A Roman abacus in London

Roman abacus
Science Museum (London)
Photography by Carlos Dorce

This is a replica of an ancient Roman abacus which we can find in the great Science Museum of London (there are some abacus like this in other museums as the British Museum or the National Library of Paris). It consists in a small metallic plate with nine parallel slits: the right slot is related with ounces and next to it, from right to left, the other slots are for units, tens, hundreds, thousands units, thousand tens, thousand hundreds and millions, with its corresponding figures:

Roman figures

The seven left slots are divided in two different sections: the upper one have one moving pieces and the lower have four moving pieces. The Roman represented the units of each power of 10 putting the lower pieces near the centre of the abacus if they were less than 5. When they need to represent 5 units, they only moved one upper piece to the centre. Thus, number 6 was one upper piece and one lower piece in the centre, 7 was one upper piece and two lower ones,… For example, the abacus located in the British Museum represents number 7.656.877 (or a similar number):

Roman abacus
British Museum (London)
Font: BM website

The two first right slots corresponded to the ounces: the Roman unit (= as) were divided in 12 equal ounces. The slot marked with the symbol O had five moving pieces in the lower slot and it was used to count the multiples of 11 and 12 ounces. The first slot was divided in three parts with four moving pieces:

If the upper piece was next to the “pound” symbol (in the left), the piece value was 1/2 ounce or 1/24 of as (= semuncia); if it was next to the symbol in the middle of the slot (= sicilius), the piece value was 1/4 ounce or 1/48 of as; and if it was next to the “number 2” (in the right), the piece value was 1/72 of as (= duella).

This kind of abacus were very popular as small fast calculators among the Romans as we can see in a marble sarcophagus in the Capitoline Museums of Rome: there is a young boy standing at his feet holding an abacus (he is probably counting the money which the deceased is holding in a money purse):

A Roman abacus represented in a sarcophagus (IInd c. AD)
Capitoline Museums (Rome)

 Location: Science Museum at London (map)

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