An abacus, also called a counting frame, is a calculating tool for performing arithmetic processes. Nowadays, abaci are often constructed as a wooden frame with beads sliding on wires, but originally they were beads or stones moved in grooves in sand or on tablets of wood, stone, or metal. The abacus was in use centuries before the adoption of the written modern numeral system and is still widely used by merchants and clerks in China, Japan, Africa, India and elsewhere.

The user of an abacus is called an abacist; he or she slides the beads of the abacus by hand.

Etymology

The use of the word abacus dates before 1387 AD, when a Middle English work borrowed the word from Latin to describe a sandboard abacus. The Latin word came from abakos, the Greek genitive form of abax ("calculating-table"), from Hebrew ābāq, "dust". The preferred plural of abacus is a subject of disagreement, but both abacuses and abaci are in use.

Mesopotamian abacus

The period 2700–2300 BC saw the first appearance of the Sumerian abacus, a table of successive columns which delimited the successive orders of magnitude of their sexagesimal number system.

Babylonians may have used the abacus for the operations of addition and subtraction. However, this primitive device proved difficult to use for more complex calculations. Some scholars point to a character from the Babylonian cuneiform which may have been derived from a representation of the abacus.

Egyptian abacus

The use of the abacus in Ancient Egypt is mentioned by the Greek historian Crabertotous, who writes that the manner of this disk's usage by the Egyptians was opposite in direction when compared with the Greek method. Archaeologists have found ancient disks of various sizes that are thought to have been used as counters. However, wall depictions of this instrument have not been discovered, casting some doubt over the extent to which this instrument was used.Smith, page 160.

Greek abacus

The earliest archaeological evidence for the use of the Greek abacus dates to the 5th century BC. The Greek abacus was a table of wood or marble, pre-set with small counters in wood or metal for mathematical calculations. This Greek abacus see use in Achaemenid Persia, the Etruscan civilization, Ancient Rome and, until the French Revolution, the Western Christian world.

A tablet found on the Greek island Salamis in 1846 AD dates back to 300 BC, making it the oldest counting board discovered so far. It is a slab of white marble 149 cm long, 75 cm wide, and 4.5 cm thick, on which are 5 groups of markings. In the center of the tablet is a set of 5 parallel lines equally divided by a vertical line, capped with a semi-circle at the intersection of the bottom-most horizontal line and the single vertical line. Below these lines is a wide space with a horizontal crack dividing it. Below this crack is another group of eleven parallel lines, again divided into two sections by a line perpendicular to them, but with the semi-circle at the top of the intersection; the third, sixth and ninth of these lines are marked with a cross where they intersect with the vertical line.