File:Counting board with calculi.jpg

The exact form and use of ancient Greek, Roman, Egyptian, and other ancient counting boards (abacuses) is unknown. Few physical artifacts remain, because most counting boards were made of perishable materials such as wood, cloth, leather, or even some lines scratched in the dirt, and used common items as tokens such as pebbles, coins, or shells. No extant sources describe how to operate an ancient counting board.

This image shows a hypothetical ancient counting board made of black lines drawn on a wooden board, with pebbles (Latin calculi) used as counters. This version follows a common convention from Medieval European counting boards whereby powers of ten (1, 10, 100, 1000) were indicated by lines, with counters placed on the line representing that power of ten, while counters placed in the space between lines represented five times the adjacent power of ten (i.e. 5, 50, 500, 5000). Here each line and space is labeled with the associated Roman numeral, M = 1000, D = 500, C = 100, L = 50, X = 10, V = 5, I = 1, but historical counting boards might have used unlabeled lines.

The specific number shown, 2648, can be broken into 2 × 1000 + 1 × 500 + 1 × 100 + 4 × 10 + 1 × 5 + 3 × 1, each of which can be represented with a pebble. In Roman numerals, this number is written MMDCXXXXVIII.