Ancient Mesopotamian units of measurement originated in the loosely organized city-states of Early Dynastic Sumer. Each city, kingdom and trade guild had its own standards until the formation of the Akkadian Empire when Sargon of Akkad issued a common standard. This standard was improved by Naram-Sin, but fell into disuse after the Akkadian Empire dissolved. The standard of Naram-Sin was readopted in the Ur III period by the Nanše Hymn which reduced a plethora of multiple standards to a few agreed-upon common groupings. Successors to Sumerian civilization including the Babylonians, Assyrians, and Persians continued to use these groupings. Akkado-Sumerian metrology has been reconstructed by applying statistical methods to compare Sumerian architecture, architectural plans, and issued official standards such as Statue B of Gudea and the bronze cubit of Nippur.

Archaic system

The systems that would later become the classical standard for Mesopotamia were developed in parallel with writing in Sumer during Late Uruk Period (c. 3500–3000). Studies of protocuneiform indicate twelve separate counting systems used in Uruk IV-III. Seven of these were also used in the contemporary Proto-Elamite writing system.Dahl, Jacob L., "The Proto-Elamite writing system", in The Elamite World, pp. 383–396, 2018 The bisexagesimal systems went out of use after the Early Dynastic I/II period.Bartash, Vitali, "From burden to talent", Establishing Value: Weight Measures in Early Mesopotamia, Berlin, Boston: De Gruyter, pp. 16-35, 2019 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 Bisexagesimal System B used to count cereal, bread, fish, milk products Bisexagesimal 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 DUGb System Db used to count milk by volume DUGc System Db used to count beer by volume

In Early Dynastic Sumer (–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.Melville 2006. 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 = correction when planning rations with a 360-day year Leimma = conversion from decimal to a sexagesimal number system Diesis = Euboic =

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.

Classical system

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. His reform is considered the first standardized system of measure in Mesopotamia. The royal gur-cube (Cuneiform: LU2.GAL.GUR, ; 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 Neo-Babylonian Empire, Neo-Assyrian Empire, and Achaemenid Empire.

Length Units of length are prefixed by the logogram DU () a convention of the archaic period counting system from which it was evolved. Basic length was used in architecture and field division. Basic LengthUnit Ratio Sumerian Akkadian Cuneiform grain še uţţatu finger šu-si ubānu foot šu-du3-a šīzu cubit 1 kuš3 ammatu step 2 ĝiri3 šēpu reed 6 gi qanû rod 12 nindan nindanu cord 120 eše2 aslu

Distance units were geodectic as distinguished from non-geodectic basic length units. Sumerian geodesy divided latitude into seven zones between equator and pole.

DistanceUnit Ratio Sumerian Akkadian Cuneiform rod nidan nindanu cord eše2 aslu cable 1 uš uš league 30 da-na bêru The cable is approximately equal to 357.8 metres or 360 steps.

Area The GAN2 system G counting system evolved into area measurements. A special unit measuring brick quantity by area was called the brick-garden (Cuneiform: SIG.SAR ; Sumerian: šeg12-sar; Akkadian: libittu-mūšaru) which held 720 bricks.

Basic AreaUnit Ratio Dimensions Sumerian Akkadian Cuneiform shekel 1 kuš3 × 1 kuš3 gin2 šiqlu garden 1 12 kuš3 × 12 kuš3 sar mūšaru quarter-field 25 60 kuš3 × 60 kuš3 uzalak ? half-field 50 120 kuš3 × 60 kuš3 upu ubû field 100 120 kuš3 × 120 kuš3 iku ikû estate 1800 bur būru The garden is equal to approximately 36 square metres.

Capacity or volume

Capacity was measured by either the ŠE system Š for dry capacity or the ŠE system Š* for wet capacity. Basic VolumeUnit Ratio Sumerian Akkadian Cuneiform shekel gin2 šiqlu bowl 1 sila3 qû vessel 10 ban2 sutū bushel 60 ba-ri2-ga (barig) parsiktu gur-cube 300 gur kurru

A sila was about 1 liter.Sumerian Beer: The Origins of Brewing Technology in Ancient Mesopotamia

Mass or weight

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 46.6±1.9 mg še uţţatu shekel 1 8.40±0.34 g gin2 šiqlu mina 60 504±20 g ma-na manû talent 3,600 30.2±1.2 kg gun2 biltu or kakaru

Time

In the Archaic System time notation was written in the U4 System U. Multiple lunisolar calendars existed; however the civil calendar from the holy city of Nippur (Ur III period) was adopted by Babylon as their civil calendar.Ronan, 2008 The calendar of Nippur dates to 3500 BCE and was itself based on older astronomical knowledge of an uncertain origin. The main astronomical cycles used to construct the calendar were the month, year, and day.

Basic Time Unit Ratio Sumerian Akkadian Cuneiform gesh mu-eš geš watch da-na bêru day 1 ud immu month 30 itud arhu year 360 mu šattu

Relationship to other metrologies The Classical Mesopotamian system formed the basis for Elamite, Hebrew, Urartian, Hurrian, Hittite, Ugaritic, Phoenician, Babylonian, Assyrian, Persian, Arabic, and Islamic metrologies.Conder 1908, p. 87. The Classical Mesopotamian System also has a proportional relationship, by virtue of standardized commerce, to Bronze Age Harappan and Egyptian metrologies.

See also Assyrian lion weights Babylonian mathematics Historical weights and measures Weights and measures

References Citations

Bibliography

Further reading

External links An online calculator