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Old Babylonian Weights and Measures

The metrology of ancient Mesopotamia is very complicated, but key to understanding
much of the mathematics as units are often silently converted in the middle
of a problem. Units of length, weight, area, capacity and so on and the
relationships between them changed frequently in both space and time. However,
by the Old Babylonian period, the systems were much simpler than during
the Sumerian
period. For the large bulk of mathematical problem texts, there is a relatively
standardized set of measurements, although there are plenty of exceptions.
The tables below give the main units in this standard set, but are by no
means comprehensive. For up-to-date and detailed references on the different
systems, see the articles by Marvin Powell in RLA
and
*Civilizations
of the Ancient Near East*.
Even in the Old Babylonian times, metrology had a rich collection of
units. Most of the conversion factors are simple fractions or multiples
of the base 60. Key units are the kush (cubit) for length, sar (garden-plot)
for area and volume, sila for capacity and mana for weight. At the base
of the system is the barleycorn, she, used for the smallest unit in length,
area, volume and weight.

Akkadian made use of a letter š called a shin, pronounced as 'sh'. The
barleycorn is a 'še', pronounced 'shay' and which we shall write as 'she.'

###
Length

Smallest unit of length is the she (barleycorn), of about 1/360 meter.
6 she |
= |
1 shu-si (finger) |

30 shu-si |
= |
1 kush (cubit - about 1/2 m.) |

6 kush |
= |
1 gi / *qanu* (reed) |

12 kush |
= |
1 nindan/ GAR (rod - 6 m.) |

10 nindan |
= |
1 eshe (rope) |

60 nindan |
= |
1 USH (360 m.) |

30 USH |
= |
1 beru (10.8 km.) |

length
conversion calculator
###
Area

The basic area unit is the sar, an area of 1 sq. nindan, or about 36 sq.
m. The area she and gin are used as generalized fractions of this basic
unit.
180 she |
= |
1 gin |

60 gin |
= |
1 sar (garden plot 1 sq. nindan - 36 sq. m.) |

50 sar |
= |
1 ubu |

100 sar |
= |
1 iku (1 sq. eshe - 0.9 acre, 0.36 ha.) |

6 iku |
= |
1 eshe |

18 iku |
= |
1 bur |

1 bur is an area 1 *beru* long by 1 nindan wide. area
conversion calculator
###
Volume

Volume units are the same as the area units and follows the relationship
that

1 volume-unit = 1 area-unit x 1 kush.

For example, a volume-sar is the volume of the solid with base 1 area-sar
and height 1 kush (cubit).
Bricks are considered to be rectangular solids such that 720 bricks
make one brick-sar. There are numerous (fairly standard) sizes of bricks
in use in Old Babylonian mathematics texts.

Capacity: used for measuring volumes of grain, oil, beer, etc. The basic
unit is the sila, about 1 liter. The semi-standard Old Babylonian system
used in mathematical texts is derived from the ferociously complex mensuration
systems used in the Sumerian
period.

180 she |
= |
1 gin |

60 gin |
= |
1 sila - 1 liter |

10 sila |
= |
1 ban |

6 ban |
= |
1 bariga |

5 bariga |
= |
1 gur |

volume
conversion calculator
###
Weight

The basic unit of weight is the mana, about 1/2 kilogram.
180 she |
= |
1 gin/ *shiqlu* (shekel) |

60 gin |
= |
1 mana (mina - 500 gm.) |

60 mana |
= |
1 gu/ *biltu* (talent, load - 30 kg.) |

weight
conversion calculator

Go up to Mesopotamian
Mathematics.

Last modified: 6 June 2001

Duncan J. Melville

dmelville@stlawu.edu