Chinese Abacus

Timeline

1. 1100–1250Jiangnan commercial cities · Song dynastiesAround the Song–Yuan transition, the abacus form with one beam, two upper beads and five lower beads became standardized; pictorial sources such as Zhang Zeduan's Along the River During the Qingming Festival and mathematical works like the Shushu Jiuzhang reflect that abacus arithmetic had penetrated market and government accounting settings.
2. 1251–1260Lin'an prefecture and the Quanzhou Maritime Trade Office · Fujian CircuitAgainst the backdrop of war, military pay, grain transport, and overseas trade settlements surged in volume; maritime trade offices, salt and iron transport agencies, and merchant-guild counting houses all commonly used the abacus for large-number multiplication and division and double-entry bookkeeping, and abacus mnemonic formulas became an essential skill for professional accountants.
3. 1260–1300Dadu and the yamen of the various provinces · YuanAfter the Yuan court standardized weights, measures, and tax accounting, the abacus continued as a common calculating tool of government and merchants, operating alongside paper-note denomination conversion and land surveying, and became an infrastructure of daily imperial administrative computation.