Ancient Mesopotamian units of measurement

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 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
* DUGb System Db used to count milk by volume
* DUGc 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.Melville 2006. In general however, length, volume, and mass are derived from a theoretical standard cube, called 'gur', filled with barley, wheat, water, or oil. The mass of a gur-cube, called 'gun2' is defined as the weight a laden ass can carry. 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 (432g). 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.Powell 1995, p.1955. 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 6m × 6m × 0.5m 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.
===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 Length	Basic Length	Basic Length	Basic Length	Basic Length	Basic Length	Basic Length
Unit 	Ratio 	Sumerian 	Akkadian 	Cuneiform 	 	
grain 	1/180 	še 	uţţatu 	 	 	
finger 	1/30 	šu-si 	ubānu 	 	 	
foot 	2/3 	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.
Distance	Distance	Distance	Distance	Distance 	Distance	Distance
Unit 	Ratio 	Sumerian	Akkdian 	Cuneiform	 	
rod 	1/60 	nidan 	nindanu 	 	 	
cord 	1/6 	eše2 	aslu 	 	 	
cable 	1 	uš 	uš 	 	 	
league 	30 	da-na 	bêru 	 	 	
===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 Area 	Basic Area	Basic Area 	Basic Area	Basic Area	Basic Area	Basic Area
Unit 	Ratio 	Dimensions 	Sumerian 	Akkdian 	Cuneiform 	
shekel 	1/60 	1kuš3 × 1kuš3 	gin2 	šiqlu 	 	
garden 	1 	12kuš3 × 12kuš3 	sar 	mūšaru 	 	
quarter-field	5 	60kuš3 × 60kuš3 	uzalak 	? 	 	
half-field 	10 	120kuš3 × 60kuš3 	upu 	ubû 	 	
field 	100 	60ĝiri3 × 60ĝiri3	iku 	ikû 	 	
estate 	1,800 	3eše2 × 6eše2 	bur 	būru 	 	
===Capacity===
Capacity was measured by either the ŠE system Š for dry capacity or the ŠE system Š* for wet capacity
Basic Volume	Basic Volume	Basic Volume	Basic Volume	Basic Volume	Basic Volume	Basic Volume
Unit 	Ratio 	Sumerian 	Akkdian 	Cuneiform 	 	
shekel 	1/60 	gin2 	šiqlu 	 	 	
bowl 	1 	sila3 	qû 	 	 	
vessel 	10 	ban2 	sutū 	 	 	
bushel 	60 	ba-ri2-ga 	parsiktu 	 	 	
gur-cube 	300 	gur 	kurru 	 	 	
===Mass===
thumb|right|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	Basic Mass	Basic Mass 	Basic Mass	Basic Mass	Basic Mass	Basic Mass
Unit 	Ratio 	Mean Value 	Sumerian 	Akkdian 	Cuneiform 	
grain 	1/180 	46.6mg ±1.9mg	še 	uţţatu 	 	
shekel 	1 	8.40g ±0.34g 	gin2 	šiqlu 	 	
pound 	60 	504g ±20g 	ma-na 	manû 	 	
load 	3600 	30.2kg ±1.2kg	gun2 	biltu 	 	
https://www.academia.edu/2916303/Mesopotamian_Mensuration_Balance_Pan_Weights_from_Nippur
https://www.academia.edu/2916278/Weighing_in_Mesopotamia_The_Balance_Pan_Weights_from_Ur
===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 synodic month, equinox year, and sidereal day.
Basic Time	Basic Time	Basic Time	Basic Time	Basic Time	Basic Time	Basic Time
Unit 	Ratio 	Sumerian 	Akkdian 	Cuneiform 	 	
gesh 	1/360 	mu-eš 	geš 	 	 	
watch 	1/12 	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
==Notes==
==References==
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==Further reading==
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==External links==
*An online calculator 
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Category:Sumerian art and architecture
Category:Babylonia
Category:Sumer
Measurement
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