ancient Mesopotamian units of measurement

File:Gudea of Lagash Girsu.png carved diorite]]

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
• DUG_b System Db used to count milk by volume
• DUG_c System Db used to count beer by volume

In Early Dynastic Sumer ({{circa|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.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.{{citation needed|date=September 2013}} These coefficients are given as:

• Komma = {{frac|80|81}} correction when planning rations with a 360-day year
• Leimma = {{frac|24|25}} conversion from decimal to a sexagesimal number system
• Diesis = {{frac|15|16}}
• Euboic = {{frac|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).{{citation needed|date=September 2013}} This standard is the main reference used by archaeologists to reconstruct the system.

File:Royal gur.svg

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.{{Cite book|last=Powell|first=Marvin A.|contribution=Metrology and Mathematics in Ancient Mesopotamia|year=1995|title=Civilizations of the Ancient Near East|editor-last=Sasson|editor-first=Jack M.|volume=III|page=[https://archive.org/details/isbn_9780684192796/page/1955 1955]|place=New York, NY|publisher=Charles Scribner's Sons|isbn=0-684-19279-9|url-access=registration|url=https://archive.org/details/isbn_9780684192796/page/1955}} His reform is considered the first standardized system of measure in Mesopotamia. The royal gur-cube (Cuneiform: LU₂.GAL.GUR, {{cuneiform|𒈚}}{{cuneiform|𒄥}}; 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.

Units of length are prefixed by the logogram DU ({{cuneiform|𒁺}}) a convention of the archaic period counting system from which it was evolved. Basic length was used in architecture and field division.

The step is equal to the length of a pendulum which completes half of its period in 1 second: 993.7 millimetres.{{Cite web |last=Boucher |first=Roland |date=2018 |title=The Pendulum and the Foot in Ancient Metrology 2013 |url=https://rolandboucher.com/2013/01/05/the-pendulum-and-the-foot-in-ancient-metrology/#:~:text=Details%20of%20the%20Sumerian%20Measurement,also%20defined%201000%20Sumerian%20feet.}}

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

The cable is approximately equal to 357.8 metres or 360 steps.

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 {{cuneiform|𒊬}}{{cuneiform|𒋞}}; Sumerian: šeg₁₂-sar; Akkadian: libittu-mūšaru) which held 720 bricks.

The garden is equal to approximately 36 square metres.{{Cite web |title=Old Babylonian metrology |url=https://myslu.stlawu.edu/~dmel/mesomath/obmetrology.html#:~:text=length%20conversion%20calculator-,Area,fractions%20of%20this%20basic%20unit.&text=1%20sar%20(garden%20plot%201,m.)&text=1%20iku%20(1%20sq.,0.9%20acre,%200.36%20ha.) |access-date=2025-05-29 |website=myslu.stlawu.edu}}

{{anchor|Volume}}

Capacity was measured by either the ŠE system Š for dry capacity or the ŠE system Š^* for wet capacity.{{Citation needed|date=May 2025}}

A sila was about 1 liter.[https://cdli.mpiwg-berlin.mpg.de/articles/cdlj/2012-2 Sumerian Beer: The Origins of Brewing Technology in Ancient Mesopotamia]

File:Mesopotamian weights made from haematite.JPG

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.

{{Cite journal|url=https://www.academia.edu/2916303|title=Mesopotamian Mensuration: Balance Pan Weights from Nippur|date=December 13, 2005|journal=Journal of the Economic and Social History of the Orient|volume=48|issue=3|pages=345–387|doi=10.1163/156852005774342894|via=www.academia.edu}}

{{Cite journal|url=https://www.academia.edu/2916278|title=Weighing in Mesopotamia: The Balance Pan Weights from Ur|first=William B.|last=Hafford|date=August 1, 2012|journal=Akkadica|via=www.academia.edu}}

{{Cite book|url=https://books.google.com/books?id=wt6mDwAAQBAJ&pg=PA91|title = West Semitic Vocabulary in the Akkadian Texts from Emar|isbn = 9789004369870|last1 = Pentiuc|first1 = Eugen J. |author-link=Eugen J. Pentiuc|date = 14 August 2018| publisher=BRILL }}

{{main|Babylonian calendar}}

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.

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.

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

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{{systems of measurement}}

{{Means of Exchange}}

Category:Sumerian art and architecture

Category:Babylonia

Category:Sumer

Measurement

Mesopotamian

Mesopotamian

Mesopotamian

Mesopotamian