Sexagenary Cycle

In the last two posts, I listed the ten Heavenly Stems and the twelve Earthly Branches. I think that knowledge of these things is useful. And it’s just not very difficult. Of course, if you plan to take much of an interest in Chinese history, it could be essential.

Ten times twelve equals sixty

For much of Chinese history, years were listed by a combination of the Stems and Branches. This gives us sixty years in a cycle, not a hundred and twenty, as will become clear. If sixty years doesn’t seem very helpful, remember that only the Qianlong Emperor lasted a full cycle on the throne. With a little knowledge of Chinese history, you can pinpoint all kinds of dates, or at  least work out how many years passed between certain dates within a limited span.

Firstly, we need to look at how the two sequences combine.

The inner wheel rolls round the inside of the outer wheel.


As there are twelve branches (outer wheel) and only ten stems (inner wheel), the cycle shifts by two places each turn, meaning that only half of the possible combinations of stems and branches are used. The odd-placed (red) stems only ever match up with the odd-placed (red) branches, even (yellow) stems and even (yellow) branches fit together.

The Heavenly Stem comes first, and the Earthly Branch comes second.

Parallel Stems

So the first year  in the sequence is 甲子 jiǎǐ Then come 乙丑 yǐchǒu, 丙寅 bǐngyín, through to the tenth year, 癸酉 guǐyǒu. Now the first character (the stem) returns to the beginning of the sequence: 甲戌 jiǎxū is the eleventh year of the cycle. After all twelve branches have been used, they too return to the start of the sequence giving 丙子 bǐngzǐ, the thirteenth year.

Five cycles round the twelve branches gives us sixty years. Then you start again.

Putting it into practice

Let’s look at an example of some dates usually referred to using the Sexagenary Cycle.  The First Sino-Japanese War is called 甲午战争 Jiǎwǔ Zhànzhēng. You know this took place sometime toward the end of the Qing Dynasty, but may be a little hazy about exactly when. The Xinhai Revolution 辛亥革命 Xīnhài Gémìng brought a close to the Qing. Somewhere during this period there was also the Hundred Days Reform, or 戊戌变法 Wùxū Biànfǎ. Actually, it’s not too hard to work out how these dates relate to each other.

天干So we have three dates in sexagenary form:

甲午战争 Jiǎwǔ Zhànzhēng

戊戌变法 Wùxū Biànfǎ

辛亥革命 Xīnhài Gémìng

Remember, our dates are in the form:

Stem – Branch

First count the number of stems from 甲 jiǎ to 戊 wù:

乙 yǐ,丙 bǐng,丁 dīng,戊 wù = 4 places1.

If you’ve not got the Heavenly Stems fixed on the fingers – no matter; that inner wheel turns, after all. But this is where it’s useful to have the twelve Earthly Branches really nailed to those fingers.

If you’ve not managed to learn them off by heart, here’s nothing wrong with actually writing the Earthly Branches on your left hand at this stage. You need to be able move your left thumb around the circle, stopping at any of the twelve points and naming it.

地支As we have counted four stems, from 甲 jiǎ to 戊 wù, we now need to move four places on the Earthly Branches forward from the 午 wǔ of 甲午 jiǎwǔ:

Press the thumb of the left hand against tip of the middle finger and count clockwise, as shown…未 wèi, 申shēn, 酉yǒu, 戌 xū.

It just happens that 戌 xū is the Heavenly Branch of the year we were looking for. We  have moved forward four places –  four years – from 甲午 jiǎwǔ, to 戊戌 wùxū.

The Hundred Days Reform (戊戌变法 Wùxū Biànfǎ) came four years after the start of the First Sino-Japanese War (甲午战争 Jiǎwǔ Zhànzhēng). That was easy enough. The two dates were close together. Our inner wheel didn’t have time to complete a full turn.

Let’s have a look the next date.

How many years after 戊戌变法 Wùxū Biànfǎ did the Xinhai Revolution, 辛亥革命 Xīnhài Gémìng, begin?

First, remember, we count the Heavenly Stems – first heaven, then earth. Our staring place is 戊 wù, so we count 己 jǐ, 庚 gēng, 辛 xīn – 3 places.

Our first date was 戊戌 wùxū, so find the branch 戌 xū (hint: it’s on the little finger) with the thumb of your left hand. Count forward three places starting from 戌 xū. You should reach the base of your middle finger, which holds 丑 chǒu. This position represents the year 辛丑 xīnchǒu, three years after 戊戌 wùxū. We’ve advanced three places, which means that both the stems and the branches have advanced three places.

But we’re looking for 辛亥 xīnhài and not 辛丑 xīnchǒu.

At this point we might try counting out another ten places and find that we reach our target, but there’s an easier way.

As we have a ten and a twelve scale together, instead of advancing ten places, we can just jump back two. So from the base of the middle finger we jump checkers-style back to the base of the little finger, adding ten years as we go.

The base of the little finger is exactly where we want to be – 亥 hài, 辛亥 xīnhài indeed.


The Xinhai Revolution (辛亥革命 Xīnhài Gémìng) was 13 years after the Hundred Days Reform (戊戌变法 Wùxū Biànfǎ).

You can keep jumping back two places, adding ten years at a time if you wish; 辛酉 – 23 years later, 辛未 – 33 years, etc. This saves us counting round and round the fingers. We never have to move more than a few places to find the date we’re looking for.

Switching Calendars

Sooner or later, you’re going to want to pin all this to more familiar calendar dates.















































You may have already spotted that the first character in the sexagenary date (the Heavenly Stem) will match up with the final digit in the year as it’s conventionally written. After all, there are ten Heavenly Stems, and we step through them year by year.

As it happens, during the Common Era, or AD, the first Heavenly Stem, 甲 jiǎ, is always a year ending in 4. 1984, 1994, 2004 were all 甲 jiǎ years. A quick count on your fingers, starting from 4 – 甲 jiǎ, will tell you that years ending in zero are all 庚 gēng years.

This isn’t going to be too difficult, is it?

Any century divisible by 3(00) is going to be a 庚申 gēngshēn year. So 1200, 1500 and 1800 were all 庚申 gēngshēn years. The century year after one of these will be a 庚子 gēngzǐ year, the one before will be a 庚辰 gēngchén year. So 1900 was 庚子 gēngzǐ; and the year 2000 庚辰 gēngchén.

As 申 shēn is the monkey year, you might think of the three wise monkeys. Century years divisible by three hundred are monkey years in the common era. I’m sure you can come up with a way to remember the other two.

Let’s suppose you want to know which year 1988 was. Well, 1900 was a 庚子 gēngzǐ year, so 1960 must have been too. Remember, the Earthly Branches are fixed to your fingers, let’s free the Heavenly Stems from their moorings to save a little time:

子 zǐ is the base of the ring finger. Press here but say 庚 gēng. Now jump back twice – two places each time, remember. This takes you forward 20 years. 庚子 gēngzǐ,  庚戌 gēngxū, 庚申 gēngshēn (the tip of your little finger); this is 1980. We now need to count forwards, counting Heavenly Stems, eight places from here; 辛 xīn,壬rén,癸 guǐ,甲 jiǎ,乙 yǐ,丙 bǐng,丁 dīng,戊 wù and you should have reached 戊 wù on the second joint of your forefinger, which you know is the position for 辰 chén, so you have your answer:

1988 is 戊辰 wùchén.

Try working out some familiar dates. You’ll have it down in no time.

Stems are free to roll around,
But branches are never played.
The stems count units with the clock,
And the branches jump back a decade.

You’ll need to exercise a little care if you want to move to dates BCE, but it shouldn’t be too difficult to work out once you have the basics down.

1Note: If you want to work out, say, which year of an Emperor’s reign an event took place in, you must obviously count the first year as one. This will give you the nth year.

For the translation of this little piece of doggerel, I accept full responsibility. The original, and much of the above explanation came from Baidupedia. For anyone interested in other ways of working out the Sexagenary Cycle, there’s plenty more to go at.

12 responses to “Sexagenary Cycle”

  1. Matt says:

    This is really cool. I study oracle-bone inscriptions, so I have to know the heavenly stems & earthly branches in order, and I can draw up a chart within a minute or two to figure out any particular date if I need to (I’ve done this exactly once, though—I usually have access to either my computer, my phone, or my wallet, each of which has a nice chart in it). But I like the idea of just being able to figure it out on my fingers, so I think I’ll learn this. Thanks!

    • Sima says:

      Matt, I hope it’s useful.

      I’ll be very interested to know how you get on. I got the stems and branches fixed on the fingers pretty quickly, and have been pleasantly surprised by how much assigning positions to them helped. I don’t have to use dates in this form very often, so I’m still pretty mechanical with the calculation. If you manage to develop a real fluency, I’d love to hear any insights.

      I have a suspicion that this particular arrangement on the fingers, with 甲-寅 aligned, rather than 甲-子, and the stems on three fingers, vertically, might lead to a further trick or shortcut, but I’ve not yet been able to work it out.

  2. David Lloyd-Jones says:

    Thank you! This twelve times ten thing has been driving me crazy for years — not least because I can’t figger out how the human race can generate so many editors stupid enough to let all the non-explanations into print.

    Good work. Well done.


    • Sima says:

      David, I stumbled on the finger counting thing by chance, but it was surprisingly difficult to track down how it all worked. The information online is pretty scattered, with some sites having a picture or two but no proper explanation. The Baidu page I linked to, above, had a pretty detailed explanation, but would have been beyond me, I suspect, had I not already started to make sense of some of the pictures I’d turned up.

      Anyway, I hope you find it useful.

  3. hanmeng says:

    I didn’t try to master the whole cycle until relatively recently. I swim 30 laps and use the cycle to count my 60 lengths–merely counting by number, I seem to lose count more easily. However, I can’t say I’ve really memorized the series, in the sense that someone could shout out a particular pair and I could immediately tell where it was in the cycle, much less match it to a particular year (aside from辛亥).

  4. Sima says:

    hanmeng, I hope you don’t have to go back to the beginning when you lose count.

    • hanmeng says:

      Not yet. For me, the advantage of using the sexagenary cycle is that each counting unit has two elements, and so it’s easier for me to remember more or less where I’m supposed to be. Other advantages: it’s extremely geeky (I’ve never even considered explaining it to a swimmer unfamiliar with the system), and it’s much less boring than mere numbers.

      • Sima says:

        That’s interesting. You feel that you have a better sense of your progress, or position, with this system that when you simply count 22, 23, 24?

        The geekiness and boredom reduction I can understand. Training routines need, I think, to be personalised. A certain amount of imagination can add meaning to the process, and increase ‘focus’. Do you think it can be a bit of a diversionary tactic? (i.e. higher mental effort in counting the laps keeps your attention away from feeling the pain in your tiring limbs.)

        • hanmeng says:

          I don’t swim hard enough for pain. And as for diversionary, I should probably pay more attention to my stroke & kick.

  5. Jonathan says:

    For kicks I’ll share a device I came up with, if of interest to anyone… it is a little tricky to describe but, once grasped, easy to implement for mental transformations SB > numeral or vice-versa. (The principles could be learned more or less instantly from a nice animated .gif, but that’s beyond my competence.)

    Anyway, imagine a clock-face of a sort, numbered from 1 at bottom clockwise around to 12 (12 thus at conventional “5” position).

    There are two hands (let’s call them red and blue) running simultaneously; both begin at bottom (pointing to 1).

    On the first cycle, the hands run together from 1 through 10 (recall 10 is at the conventional “3” position); naturally enough, these positions represent the ten numbers 1-10.

    On the second cycle, the red hand runs from 1-10 again, but the blue hand trails it by 2 positions (that is, by a gap of 10 minutes on a conventional clock — it’s useful to think of a gap of this size as one “unit.”) This means that when the red hand finishes this cycle at 10 (the “3” position”!), the blue hand is trailing at 8 (the “1” position”!). These ten positions represent the ten numbers 11-20.

    On the third cycle, the red hand runs from 1-10 again, but the blue hand trails it by two “units” (= gap of 20 minutes on conventional clock). These ten positions represent the ten numbers 21-30.

    Fourth cycle, same, blue hand trails by 3 units (= 180 degrees)

    Fifth cycle, same, blue hand trails by 4 units

    Sixth cycle, same, blue hand trails by 5 units

    And we’re back where we began.

    Now conversions:
    43 = red on 3; blue trails by 4 units (so, just for reference, looks like conventional 8 o’clock if red = hour hand)
    27 = red on 7 (= top); blue trails by 2 units (so looks basically like conventional 20 to 12)
    59 = red on 9; blue trails by 5 units
    8 = both on 8
    or vice-versa
    red on 1; blue trails by 3 units (looks like 6 o’clock) = 31

    Red hand = Stems hand, blue hand = Branches hand. Mentally fix Stems at 1-10, Branches at 1-12 (a bit more mental exertion involved here, obviously). After a bit of practice, do stuff like xinhai = red at 8, blue trails by 4 units = 48, or 13 = red at 3, blue trails by one unit = bingzi automatically. Also leads to more intuitive understanding of the cycle, with “gap size” corresponding to the tens unit of the corresponding Arabic numeral, leading hand (Stems hand) position to the ones unit… positions where hands are separated by half units are illegal… etc.

    • Sima says:

      Wow. Is this a device you have actually made – an adapted clock, perhaps, with the stems and branches written on – or is it just a mental construction?

      • Jonathan says:

        No, just a mental device to do conversions to/from Arabic numerals 1-60 easily (I rarely need to worry about correspondences with Western dates)… extremely easy to use, though looking at the post again it might all seem rather monstrous…

Leave a Reply