ABACUS

a calculator for the calculator
Arabic
0
Roman
nulla
Per rod
·
How to use

Practice mode — tap any bead to slide it. Heaven beads (above the bar) are worth 5; earth beads (below the bar) are worth 1. A bead "counts" only when pushed against the bar. Each rod is a decimal place — leftmost is trillions, rightmost is ones. The dot under a rod marks the unit rod. Tap a digit on the pad to push it in from the right; tap ← to shift back; tap C to clear the abacus.

Calculator mode — type an expression (e.g. 137 × 89) using the pad, then tap =. The beads animate to the result. Integer arithmetic; division truncates. Switch back to practice anytime to manipulate the result by hand.

Roman numerals use the standard subtractive notation (IV, IX, XL, etc.) up to 3,999. Above that, single-overlined groups represent thousands (V̄ = 5,000), double-overlined represent millions, triple-overlined represent billions — the same vinculum convention Romans actually used.

About

The soroban (Japanese 4+1 abacus, refined from the Chinese suanpan) is a 2,000-year-old mechanical computer. A trained operator can add long columns of numbers faster than someone with a calculator, because the answer is already half-formed by the bead positions during entry. This is a faithful digital rendering — the mechanics are exactly what a physical soroban does.

The irony: this calculator app contains an abacus simulating a calculator running on a calculator (your phone) that contains roughly a billion abacuses' worth of computational power. Use it to add 2 + 2.

About Abacus

A playable Japanese soroban (1:4 bead layout) with a calculator pad, practice mode, and live conversion to Arabic and Roman numerals. Tap beads or type digits — the abacus and displays stay in sync.

How to read the soroban

Each column is a decimal place. The upper bead counts 5 when pushed down; each lower bead counts 1 when pushed up. Addition and subtraction follow standard soroban carries.

Learning the technique? The soroban technique guide covers what the bead values alone don't: the five- and ten-complements, how carrying actually works, and worked addition and subtraction step by step.

Frequently asked questions

What is a soroban?

The Japanese abacus — one heaven bead (5) and four earth beads (1) per rod, decimal from right to left.

Can I use the keyboard?

Yes — digits, operators, Enter, Backspace, and C/Escape map to the calculator pad.

Related

How to Use a Soroban — Japanese Abacus Technique

The soroban is the Japanese abacus: one heaven bead worth 5 above the bar, four earth beads worth 1 below it, on each rod. A bead counts only when pushed against the bar. That much you can read off the device in a minute. What takes practice — and what almost no page actually explains — is the technique that makes it fast: you never “think” an addition, you execute a fixed rule about which beads to move.

Setting a number

Each rod is one decimal place, ones on the right. To set 7, push the heaven bead down (5) and two earth beads up (2). To set 3, push three earth beads up. There is no ambiguity: every digit 0–9 has exactly one bead configuration.

The unit rod. Pick a rod and call it the ones column — on most sorobans it is marked with a dot. Everything else follows from it. Beginners who do not fix a unit rod lose their place the first time they carry.

The whole skill: complements

You add by moving beads. The problem is that sometimes the beads you need are not free — you want to add 4 but only two earth beads remain. Rather than pause and think, the soroban operator applies a complement: add the larger unit, take back the difference. There are only two families to learn.

Five-complements (within one rod)

When you need to add 1–4 but lack the earth beads, add the heaven bead (5) and remove the complement to 5:

To addDo thisBecause
1+5, then −41 = 5 − 4
2+5, then −32 = 5 − 3
3+5, then −23 = 5 − 2
4+5, then −14 = 5 − 1

The pairs are simply 1–4, 2–3 and their reverses. Subtraction runs the same table backwards: to subtract 4 when you cannot, remove the heaven bead and add 1.

Ten-complements (carrying to the next rod)

When a whole rod cannot absorb the digit, carry: add 1 to the rod on the left and remove the complement to 10 from the current rod.

To addDo thisTo addDo this
1carry 1, −96carry 1, −4
2carry 1, −87carry 1, −3
3carry 1, −78carry 1, −2
4carry 1, −69carry 1, −1
5carry 1, −5

Worked example: 8 + 7

  1. Set 8 on the unit rod — heaven bead down (5) plus three earth beads up (3).
  2. You want to add 7. There is no room: only one earth bead is free.
  3. Apply the ten-complement for 7 — carry 1 to the tens rod, then subtract 3 from the unit rod.
  4. Subtracting 3 from 8 within the rod needs its own five-complement: remove the heaven bead (−5) and add two earth beads (+2), leaving 5.
  5. Read the board: 1 on the tens rod, 5 on the units. 15.

Notice you never computed 8 + 7. You applied two lookup rules. That is the entire trick, and it is why a trained operator keeps pace with someone typing.

Worked example: 23 − 8

  1. Set 23 — two earth beads on the tens rod, three on the units.
  2. Subtract 8 from the unit rod: 3 is not enough, so borrow. Take 1 from the tens rod and add the complement, 2, to the units.
  3. Units: 3 + 2 = 5 — clear the three earth beads and push the heaven bead down.
  4. Tens now reads 1, units reads 5. 15.

Why it stays faster than it should be

The answer is half-formed while you enter the numbers. There is no separate “compute” step — by the time the last digit is set, the board already holds the total. Japanese schools still teach it, and advanced students graduate to anzan: visualising the board and moving imaginary beads, with no device at all. Competitive anzan practitioners add ten three-digit numbers in a couple of seconds.

Practice order that works: set random digits until the bead patterns are automatic, then drill the four five-complements, then the ten-complements, and only then attempt multi-rod sums. Skipping straight to arithmetic is the usual reason people bounce off the soroban.

The Board Gaming Hub soroban has a practice mode where you slide the beads yourself, plus live conversion to Arabic and Roman numerals so you can check yourself as you go.