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 called a shin, pronounced as 'sh'. The barleycorn is a 'e', 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