every date counted below at least two are empty, and most dates leave four or five empty.

This page shows how the grid is drawn, the two versions calculators use, and what a count of every calendar date from 1 January 1926 to 31 December 2025 (36,525 dates) shows about missing numbers. It does not say what any number, gap or line means, and it gives no remedies. Those are readings, and the arithmetic cannot check them.

The Square Itself

The boxes are not in counting order. The top row reads 4, 9, 2, the middle 3, 5, 7 and the bottom 8, 1, 6, which makes the Lo Shu a magic square: every row, column and diagonal adds up to 15. Chinese legend says it was first seen as a pattern of dots on the shell of a turtle that came out of the Luo river, and the name means roughly “the Luo river writing”. Filling it with the digits of a birth date is a modern practice. It is not part of Vedic ank jyotish, which works from the moolank and the bhagyank and gives each digit a ruling graha.

How to Draw It: Born 15 August 1990

Write the date in full as 15 08 1990 and set aside the zeros. The digits left are 1, 5, 8, 1, 9 and 9. Each goes into its box, so a digit that appears twice is written twice:

The five empty boxes, 2, 3, 4, 6 and 7, are this date’s missing numbers, and 1 and 9 are its repeated ones.

With or Without the Moolank and Bhagyank

Calculators differ on one step. Some add two more numbers to the grid: the moolank (driver number), which is the birth day reduced to one digit, and the bhagyank (conductor number), which is the whole date reduced to one digit. For 15 August 1990 both are 6 (the whole date adds to 33, a master number, but the grid takes its single digit), so the 6 box gets two entries and the missing numbers drop to 2, 3, 4 and 7. Some versions also add a Kua number from the birth year, a feng-shui figure this page leaves out. Neither of the two is more correct. They are two conventions, so check which one a calculator follows before comparing its grid with another.

A Second Example: Born 3 January 2001

The date 03-01-2001 gives only 3, 1, 2 and 1 once the zeros go, so six boxes are empty: 4, 5, 6, 7, 8 and 9. Adding the moolank 3 and the bhagyank 7 fills the 7 box and leaves 4, 5, 6, 8 and 9. Births after 2000 often look like this, for a reason the census makes plain.

How Often Each Number Is Missing

Share of all 36,525 dates from 1926 to 2025 on which each number’s box is empty:

The year decides most of this. Every year from 1926 to 1999 starts with 1 and 9, so those two boxes are never empty for a birth from 1926 to 1999, which is why 1 is missing on only 5.5% of dates and 9 on 19.9%. Every year from 2000 starts with 2 and 0, so 2 is never missing after 1999. The numbers 3 to 8 can only come from the day, the month or the last two digits of the year, and each is missing on about two dates in three. So a missing 5 is the usual case: 66.8% of dates have no 5, or 55% with the moolank and bhagyank added.

How Many Numbers a Grid Misses

On the date digits alone, a grid misses 4.6 numbers on average. 70.2% of dates miss four or five, only 360 dates miss as few as two, and 12 dates miss eight, the most possible. Adding the moolank and bhagyank lowers the average to 3.7. It also makes a full grid possible, though only just: six dates in the century have every box filled, all of them on a 26th (26 July 1934, 26 April 1937, 26 July 1943, 26 March 1947, 26 April 1973 and 26 March 1974).

Born Before or After 2000

The two centuries give different-looking grids, on the date digits alone:

A birth from 2000 onwards has about one more empty box than a 1900s birth (5.4 against 4.2), because 20 gives the grid only a 2, where 19 gives both a 1 and a 9. Its 9 is missing on 76.6% of dates, where a 1900s birth never lacks one, and its 1 is missing on 21%. Any comparison of grids across generations is mostly a comparison of years.

Full Rows, Columns and Diagonals

Practitioners give names to a row, column or diagonal whose three boxes are all filled, calling it a plane or an arrow. Here is how often each line is complete:

The commonest full line is the centre column, 9-5-1, complete on 27% of dates, because it holds the 1 and the 9 that a 1900s year always supplies. The rarest is the 4-5-6 diagonal, complete on 1.8%. No box holds one digit more than six times on the date alone (first on 11 November 1931, six 1s), or seven times with the two extra numbers (first on 11 November 1941).

What This Page Does Not Give

It gives no meaning for a missing number, a repeated number or a full line, and no remedy for an empty box. Nothing in the counting can test such readings. It gives no lucky number, colour, day or direction either. The counts are of calendar dates, one per day, not of people. A share here is the share of dates, not the share of a population.

The two extra numbers come from the same arithmetic as the site’s numerology pages. The life path number guide shows how the bhagyank is reduced and why calculators can disagree on 11, 22 and 33. The lucky number by date of birth page explains how ank jyotish uses the moolank instead of a grid. In Hindi: लो शू ग्रिड कैसे बनाएं: जन्मतिथि से गायब अंकों की गिनती.

In Brief

• The square: 4 9 2 / 3 5 7 / 8 1 6, every line adding to 15; zeros have no box
• Two versions: date digits only, or with the moolank and bhagyank added; check which one a calculator uses
• Always missing something: at least two empty boxes on the date alone; six full grids in a century with the extra two
• 3 to 8: each missing on about two dates in three; 1 and 9 never missing for a 1900s birth, 2 never after 1999
• No readings: no meanings or remedies are given for any number or line