Rod calculus

Rod calculus

Rod calculus or rod calculation is the method of mathematical computation with counting rods in China from The Warring States to Ming dynasty before the counting rods were replaced by more convenient and faster abacus.


The basic equipment for carrying out rod calculus is a bundle of counting rods and a counting board. The counting rods are usually made of bamboo sticks, about 12cm- 15mm in length, 2mm to 4 mm diameter, sometimes from animal bones, or ivory and jade (for well heeled merchants). A counting board could be a table top, a wooden board with or without grid, on the floor or on sand.

In 1971 Chinese archeologists unearthed a bundle of well preserved animal bone counting rods stored in a silk pouch from a tomb in Qian Yang county in Shanxi province, dated back to the first half of Han dynasty(206 BC - 8AD). In 1975 a bundle of bamboo counting rods was unearthed.

The use of counting rods for rod calculus flourished in the Warring States, although no archeological artifacts were found earlier than the Western Han Dynasty(the first half of Han dynasty, however archeologist did unearth software artifacts of rod calculus dated back to the Warring States); since the rod calculus software must have went along with rod calculus hardware, there is no doubt that rod calculus was already flourishing during the Warring States more than 2200 years ago.


The key software required for rod calculus was a simple 45 phrase positional decimal multiplication table used in China since antiquity, called the nine-nine table, which were learned by heart by pupils, merchants, government officials and mathematicians alike.

Rod numbers

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