Napier's Rods


In a book published in the year of his death, Scottish mathematician and laird John Napier (1550-1617) described several aids to arithmetic computations. One, since known as Napier’s rods or Napier’s bones, was a set of rods marked with the multiples of the digits from 0 to 9. Napier explained how to use these rods to assist in multiplication and division and, with the use of a special additional rod, take square roots and cube roots.

This set of Napier’s rods contains ten short wooden number rods with square cross section, and an eleventh, wider rod for square and cube roots. Each face of each number rod contains the first ten multiples of a digit. Each square containing a multiple is divided diagonally, with the tens value of the number written in the upper left corner and the ones value in the lower right corner. The number rods have multiples of the following numbers:

3 rods have multiples of 0, 1, 9, and 8

2 rods have multiples of 1, 5, 8, and 4

3 rods have multiples of 3, 2, 6, and 7

2 rods have multiples of 3, 4, 6, and 5

Four digits on the top of each rod indicates which multiples it contains. The sum of the digits whose multiples are on opposite sides of a rod always totals 9. All four of these types of rods are described in Napier's Rabdology. However, Napier suggested using ten distinct rods. The digits on the larger rod do follow Napier's description. The rods fit in a red leather-covered case.

For accounts of the use of the rods, see Napier, Bryden, or online sources. Napier also discovered logarithms, which had a more lasting influence on calculations as they came to be embodied inan instrument called the slide rule.

This set of rods was acquired by purchase. The case is a modern reproduction produced by the vendor.


John Napier, Rabdology, trans. William F. Richardson with an introduction by Robin Rider, Cambridge, Mass.: MIT Press and Los Angeles: Tomash Publishers, 1990.

D.J. Bryden, Napier's Bones: A History and Instruction Manual, London: Harriet Wynter Publications, Ltd., 1992.

Accession file.

Location: Currently not on view

Place Made: United Kingdom: Grand Bretagne

Subject: Mathematics


See more items in: Medicine and Science: Mathematics


Exhibition Location:

Data Source: National Museum of American History

Id Number: MA.316584Catalog Number: 316584Accession Number: 225998

Object Name: calculating rods

Physical Description: wood (overall material)leather (overall material)Measurements: overall: 2.3 cm x 9.8 cm x 7.4 cm; 29/32 in x 3 27/32 in x 2 29/32 in


Record Id: nmah_690812

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