An Abacus consists of beads or stones on rods or wires each representing a numerical value. Beads are manipulated to perform addition, subtraction, multiplication and division.
The one shown here has nine beads on each rod. A horizontal beam divides the rods into an upper and a lower section such that one bead on each rod is above the beam and four are below. The bead above the beam has the value of 5, those below each have a value of one. The illustration above shows the number ‘1940’ set against the beam. Numbers are set from left to right. Numbers obtain a value when they are placed against the beam and lose their value when moved away.
For convenience in calculation the beam is marked with a unit point at every third rod. These unit points indicate the decimal pint and other units of decimal measures. For example, the ‘0’ of the number 1940 above is set on a unit rod which is chosen to be the second point from the right. Beads are best moved using the index finger in cooperation with the thumb.
Mode of Operation
When undertaking an arithmetic calculation, the main difference between the operation of an abacus and a human with pencil and paper is that with the latter calculations proceed from right to left, while with the abacus it is from left to right. It is recommended to use the index finger to move 5-units beads up and down and to move 1-unit beads down, while using the thumb only to move 1-unit beads up.
A full description of the theory and use of the abacus is available for download here. A simple example of addition using the abacus is described in the post relating to the slide calculator, which also operates from left to right when entering numbers.
History of the Abacus
The English word ‘abacus’ is derived from the Greek ‘abax’ meaning a reckoning table covered with dust, which in turn comes from a Semitic word with a similar meaning. This was superseded by a ruled table with counters or disks arranged on lines to indicate numbers and by a variant using moveable counters sliding up and down grooves. All these types were present in ancient Rome. Finally, the groove-based design became replaced by one with beads sliding on rods.
In Japan, the abacus is called soroban (“counting tray”). It was imported from China in the 14th century. The 1:4 abacus, which removes the seldom-used second and fifth bead, became popular in the 1940s.
A recently purchased Suanpan
This Chinese made example is nicely constructed with supporting brass corners.
The Abacus versus an Electronic Calculator
The number of simultaneous finger movements needed to undertake addition, subtraction, division or multiplication is not dissimilar between operation of an abacus and a calculator with the latter needing an ‘enter’ button to be depressed – a movement not needed on an abacus as the results arise naturally as beads are moved. Hence an experienced abacus user can complete such calculations as rapidly as one using the electronic calculator, although this is less likely for more complex multiplication and divisions. This was evidenced in a competition held in 1942 involving a number of addition, subtraction, multiplication, division and composite calculations resulting in a win of 4 pints to 1 for the abacus operator.
Sources of Information
The Japanese Abacus – Its Use and Theory by Takashi Kojima. Published by Charles E. tuttle Company 1954. Available for download here
Advanced Abacus. Japanese Theory and Practice by Takashi Kojima. Published by Charles E. tuttle Company 1991
Types of Abacus described in the Abacus Academy
Japan Society lessons with downloads