How to calculate your I Ching hexagram

Every consultation of the I Ching arrives at the same point: six lines that together form one of the 64 hexagrams. Between the throw and that hexagram sits a small calculation, and that is where mistakes creep in: a line in the wrong place, a trigram read the wrong way. Once you know the four line values and build from the bottom up, you can convert any throw without error. Here is how the arithmetic works, step by step.

The four line values: 6, 7, 8 and 9

Every line of a hexagram starts as a number, and that number can only take four values:

• 7: young yang, an unbroken line at rest;
• 8: young yin, a broken line at rest;
• 9: old yang, an unbroken line about to move;
• 6: old yin, a broken line about to move.

The memory aid: even is yin, odd is yang. And the extremes, 6 and 9, are "old": so full that they are about to tip into their opposite. More on that below.

With three coins: adding 2s and 3s

In the coin method every head counts as 3 and every tail as 2. You throw three coins at once and add up the values. Only four sums are possible: 2+2+2 = 6, 2+2+3 = 7, 2+3+3 = 8 and 3+3+3 = 9. Throw six times, write down six numbers, done.

With yarrow stalks: three counts

The classical method works with a bundle of fifty stalks, forty-nine of which take part. For each line you divide and count the bundle three times, and each counting round ultimately yields a 2 or a 3. Three counts together again give a number from 6 to 9, only with different odds than the coins: with stalks a 6 is rare and an 8 the most common outcome. The full counting ritual is described in the article on the yarrow stalks; if you have no bundle of your own, you can consult the oracle online with stalks.

Building from the bottom up

The first line you throw is the bottom line of the hexagram. You build upwards, the way a plant grows: first the root, then the stem, the crown last. So write your six numbers down from bottom to top. Reverse the order and you will neatly calculate the wrong hexagram, which is by far the most common mistake in the whole process.

Two trigrams, one number

Six lines form two trigrams of three lines each: lines one to three make the lower trigram, lines four to six the upper one. There are eight trigrams (heaven, earth, thunder, water, mountain, wind, fire and lake), and eight times eight gives exactly 64 combinations. Which combination carries which number is fixed in the King Wen sequence; you look that number up in a table or in the overview of all 64 hexagrams.

An example. From the bottom up you throw 7, 8, 8, 9, 7, 8. The lowest three lines (yang, yin, yin) form the trigram thunder; the top three (yang, yang, yin) form the trigram lake. Thunder below and lake above: that is hexagram 17, Following.

Old lines: where the movement is

For the reading itself, only yin or yang counts at first: a 6 reads as a broken line, a 9 as an unbroken one. But then the old lines do something extra: they flip. Every 9 becomes a broken line, every 6 an unbroken one, and out of that reversal a second hexagram appears, showing where the situation is heading. In the example above the 9 in fourth place changes, and hexagram 17 becomes hexagram 3, Difficulty at the Beginning. How to read that movement is covered in the article on changing lines.

Already cast? Enter your hexagram

If you have thrown coins or stalks at home and want the interpretation to go with it, there is nothing to look up. On theiching.app, choose the input option Cast by hand and enter the value for each line, from bottom to top; the app calculates the hexagram, the moving lines and the second hexagram for you.

Good to know: every reading gets a fixed web address ending in ?w= followed by six digits, the line values from bottom to top. The throw from the example becomes ?w=788978. That notation doubles as a compact way to keep a throw on paper or share it with someone: six digits, and the whole hexagram is there.

Frequently asked questions

What do the numbers 6, 7, 8 and 9 mean in the I Ching?

They are the four possible values of a single line. 7 is young yang (unbroken, at rest), 8 is young yin (broken, at rest), 9 is old yang and 6 is old yin; the last two are moving lines that flip into their opposite.

Do you build a hexagram from the top or from the bottom?

Always from the bottom up: the first throw is the bottom line, the sixth throw the top line. Reverse the order and you end up with a different hexagram, so write your numbers down from bottom to top.

How do I find the number of my hexagram?

Read the lowest three lines as the lower trigram and the top three as the upper trigram, then look that combination up in a trigram table or in the hexagram overview. Every combination of two trigrams has a fixed number in the King Wen sequence.

Can I enter a hexagram I have already cast into the app?

Yes. On theiching.app, choose the Cast by hand input option and enter the six line values from bottom to top. The app then calculates the hexagram, the moving lines and the second hexagram, complete with the full interpretation.