Ancient Mesopotamian units of measurement

Gudea Statue I carved diorite

The systems that would later become the classical standard for Mesopotamia were developed in parallel with writing during Uruk Period Sumer (c. 4000 BCE). Studies of protocuneiform indicate twelve separate counting systems used in Uruk.

• Sexagesimal System S used to count slaves, animals, fish, wooden objects, stone objects, containers.
• Sexagesimal System S' used to count dead animals, certain types of beer
• Bi-Sexagesimal System B used to count cereal, bread, fish, milk products
• Bi-Sexagesimal System B^* used to count rations
• GAN₂ System G used to count field measurement
• ŠE system Š used to count barley by volume
• ŠE system Š' used to count malt by volume
• ŠE system Š" used to count wheat by volume
• ŠE System Š^* used to count barley groats
• EN System E used to count weight
• U₄ System U used to count calendrics
• DUG_b System Db used to count milk by volume
• DUG_c System Db used to count beer by volume

In Early Dynastic Sumer (c. 2900–2300 BCE) metrology and mathematics were indistinguishable and treated as a single scribal discipline. The idea of an abstract number did not yet exist, thus all quantities were written as metrological symbols and never as numerals followed by a unit symbol. For example there was a symbol for one-sheep and another for one-day but no symbol for one. About 600 of these metrological symbols exist, for this reason archaic Sumerian metrology is complex and not fully understood.[1] In general however, length, volume, and mass are derived from a theoretical standard cube, called 'gur(also spelled kor in some literature)', filled with barley, wheat, water, or oil. However, because of the different specific gravities of these substances combined with dual numerical bases (sexagesimal or decimal), multiple sizes of the gur-cube were used without consensus. The different gur-cubes are related by proportion, based on the water gur-cube, according to four basic coefficients and their cubic roots. These coefficients are given as:

• Komma = 80⁄81 correction when planning rations with a 360-day year
• Leimma = 24⁄25 conversion from decimal to a sexagesimal number system
• Diesis = 15⁄16
• Euboic = 5⁄6

One official government standard of measurement of the archaic system was the Cubit of Nippur (2650 BCE). It is a Euboic Mana + 1 Diesis (432 grams). This standard is the main reference used by archaeologists to reconstruct the system.

Royal Gur Cube of Naram-Sin

A major improvement came in 2150 BCE during the Akkadian Empire under the reign of Naram-Sin when the competing systems were unified by a single official standard, the royal gur-cube.[2] His reform is considered the first standardized system of measure in Mesopotamia.[2] The royal gur-cube (Cuneiform: LU₂.GAL.GUR, 𒈚𒄥; Akkadian: šarru kurru) was a theoretical cuboid of water approximately 6 m × 6 m × 0.5 m from which all other units could be derived. The Neo-Sumerians continued use of the royal gur-cube as indicated by the Letter of Nanse issued in 2000 BCE by Gudea. Use of the same standard continued through the Babylonian, Assyrian, and Persian Empires.[1]

Mass or weight

A series of old Babylonian weights ranging from 1 mina to 3 shekels

Mass was measured by the EN system E

Values below are an average of weight artifacts from Ur and Nippur. The ± value represents 1 standard deviation. All values have been rounded to second digit of the standard deviation.

Basic Mass
Unit	Ratio	Mean Value	Sumerian	Akkadian	Cuneiform
grain	1⁄180	46.6±1.9 mg	še	uţţatu	𒊺
shekel	1	8.40±0.34 g	gin2	šiqlu	𒂆
mina	60	504±20 g	ma-na	manû	𒈠𒈾
talent	3,600	30.2±1.2 kg	gun2	biltu or kakaru	𒄘

[4] [5] [6]

The Classical Mesopotamian system formed the basis for Elamite, Hebrew, Urartian, Hurrian, Hittite, Ugaritic, Phoenician, Babylonian, Assyrian, Persian, Arabic, and Islamic metrologies.[8] The Classical Mesopotamian System also has a proportional relationship, by virtue of standardized commerce, to Bronze Age Harappan and Egyptian metrologies.

• Assyrian lion weights
• Babylonian mathematics
• Historical weights and measures
• Weights and measures

• Katz, Victor, J (2007). The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press. p. 712. ISBN 978-0-691-11485-9.{{cite book}}: CS1 maint: multiple names: authors list (link)
• Nissen, Hans Jörg; Peter Damerow; Robert K. Englund; Paul Larsen (1993). Archaic Bookkeeping: Early Writing and Techniques of Economic Administration. University of Chicago Press. p. 169. ISBN 0-226-58659-6.
• Robson, Eleanor (1999). Mesopotamian Mathematics, 2100–1600 BC: Technical Constants in Bureaucracy. Oxford University Press. ISBN 0-19-815246-9.
• Sarton, George (1993). Ancient science through the golden age of Greece. Courier Dover Publications. p. 646. ISBN 0-486-27495-0.

• An online calculator Archived 2017-02-13 at the Wayback Machine
• Robson, Eleanor (2007). "Digital Corpus of Cuneiform Mathematical Texts". Archived from the original on 2009-01-16. Retrieved 2008-08-13.
• Aleff, H. Peter (2008). "Auspicious latitudes". Retrieved 2008-08-13.
• Kreidik, L. G.; T. S. Kortneva; G. P. Shpenkov (2005). "4. Fundamental periods of the World and ancient metrology". Journal of Theoretical Dialectics-Physics-Mathematics. Dialectical Academy, Russia-Belarus. Retrieved 2009-08-20.