The structure of a European abacus

Contrary to a traditional Chinese abacus, the orbs on a European abacus are horizontal. Usually there are 10 rows each with 10 orbs, so you have a total of 100 orbs. They are normally of different colors to keep a better overview and not have to count each orb.

How to calculate using a European abacus

In the simplest variant, each orbs is given the value of “1”. This way you can do simple addition and subtraction by moving the orbs. Because this variant doesn't make much more sense than to count with your fingers, apples or pears, it is usually used as a counting tool for kindergarden and elementary school children.

In the more challenging variant you can count up to 10,000,000,000 (ten billion). This is also the variant which we will discuss in more detail.

The orbs in the lowest row are given the value “1”.

The orbs in the second row from the bottom are given the value “10”.

The orbs in the third row from the bottom are given the value “100”.

This continues row for row. Therefore, the orbs in the top row are given the value “1,000,000,000”.

In the starting position all the orbs are to the left. You simply need to slide the correct amount of orbs to right in order to calculate. This is best illustrated by a little exerciser:



ADDITION with a abacus: 134 + 81 + 247 = ?


1st Step: 134

First the number 134 is moved to the right. This means:

1 x orb “100” (3rd row from the bottom)
3 x orbs “10” (2nd row from the bottom)
4 x orbs “1” (1st row from the bottom)





2nd Step: + 81

Next the value 81 is added. This means:

8 x orbs “10” (2nd row from the bottom)
1 x orb “1” (1st row from the bottom)

By now we have a little “problem”. Since in the first step 3 orbs with the value of “10” have been moved, there are now only 7 orbs on the left side. However, to calculate “80” we need 8 orbs.

Therefore, we move the 7 orbs (for “70”) to the right, so that all orbs with the value of “10” are now on the right side. These 10 orbs are moved to the left and in their place one orbs with the value of “100” is moved tot he right (10 orbs with the value of 10 = 10 x 10 = 100).

Since we have now only added 70 instead of 80, we move one orb with the value of “10” to the right.

Of the “81” only the “1” is missing, which we move to the right in the bottom row.





3rd Step: + 247

The orbs are to be moved as follows:

2 x orbs “100” (3rd row from the bottom)
4 x orbs “10” (2nd row from the bottom)
5 x orbs “1” (1st row from the bottom)
10 x orbs “1” moved left, replaced by
1 x orb “10” (2nd row from the bottom) to the right and finally
2 x orbs “1” (1st row from the bottom)

Now we can read the sum, from top to bottom:

4 x orbs “100”
6 x orbs “10”
2 x orbs “1”

The sum is: 134 + 81 + 247 = 462

If you don't believe it, you can recalculate using a calculator...
… or under the Calculator tab, using our virtual abacus :-)