I Ching essentials

How to Calculate Your I Ching Birth Hexagram by Hand

To calculate your I Ching birth hexagram, turn your birth date into four Chinese lunar numbers: the year branch, the lunar month, the lunar day and the hour. Add year, month and day and divide by 8: the remainder gives the upper trigram. Add the hour, and the remainders of that total after dividing by 8 and by 6 give the lower trigram and the changing line. Every step below can be done with a pen and your own birth date.

This is the Plum Blossom method, Mei Hua Yi Shu (梅花易数), in the birth-date form HexWave uses. The formula comes from the classical text of that name, traditionally attributed to the Song dynasty scholar Shao Yong, and practitioners differ on the calendar boundaries around it: some start the year at a solar term instead of the lunar new year, some roll the day at 23:00, some treat leap months differently. This page follows HexWave's convention to the letter, so if you follow it too, you will arrive at the same Birth Hexagram Triad the app gives you.

The example running down the page is 7 February 1995, with no birth time. Work your own date alongside it as you go.

What you need before you start

Three things, and only the first is required.

Your birth date. Day, month and year. It is the one input the method cannot do without.

Your birth time, if you know it. It only has to be accurate enough to place you in the right two-hour block. Without it, the method uses noon and still gives a complete triad.

A lunar calendar converter. Any Chinese lunar calendar converter will turn your date into a lunar month and day. You can also let the app do the conversion and follow along here to see where its numbers come from.

HexWave labels a reading from the date alone as approximate, because the hour feeds two of the three remainders. A birth time sharpens the reading, and a birthplace sharpens it again. The page on how HexWave calculates your birth hexagram explains what each one changes and why; this page stays with the arithmetic.

Step 1: Find your year number

Chinese years run in a cycle of twelve Earthly Branches, the same cycle as the twelve zodiac animals. Your year number is your animal's place in that cycle.

A shortcut if you know the year but not the animal: subtract 3 from your birth year and divide by 12. The remainder is your year number, and a remainder of 0 counts as 12. For 1995, 1992 divided by 12 leaves 0, so the year number is 12: Hai, the Pig.

The one trap is the new-year boundary: the lunar year begins at the lunar new year, which falls between 21 January and 20 February, not on 1 January. If you were born in January or February, look up the lunar new year for your birth year. If your birthday comes before it, you belong to the previous year's animal, so take one off your year number (1 becomes 12).

In 1995 the lunar new year fell on 31 January, so 7 February 1995 is already the year of the Pig. Year number: 12.

Step 2: Find your lunar month and day

Put your birth date into a lunar calendar converter and write down two numbers: the lunar month, from 1 to 12, and the lunar day, from 1 to 30. Lunar months begin at a new moon and run three to seven weeks behind the Western calendar, so a birthday in early March falls in the first or second lunar month, never the third.

Two rules in HexWave's convention. Some lunar years repeat a month, called a leap month; if you were born in one, keep the number of the month it repeats. And the lunar day changes at midnight, so a birth at 23:30 still belongs to that day, not the next.

For 7 February 1995 the converter gives lunar month 1, lunar day 8.

Step 3: Find your hour number

The traditional Chinese day has twelve double hours, two clock hours each, named after the same twelve branches. Find the block your birth time falls in:

If you do not know your birth time, use 7, the Wu hour around noon. Classical practice always has the hour; the noon default is HexWave's way of giving a reading when the time is unknown, and it is the reason a date-only reading is marked approximate.

The first block, Zi, spans midnight: it covers 23:00 to 23:59 late in the evening and 00:00 to 00:59 early in the morning. The lunar date from step 2 changes at midnight, so a birth at 23:30 is hour 1 and keeps the lunar day of the date you were born on. Schools that roll the day at 23:00 would use the next day's number instead; this page does not.

In the app, adding your birthplace does two things. It takes the hour from local mean time at that place rather than clock time, which can move a birth into the neighbouring block, and it reads the lunar date in Beijing time, so an afternoon or evening birth in Europe or the Americas can land on the next lunar day. By hand, use your local date and clock time.

The example has no birth time, so its hour number is 7.

Step 4: Add, then divide

You now have four numbers. Make two sums and three divisions. For each division, keep only the remainder: what is left over after dividing as many whole times as you can.

Sum A = year + month + day
Sum B = Sum A + hour
Upper trigram = the remainder of Sum A ÷ 8
Lower trigram = the remainder of Sum B ÷ 8
Changing line = the remainder of Sum B ÷ 6

A remainder of 0 counts as 8 for a trigram and as 6 for the line. There is a full example of that further down. For 7 February 1995:

Sum A = 12 + 1 + 8 = 21
Sum B = 21 + 7 = 28
21 ÷ 8 = 2, remainder 5 → upper trigram 5
28 ÷ 8 = 3, remainder 4 → lower trigram 4
28 ÷ 6 = 4, remainder 4 → changing line 4

Step 5: Turn the two remainders into trigrams

Each number from 1 to 8 names one of the eight trigrams, in the Early Heaven order:

In the example, 5 is Xun, Wind, and 4 is Zhen, Thunder. Wind goes on top and Thunder underneath.

Step 6: Look up your hexagram

Start with your lower trigram, the second remainder, down the left side, then move across to your upper trigram, the first remainder, along the top. The cell where they meet is your Primary Hexagram, numbered in the traditional King Wen order. Each cell links to that hexagram's page; hover or focus a cell for its name.

Thunder row, Wind column: Hexagram 42, Increase. That is the Primary Hexagram for 7 February 1995 on the date alone.

Step 7: Flip the changing line

Hexagram lines are counted from the bottom. Lines 1, 2 and 3 form the lower trigram, and lines 4, 5 and 6 the upper one. Your third remainder points at one of those six lines, and that line is your Changing Line.

Flip it: a solid line becomes broken, a broken line becomes solid, and the other five stay as they are. Only one trigram changes, so you can find the new trigram in the step 5 table and look up the new pair in the step 6 table. That second hexagram is your Resultant Hexagram.

In the example, line 4 is the bottom line of the upper trigram. Wind is broken at the bottom and solid above it. Flipping that bottom line makes all three lines solid, which is Qian, Heaven. Heaven above Thunder is Hexagram 25, Innocence.

So 7 February 1995, on the date alone, gives Hexagram 42, Increase, with a changing fourth line, moving toward Hexagram 25, Innocence. That is the whole triad.

When a remainder comes out as zero

Sometimes a sum divides exactly. Take 9 September 1988, again with no birth time: year number 5 (Chen, the Dragon), lunar month 7, lunar day 29, and the noon hour, 7.

Sum A = 5 + 7 + 29 = 41
Sum B = 41 + 7 = 48
41 ÷ 8 = 5, remainder 1 → upper trigram 1, Qian, Heaven
48 ÷ 8 = 6, remainder 0 → counts as 8, Kun, Earth
48 ÷ 6 = 8, remainder 0 → counts as line 6

Earth below and Heaven above is Hexagram 12, Standstill. Line 6 is the top line of Heaven, and flipping it to broken turns Heaven into Lake. Lake above Earth is Hexagram 45, Gathering Together.

A zero never means a step went wrong. The count landed exactly on the last place, so it takes the last number: 8 for a trigram, 6 for a line.

Common questions

Check your answer

Once you have your triad, check it against the Birth Hexagram Calculator: pick your birthday, choose your birth year, and add your birth time if you used one. It runs the same engine as the app.

If your answer differs, look first at the places where hand calculation usually slips: a January or February birthday that falls before the lunar new year, a late-evening birth given the wrong lunar day, or a birth time sitting on the edge of a two-hour block.

Then read what you found. The Birth Hexagram Triad explains what the Primary Hexagram, the Changing Line and the Resultant Hexagram each describe.

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