Ancient Mesopotamian units of measurement

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Sumerian Metrology

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[edit]

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
  • 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.[1] 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.[citation needed] 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).[citation needed] This standard is the main reference used by archaeologists to reconstruct the system.

Classical system[edit]

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 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.[1]


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

Basic Length
Unit Ratio Ideal Value Sumerian Akkadian Cuneiform
grain 1/180 0.0025m še uţţatu 𒊺
finger 1/30 0.015m šu-si ubānu 𒋗𒋛
foot 2/3 0.333m šu-du3-a šīzu 𒋗𒆕𒀀
cubit 1 0.497m kuš3 ammatu 𒌑
step 2 1.000m ĝiri3 šēpu 𒈨𒊑
reed 6 3.000m gi qanû 𒄀
rod 12 6.000m nindan nindanu 𒃻
cord 120 60.000m eše2 aslu 𒂠

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

Unit Ratio Ideal Value Sumerian Akkdian Cuneiform
rod 1/60 6.000m nidan nindanu 𒃻
cord 1/6 60.000m eše2 aslu 𒂠
cable 1 360m 𒍑
league 30 10,800m da-na bêru 𒁕𒈾


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 𒊬𒋞; Sumerian: šeg12-sar; Akkadian: libittu-mūšaru) which held 720 bricks.

Basic Area
Unit Ratio Dimensions Ideal Value Sumerian Akkdian Cuneiform
shekel 1/60 1kuš3 × 1kuš3 1 gin2 šiqlu 𒂆
garden 1 12kuš3 × 12kuš3 36 sar mūšaru 𒊬
quarter-field 5 60kuš3 × 60kuš3 900 uzalak ? 𒀺
half-field 10 120kuš3 × 60kuš3 1,800 upu ubû 𒀹𒃷
field 100 60ĝiri3 × 60ĝiri3 3,600 iku ikû 𒃷
estate 1,800 3eše2 × 6eše2 64,800 bur būru 𒁓


Capacity was measured by either the ŠE system Š for dry capacity or the ŠE system Š* for wet capacity

Basic Volume
Unit Ratio Capacity Ideal Value Sumerian Akkdian Cuneiform
shekel 1/60  ?L ? gin2 šiqlu 𒂆
bowl 1 1L 0.001 sila3 𒋡
vessel 10 10L 0.01 ban2 sutū 𒑏
bushel 60 60L 0.06 ba-ri2-ga parsiktu 𒁀𒌷𒂵
gur-cube 300 300L 0.3 gur kurru 𒄥


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

Mass was measured by the EN system E

Basic Mass
Unit Ratio Ideal Value Sumerian Akkdian Cuneiform
grain 1/180 0.05g še uţţatu 𒊺
shekel 1 9g gin2 šiqlu 𒂆
pound 60 497.7g ma-na manû 𒈠𒈾
load 3600 30,000g gun2 biltu 𒄘


Main article: 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.[3] 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
Unit Ratio Ideal Value Sumerian Akkdian Cuneiform
gesh 1/360 240s mu-eš geš 𒈬𒍑
watch 1/12 7,200s da-na bêru 𒂆
day 1 86,400s ud immu 𒌓
month 30 2,592,000s itud arhu 𒌗
year 360 31,104,000s mu šattu 𒈬

Relationship to other metrologies[edit]

The Classical Mesopotamian system formed the basis for Elamite, Hebrew, Urartian, Hurrian, Hittite, Ugaritic, Phoenician, Babylonian, Assyrian, Persian, Arabic, and Islamic metrologies.[4] The Classical Mesopotamian System also has a proportional relationship, by virtue of standardized commerce, to Bronze Age Harappan and Egyptian metrologies.

Although not directly derived from it, there is a 1:2 proportional relationship between SI and Sumerian metrology. SI inherited the convention of the second as 1/86,400th of a solar day from Sumer thus, two Sumerian seconds are approximately one SI second.[5]

See also[edit]



  1. ^ a b Melville 2006.
  2. ^ a b Powell 1995, p.1955.
  3. ^ Ronan, 2008
  4. ^ Conder 1908, p. 87.
  5. ^ Butler 2005


Further reading[edit]

External links[edit]