How Does An Abacus Work?

As kids, my brothers and I always played around with the ancient beaded calculator, the abacus. But to this day I have never known how people actually use them. To this day when I looked it up. :)

How To Add Two Numbers With An Abacus (via WikiHow):

Say for this example, we're adding 35 to 113.

1. Assign values to the columns in a systematic way from right to left, like here:

This mimics the way that we read numbers; with the highest magnitude as the left-most number, and they decrease to the smallest on the right (like 256 = 2 hundreds, then 5 tens, then 6 ones).

2. Row I beads will be 5 times whatever Row II beads are worth.

3. Start with all the beads towards the ends. Then place the abacus flat on the table.

4. Break down the first number into units that fit the values you assigned:
35 = 3 units of 10, and 5 units of 1
Move the beads towards the center bar accordingly:
3 beads from Row II in the "10s" column
1 bead in Row I in the "1s" column:

5. Break down the second number into units:
113 = 1 unit of 100, 1 unit of 10, and 3 units of 1
Move more beads towards center to account for those units
1 bead from Row II in the "100s" column
1 bead from Row II in the "10s" column
3 beads from Row II in the "1s" column:
If you end up needing 5 or more beads from Row II, you can replace 5 beads from Row II with 1 bead in Row I.

6. Count the beads that are by the center bar and figure out their worth to get the answer.
In this case,
"100s" Column: 1 bead from Row I = 100
"10s" Column: 4 beads from Row I = 40
"1s" Column: 1 bead from Row I, and 3 beads from Row II = 8
= 148!

If that was too complicated, there's a handy video here. I think the explanation is harder than the practice, actually!

You can imagine this could be as helpful as a calculator for adding many or larger numbers together. Brilliant, considering it's over 800 years old. When people get the hang of it, they can do it very quickly!


  1. I was pretty good at it when I was a child. And fyi, right now I am procrastinating from the real work I need to finish.

  2. I'm too confused. I'll leave this to the chinese.