I Ching essentials

How We Calculate Your Birth Hexagram

Most systems that turn a birth date into a symbol ask you to trust them. We would rather show you the arithmetic.

Your Birth Hexagram Triad is not generated, guessed, or drawn from a table. It is computed, the same way every time, from a method that is roughly a thousand years old. The same birth date always produces the same triad. Run the numbers yourself and you will land where we land.

Here is the whole calculation.

Step 1: Your birth date becomes four numbers

The method is called Plum Blossom, or Mei Hua Yi Shu (梅花易数), and it works on the Chinese lunar calendar rather than the Western one. So the first thing we do is convert your birth moment into four lunar numbers.

The year branch. Chinese years cycle through twelve Earthly Branches, the same cycle behind the zodiac animals. Each branch has a number from 1 to 12.

The lunar month. A number from 1 to 12. Lunar months do not line up with January and February, so a birthday in early March is often still the second lunar month.

The lunar day. A number from 1 to 30, counted from the new moon rather than from the first of the month.

The hour branch. The day is divided into twelve two-hour periods, each carrying one of the same twelve branches. Numbered 1 to 12.

Four numbers. Everything after this is arithmetic you can do on paper.

Step 2: Three remainders

The method takes those four numbers and divides them down to remainders. That is the whole engine of it.

Upper trigram = (year + month + day) mod 8   (a remainder of 0 counts as 8)
Lower trigram = (year + month + day + hour) mod 8   (a remainder of 0 counts as 8)
Moving line = (year + month + day + hour) mod 6   (a remainder of 0 counts as 6)

Notice what the hour touches. The upper trigram is built from the date alone. The lower trigram and the moving line both include the hour. This matters, and we come back to it below.

Step 3: Remainders become trigrams

A trigram is three stacked lines, each solid or broken, and there are exactly eight of them. The numbers 1 through 8 map onto those eight in the Earlier Heaven sequence, the arrangement Shao Yong worked with:

Stack the lower trigram underneath the upper one and you have six lines. That six-line figure is your Primary Hexagram, one of sixty-four. Hexagrams are read from the bottom up, so the lower trigram is lines 1, 2 and 3, and the upper trigram is lines 4, 5 and 6.

Step 4: One line is in motion

The moving line, that third remainder, points at one of the six lines and says: this is the part of the pattern that is changing. In HexWave we call it your Changing Line, and it is the growth edge of the reading.

Flip it. A solid line becomes broken, a broken line becomes solid, and the five other lines stay exactly as they are. That single flip produces a different hexagram: your Resultant Hexagram, the direction the pattern is tending.

Primary, Changing Line, Resultant. That is the triad.

A worked example

Take 14 March 1990, with no birth time given.

Converted to the lunar calendar, that birth date is year branch 7, lunar month 2, lunar day 18. With no time supplied we use noon, which falls in the Wu hour, branch 7.

Upper trigram = (7 + 2 + 18) = 27,  27 mod 8 = 3  ->  Li, Fire
Lower trigram = (7 + 2 + 18 + 7) = 34,  34 mod 8 = 2  ->  Dui, Lake
Moving line = (7 + 2 + 18 + 7) = 34,  34 mod 6 = 4  ->  line 4

Fire above, Lake below, gives Hexagram 38, Opposition. Flipping the fourth line turns the upper trigram from Fire into Mountain, which gives Hexagram 41, Decrease.

So a person born on 14 March 1990, on the date alone, carries Hexagram 38 with a changing fourth line, resolving toward Hexagram 41.

What your birth time changes, honestly

Now take the same date and add a real birth time of 07:45, which falls in the Chen hour, branch 5:

Upper trigram = (7 + 2 + 18) = 27,  27 mod 8 = 3  ->  Li, Fire   (unchanged)
Lower trigram = (7 + 2 + 18 + 5) = 32,  32 mod 8 = 0  ->  8, Kun, Earth
Moving line = (7 + 2 + 18 + 5) = 32,  32 mod 6 = 2  ->  line 2

That is Hexagram 35, Progress, resolving toward Hexagram 64, Before Completion. A completely different triad, from the same birth date.

We would rather you knew that than discovered it later. The upper trigram is the only part of your triad that the date alone fixes. Your hour moves the lower trigram, the changing line, and therefore the resultant hexagram too.

This is not a flaw in the method. It is the method being precise about time, which is what a time-casting oracle is for. But it does mean a reading built from a date alone is a real reading of a real pattern, and a reading built from a date, a time and a place is a sharper one.

The three precision tiers

HexWave never blocks you for having incomplete information. It tells you what it had to work with instead.

Date only. You give us a birth date. We use noon as the hour, which is an honest, stated default rather than a guess dressed up as data. You get a complete triad, and we label the reading as approximate.

Date and time. Your actual hour branch replaces the noon default. The lower trigram and changing line now reflect the hour you were really born.

Date, time and place. The most precise tier, and the one that does the most work behind the scenes. Your birth location lets us correct for Local Mean Time, which is solar time at your exact longitude rather than the political time zone your government happened to draw around you. Clock time and sun time can differ by well over half an hour, and near an hour boundary that difference changes your hour branch and therefore your triad. We read the hour branch from Local Mean Time, and the year, month and day from China Standard Time, which is the reference frame the lunar calendar is defined against.

You can move up a tier at any time by adding your birth time or birthplace, and your triad will recalculate.

Take it with you - or keep it in the browser. Your choice.

The conventions we chose, and why

Any honest implementation of a thousand-year-old method has to make a few calls. Here are ours.

The lunar day rolls at midnight. A birth at 23:30 still belongs to the current lunar calendar day. Some related systems roll the day at 23:00 instead, and our own Chinese zodiac calculation does exactly that for its day pillar, because a day pillar is a different unit from a calendar date. For Plum Blossom the calendar day is what the method asks for, so midnight is the correct boundary.

Leap months keep their number. The lunar calendar occasionally repeats a month. When it does, the repeated month keeps the number of the month it doubles.

Hexagram numbers follow the King Wen sequence. When we say Hexagram 38, we mean the thirty-eighth hexagram in the traditional ordering, the same one you will find in any standard edition of the I Ching.

Where this comes from

The Plum Blossom method is traditionally attributed to Shao Yong (1011 to 1077), a Song dynasty scholar who spent his life looking for the mathematical order underneath ordinary events. The attribution is traditional rather than documentary, as it is for most texts of that age, and we say attributed because that is what the record supports.

For the hexagrams themselves, the standard English reference remains the Wilhelm-Baynes I Ching: Richard Wilhelm's German translation, rendered into English by Cary F. Baynes and published by Princeton University Press. It is the edition most English readers have met, and the reason certain hexagram names sound familiar.

If you want the story and the philosophy rather than the arithmetic, our Plum Blossom Oracle primer covers where the method came from, and The Birth Hexagram Triad explains what the three parts mean once you have them.

What this is, and what it is not

The calculation above is deterministic. Give it the same inputs and it returns the same triad, forever, on any device. That part is mathematics and we are happy to be held to it.

What the hexagrams then mean is a different kind of claim. The I Ching is a system of symbols for thinking about change, and HexWave is a reading tool. We are precise about the arithmetic so that you can be appropriately skeptical about everything downstream of it.

Your birth date is already a number. This is simply what happens when you read it carefully.