Suanpan walkthrough

How to use a Chinese abacus

Two beads above the beam, five below, and every one of them moves. This walkthrough works a real suanpan: naming the parts, setting and reading numbers, the two ways one rod can show the same digit, and the parked rod that holds 12 until you are ready to carry. No signup, no app, nothing to install.

The parts of a suanpan

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Move the beads yourself

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The whole lesson, written out

Part one — a rod of seven beads

A wooden frame, split by a beam. The suanpan is the Chinese abacus, and it is the older of the two instruments this site teaches. Everything it does happens inside this frame: rods running top to bottom, and one horizontal beam cutting across them. Read the rods left to right, exactly like a written number.

The beam is the counting line. A bead counts only while it is touching the beam. Beads sitting away from it are switched off, however many of them there are. That single rule is the whole reading method, and nothing later contradicts it.

One rod is one place. The rod on the right is the ones, the next one along is the tens, then the hundreds. Notice what that sentence does not say: it does not say one rod holds one digit. On a suanpan a rod holds a place, and a place can be overfilled while you work.

A single rod reaches fifteen. Every bead on this rod is against the beam: two above worth 5 each, five below worth 1 each. That is 15 on one rod, and it is a legal position, not a mistake. The extra room dates from an era when Chinese merchants weighed in taels — sixteen to a catty — and a rod that could pass 9 without carrying was worth having. 5 + 5 + 1 + 1 + 1 + 1 + 1 = 15

One heaven bead, pulled down. The beads above the beam are the heaven beads, and each is worth 5. They switch on by sliding down to meet the beam. One of them down is 5.

There are two of them. This is the first thing a soroban does not have. A Japanese frame carries one heaven bead; a suanpan carries two, so the upper deck alone can reach 10. Keep that second bead in mind — most of what makes this instrument different comes back to it. 5 + 5 = 10

The beads below are worth 1 each. These are the earth beads, and they switch on by sliding up to the beam. Three of them up is 3. Two are still resting at the bottom, which is how you can see there are five in total.

All five earth beads, up. On a soroban this position does not exist — that frame has only four earth beads, so it can never show five of them. Here it is an ordinary sight, and it is the starting point for two of the most useful moves on the instrument. 1 + 1 + 1 + 1 + 1 = 5

A frame with a number on it. Three hundred and seventy-four. Read each rod separately and left to right: 3 on the hundreds, 7 on the tens, 4 on the ones. Now watch what happens when it is cleared.

Zero is a position, not an absence. The heaven beads have gone back up and the earth beads back down. Nothing touches the beam, so nothing counts, so the frame reads zero. Clearing is a move you make, and it is how every calculation starts.

The same bead, three different values. One earth bead is up on each of the three rods. They are identical beads making identical moves, and they are worth 1, 10 and 100 — the rod decides, not the bead. This is place value, in one glance.

The marked rod. On a wider frame you will see one rod tinted differently. That is the unit rod, the marker a user picks as their ones column so they do not lose their place on a long frame. Here it is the thousands, showing a single bead worth 1000.

Part two — writing numbers on it

Thumb up, index finger down. Earth beads go up with the thumb. Heaven beads come down with the index finger, and go back up with it too. One rod at a time, and never both hands on the same rod — the technique is the same one soroban players use, because the beads move the same way.

Three is three earth beads. Digits 1 to 4 are just earth beads pushed up to the beam. Nothing above the beam is involved yet, so these are the digits a complete beginner can set without being told anything else.

Five is one heaven bead. Bring a heaven bead down and the rod reads 5 with a single move, rather than five separate pushes. This is the normal, canonical way to write 5 on a rod — though, as the next chapter shows, it is not the only legal way.

Seven is five plus two. One heaven bead down and two earth beads up. Every digit from 6 to 9 works exactly like this: the heaven bead carries the 5, the earth beads carry the rest. Bead for bead, that is the pattern a soroban would show too.

Five, written with earth beads. All five earth beads against the beam. The rod is worth 5, and the readout below agrees. Nothing about this is wrong — it is simply the other way of writing the same digit.

Five, written with a heaven bead. One bead instead of five, and the rod is worth exactly the same. So a suanpan rod showing 5 can be in either of two states, and a photograph of the rod alone does not tell you which move produced it. A soroban has no such ambiguity anywhere.

Ten, one way. One heaven bead down and all five earth beads up: 5 and 5. The rod is holding 10 all by itself, which is already past what a single soroban rod can do.

Ten, the other way. Both heaven beads down, no earth beads. Also 10. Those are the only two ambiguities on the whole instrument — across all eighteen bead patterns a rod can take, nothing but 5 and 10 has a twin, and every other value has exactly one layout.

Start with the highest place. To set 472, put the 4 on the hundreds rod first. Working left to right is the standard rule and it is worth building the habit early — the alternative leaves you guessing how many rods the number needs after you have already used some.

Then the tens. Seven on the tens rod: one heaven bead down, two earth beads up. The hundreds rod does not move, and neither does the ones. Each rod is set once and then left alone.

Then the ones. Two earth beads on the ones rod, and the frame reads 472. Three rods, three independent settings, one number.

What is on this rod? The digits are switched off, so you have to read the beads. One heaven bead is against the beam and one earth bead is up: 5 and 1. The rod is 6, and the frame is 6.

Now read the whole frame. Two earth beads on the hundreds, one heaven bead on the tens, nothing on the ones. Two hundred and fifty. A heaven bead on a rod that is not the ones is the pattern beginners misread most often — it is worth 5 of whatever that rod is worth, so here it is 50.

Part three — moving, parking, settling up

Two, plus three. Two earth beads are up and three are still free. The beads you need are sitting right there, so this is the easy case: just move them. 2 + 3 = 5

And it fits. Five earth beads against the beam, and the rod reads 5. Worth stopping on: a soroban cannot do this. It runs out of earth beads at 4, so on that frame 2 + 3 already needs the five-complement. Here it is a plain push, and that is the fifth bead earning its place. 2 + 3 = 5

Now add two more. Every earth bead is already up. There is no sixth one to push, and the answer is 7, so you cannot simply reach for more beads. This is the first position on a suanpan where counting runs out — not at 4 as it would on a soroban, but at 5. 5 + 2 = ?

Back at five, stuck. The rod is worth 5 and every earth bead is committed. Before adding anything, the trick is to notice that this rod has a spare way of saying 5 — and it is not using it. 5 + 2 = 7

Trade five for one. Send all five earth beads back down and bring one heaven bead down instead. The rod still reads 5 — the readout has not moved — but all five earth beads are free again. This is the five-exchange, and it is the move the extra bead exists to make possible. 5 = 5

Now there is room. Push two earth beads up and the rod reads 7. A soroban is doing the same job constantly, but it never gets to choose the moment: with only four earth beads it can never hold five, so it must reach for the heaven bead the instant a rod passes 4. 5 + 2 = 7

Four, plus three. One earth bead is free and you need three. The exchange will not help here — there are only four earth beads up, not five, so there is nothing to trade. This is where the complements come in. 4 + 3 = 7

Add five instead. Bring a heaven bead down. You have added 5 when you only wanted to add 3, so the rod now reads 9 — too much by exactly 2. 4 + 5 = 9

Then give back two. Send two earth beads down and the rod reads 7. Two is the small friend of three, because 3 and 2 make 5. Every complement on this frame is identical to the soroban’s, rule for rule and bead for bead — so if you want to drill them, the soroban walkthrough covers all nine pairs in depth. 9 - 2 = 7

Eight, plus seven. On a soroban this forces a carry immediately, because 15 will not fit on one rod. Here, watch what the second heaven bead lets you do instead. 8 + 7 = 15

Add the five. The second heaven bead comes down and the rod reads 13. Nothing has been carried, nothing has moved on the tens rod, and the frame total below is correct. 8 + 5 = 13

Add the two. Two more earth beads and the rod reads 15 — every bead against the beam. The frame total says 15, and it is right: a rod holding more than 9 is a legal working position, not an error. This is what people mean when they say a suanpan lets you defer the carry. 13 + 2 = 15

A rod holding fifteen. You can leave a rod parked like this for as long as the calculation needs. But an answer has to be readable, and a rod showing 15 is not a digit. Settling up is how you finish.

Take ten off this rod. Send both heaven beads back up. The rod drops from 15 to 5, and the ten you just removed has to go somewhere. 15 - 10 = 5

Put it on the rod to the left. One earth bead on the tens rod, and the frame reads 15 again — one ten and five ones. Look at the totals: 15 before, 15 after. Nothing was added or lost, only rewritten. That is all carrying has ever been. 5 + 10 = 15

The instrument is yours. Five rods, nothing locked, nothing being marked. Set a number, park a rod above nine on purpose, run a five-exchange and undo it. Everything on this page was one of these moves, made slowly.

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