Suanpan Abacus Calculator Guide (Chinese Abacus, 2:5)

The suanpan (算盘) is the classic Chinese abacus with a 2:5 bead layout—two upper (5-unit) beads and five lower (1-unit) beads on each rod. This extended state space enables flexible intermediate steps and traditional techniques while remaining fully compatible with decimal arithmetic.

Suanpan fundamentals

• Place value: Each vertical rod represents ones, tens, hundreds, and so on.
• Bead values: Upper bead = 5; each lower bead = 1. Move beads toward the beam to count.
• 2:5 layout advantage: Extra beads allow intermediate positions that can reduce bead movements in multi-step operations, especially in classical multiplication/division methods.

Complements that make you fast

• To 5: 1↔4, 2↔3
• To 10: 1↔9, 2↔8, 3↔7, 4↔6, 5↔5
  Think “+7 = +10 − 3” or “−7 = −10 + 3” to minimise moves. Suanpan’s additional beads make these trades smooth.

Core operations (worked examples)

Addition (e.g., 348 + 576)

1. Enter 348.
2. Add 6 on ones: use +10 − 4 via complement to carry efficiently.
3. Add 7 tens (plus any carry).
4. Add 5 hundreds.
   Result on the frame: 924.

Subtraction (e.g., 1,002 − 587)

Use borrows and complements: when you need “−7”, do −10 + 3 and borrow from the next rod.

Multiplication (partial products)

1. Set the multiplicand.
2. For each multiplier digit, add the shifted partial product on the frame.
3. Resolve carries; the frame shows the final product.

Division (long-division style)

1. Compare divisor with the leading digits on the frame and subtract the largest multiple possible.
2. Record the quotient digit; bring down/shift and repeat to the remainder or required precision.

Suanpan vs Soroban vs Western abacus

• Suanpan (2:5): Rich intermediate states and traditional methods; modern use mirrors decimal arithmetic.
• Soroban (1:4): Streamlined for speed; excellent for competitions and schooling.
• Western/school abacus (~10 lower beads): Ideal for place-value teaching and counting.

Practice plan (10 minutes/day)

1. 2-digit additions with complements to 10.
2. Mix in subtractions using borrows.
3. Short multiplications (×1–×9) via partial products.
4. Finish with one division example for confidence.

Related tools

• Try the Suanpan Abacus Calculator → /calculator/suanpan-abacus
• Compare with Soroban → /calculator/soroban-abacus
• Learn place value on the Western abacus → /calculator/western-abacus

FAQ

Is the suanpan still useful today?
Yes. Its 2:5 layout supports efficient complements and traditional algorithms, and it’s great for building mental arithmetic.

What’s the main difference from the soroban?
The soroban uses 1 upper + 4 lower beads per rod (1:4). Suanpan’s 2:5 adds flexibility for intermediate states.

Can I do decimals?
Yes—treat rods to the right of the ones place as tenths, hundredths, etc.