An abacus (ἄβαξ, ἀβάκιον‎), a counting board, was the usual aid to reckoning in antiquity. The Greeks and Romans alike used a board with vertical columns, on which (working from right to left) units, tens, and hundreds; or (where money was in question) units of currency, for instance the Attic signs for ⅛ obol, ¼ obol, ½ obol, 1 obol, drachma and so on, could be inscribed. The Salamis abacus is an example of a type of flat, large counting board, made of stone, of which more than twenty have survived from antiquity (Figure 1).

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Figure 1. The so-called Salamis abacus, probably 4th century bce, found at Salamis and now in the Athens Epigraphical Museum.

Courtesy Epigraphical Museum, Ministry of Culture and Tourism, Athens, Hellenic Democracy (EM 11515).

There are also significantly fewer examples of small, bronze abacus. (Figure 2).

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Figure 2. 18th-century replica of a Roman abacus, bronze.

Courtesy Trustees of the British Museum, AN163123001. Creative Commons License, CC BY-NC-SA 4.0.

The extant flat, large counting boards have been found in the Greek-speaking part of the Mediterranean, whereas the small bronze abaci appear to originate in the Roman world, and are engraved with Roman numerals. There are different possible reconstructions of how calculations were carried out on the ancient Greek or Roman abacus, which would seem to indicate that different procedures were also in use in antiquity In general, with addition, the totals of the columns were carried to the left, as in ordinary 21st-century addition. Multiplications and divisions may have been performed via repeated addition and subtraction, respectively, but also via other procedures, including the so-called Egyptian method, or with the help of tables. The main calculation principle seems to have been that of substitution: when five counters or tokens were set out in one column, they were substituted by one token carried to the left. The numbers were usually marked by pebbles, counters, or pegs. In the Roman-style abacus, the counters were attached to the device.