Ancient Mesopotamian units of measurement
Ancient Mesopotamian units of measurement originated in the loosely organized city-states of Early Dynastic Sumer
Sumer was a civilization and historical region in southern Mesopotamia, modern Iraq during the Chalcolithic and Early Bronze Age....

. The units themselves grew out of the tradition of counting tokens
History of writing
The history of writing records the development of expressing language by letters or other marks. In the history of how systems of representation of language through graphic means have evolved in different human civilizations, more complete writing systems were preceded by proto-writing, systems of...

 used by the Neolithic (c 6000 BCE) cultural complex of the Near East
Near East
The Near East is a geographical term that covers different countries for geographers, archeologists, and historians, on the one hand, and for political scientists, economists, and journalists, on the other...

. The counting tokens were used to keep accounts of personal wealth and had both metrological and mathematical functions. Each city
A city is a relatively large and permanent settlement. Although there is no agreement on how a city is distinguished from a town within general English language meanings, many cities have a particular administrative, legal, or historical status based on local law.For example, in the U.S...

, kingdom
A monarchy is a form of government in which the office of head of state is usually held until death or abdication and is often hereditary and includes a royal house. In some cases, the monarch is elected...

 and trade guild
A guild is an association of craftsmen in a particular trade. The earliest types of guild were formed as confraternities of workers. They were organized in a manner something between a trade union, a cartel, and a secret society...

 had its own standards until the formation of the Akkadian Empire when Sargon of Akkad
Sargon of Akkad
Sargon of Akkad, also known as Sargon the Great "the Great King" , was an Akkadian emperor famous for his conquest of the Sumerian city-states in the 23rd and 22nd centuries BC. The founder of the Dynasty of Akkad, Sargon reigned in the last quarter of the third millennium BC...

 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
Third Dynasty of Ur
The Third Dynasty of Ur, also known as the Neo-Sumerian Empire or the Ur III Empire refers simultaneously to a 21st to 20th century BC Sumerian ruling dynasty based in the city of Ur and a short-lived territorial-political state that some historians regard as a nascent empire...

 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
Metrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement. The word comes from Greek μέτρον , "measure" + "λόγος" , amongst others meaning "speech, oration, discourse, quote, study, calculation, reason"...

 has been reconstructed by applying statistical methods to compare Sumerian architecture, architectural plan
Architectural plan
An architectural plan is a plan for architecture, and the documentation of written and graphic descriptions of the architectural elements of a building project including sketches, drawings and details.- Overview :...

s, and issued official standards such as Statue B of Gudea
Statues of Gudea
Twenty-seven statues of Gudea have been found so far . A-K were found during Ernest de Sarzec's excavations in the court of the palace of Adad-nadin-ahhe in Telloh . Statues M-Q come from clandestine excavations in Telloh in 1924; the rest come from the art trade, with unknown provenances and...

 and the bronze cubit of Nippur. In recent times archeologists have found a relationship between the Sumerian and SI metrologies.

Archaic system

The systems that would later become the classical standard for Mesopotamia were developed in parallel with writing during Uruk Period Sumer
Uruk period
The Uruk period existed from the protohistoric Chalcolithic to Early Bronze Age period in the history of Mesopotamia, following the Ubaid period and succeeded by the Jemdet Nasr period. Named after the Sumerian city of Uruk, this period saw the emergence of urban life in Mesopotamia. It was...

 (c 4000 BCE). Studies of protocuneiform
Cuneiform can refer to:*Cuneiform script, an ancient writing system originating in Mesopotamia in the 4th millennium BC*Cuneiform , three bones in the human foot*Cuneiform Records, a music record label...

 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 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
Early Dynastic Period
Early Dynastic Period may refer to:*Early Dynastic Period of Egypt*Early Dynastic Period of Mesopotamia...

 (c 2900–2300 BCE) metrology
Metrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement. The word comes from Greek μέτρον , "measure" + "λόγος" , amongst others meaning "speech, oration, discourse, quote, study, calculation, reason"...

 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 numeral
Numeral system
A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....

s 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. 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
The donkey or ass, Equus africanus asinus, is a domesticated member of the Equidae or horse family. The wild ancestor of the donkey is the African Wild Ass, E...

 can carry. However, because of the different specific gravities of these substances combined with dual numerical bases (sexagesimal or decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

), 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 (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
Naram-Sin , reigned ca. 2254–2218 BCE, short chronology, was the third successor and grandson of King Sargon of Akkad. Under Naram-Sin the Akkadian Empire reached its zenith...

 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
Cuneiform can refer to:*Cuneiform script, an ancient writing system originating in Mesopotamia in the 4th millennium BC*Cuneiform , three bones in the human foot*Cuneiform Records, a music record label...

: LU2.GAL.GUR, ; Akkadian
Akkadian language
Akkadian is an extinct Semitic language that was spoken in ancient Mesopotamia. The earliest attested Semitic language, it used the cuneiform writing system derived ultimately from ancient Sumerian, an unrelated language isolate...

: šarru kurru) was a theoretical cube of water approximately 6m × 6m × 0.5m from which all other units could be derived. The Neo-Sumerians
Third Dynasty of Ur
The Third Dynasty of Ur, also known as the Neo-Sumerian Empire or the Ur III Empire refers simultaneously to a 21st to 20th century BC Sumerian ruling dynasty based in the city of Ur and a short-lived territorial-political state that some historians regard as a nascent empire...

 continued use of the royal gur-cube as indicated by the Letter of Nanse issued in 2000 BCE by Gudea
Gudea was a ruler of the state of Lagash in Southern Mesopotamia who ruled ca. 2144 - 2124 BC. He probably did not come from the city, but had married Ninalla, daughter of the ruler Urbaba of Lagash, thus gaining entrance to the royal house of Lagash...

 . Use of the same standard continued through the Babylonia
Babylonia was an ancient cultural region in central-southern Mesopotamia , with Babylon as its capital. Babylonia emerged as a major power when Hammurabi Babylonia was an ancient cultural region in central-southern Mesopotamia (present-day Iraq), with Babylon as its capital. Babylonia emerged as...

n, Assyrian, and Persian Empires.


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
Unit Ratio Ideal Value Sumerian Akkadian Cuneiform
grain 1/180 0.0025m še uţţatu
finger 1/30 0.015m šu-si ubānu
foot 2/3 0.333m šu-du3-a šīzu
The cubit is a traditional unit of length, based on the length of the forearm. Cubits of various lengths were employed in many parts of the world in Antiquity, in the Middle Ages and into Early Modern Times....

1 0.497m kuš3 ammatu
step 2 1.000m ĝiri3 šēpu
reed 6 3.000m gi qanû
rod 12 6.000m nindan nindanu
cord 120 60.000m eše2 aslu

Distance units were geodectic as distinguished from non-geodectic basic length units. Sumerian geodesy
Geodesy , also named geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, in a three-dimensional time-varying space. Geodesists also study geodynamical phenomena such as crustal...

 divided latitude into seven zones between equator and pole.
Unit Ratio Ideal Value Sumerian Akkdian Cuneiform
rod 1/60 6.000m nidan nindanu
cord 1/6 60.000m eše2 aslu
cable 1 360m
league 30 10,800m da-na bêru


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


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
bowl 1 1L 0.001 sila3
vessel 10 10L 0.01 ban2 sutū
bushel 60 60L 0.06 ba-ri2-ga parsiktu
gur-cube 300 300L 0.3 gur kurru


Mass was measured by the EN system E
Basic Mass
Unit Ratio Ideal Value Sumerian Akkdian Cuneiform
grain 1/180 0.05g še uţţatu
shekel 1 9g gin2 šiqlu
pound 60 497.7g ma-na manû
load 3600 30,000g gun2 biltu


In the Archaic System time notation written in the U4 System U. Multiple lunisolar calendars existed; however the civil calendar from the holy city of Nippur
Nippur was one of the most ancient of all the Sumerian cities. It was the special seat of the worship of the Sumerian god Enlil, the "Lord Wind," ruler of the cosmos subject to An alone...

 (Ur III period) was adopted by Babylon as their civil calendar. 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 sideral day.
Basic Time
Unit Ratio Ideal Value Sumerian Akkdian Cuneiform
gesh 1/360 240s mu-eš geš
watch 1/12 7,200s da-na bêru
day 1 86,400s ud immu
month 30 2,592,000s itud arhu
year 360 31,104,000s mu šattu

Relationship to other metrologies

The Classical Mesopotamian system formed the basis for Elam
Elam was an ancient civilization located in what is now southwest Iran. Elam was centered in the far west and the southwest of modern-day Iran, stretching from the lowlands of Khuzestan and Ilam Province, as well as a small part of southern Iraq...

ite, Hebrew, Urartian
Urartu , corresponding to Ararat or Kingdom of Van was an Iron Age kingdom centered around Lake Van in the Armenian Highland....

, Hurrian, Hittite, Ugarit
Ugarit was an ancient port city in the eastern Mediterranean at the Ras Shamra headland near Latakia, Syria. It is located near Minet el-Beida in northern Syria. It is some seven miles north of Laodicea ad Mare and approximately fifty miles east of Cyprus...

ic, Phoenicia
Phoenicia , was an ancient civilization in Canaan which covered most of the western, coastal part of the Fertile Crescent. Several major Phoenician cities were built on the coastline of the Mediterranean. It was an enterprising maritime trading culture that spread across the Mediterranean from 1550...

n, Babylonian, Assyrian, Persian, Arabic, and Islamic metrologies. The Classical Mesopotamian System also has a proportional relationship, by virtue of standardized commerce, to Bronze Age
Bronze Age
The Bronze Age is a period characterized by the use of copper and its alloy bronze as the chief hard materials in the manufacture of some implements and weapons. Chronologically, it stands between the Stone Age and Iron Age...

 Harappan and Egyptian metrologies.

Although not directly derived from it, there is a 1:2 proportional relationship between SI
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

 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. Moreover, because both systems use a seconds pendulum
Seconds pendulum
A seconds pendulum is a pendulum whose period is precisely two seconds; one second for a swing in one direction and one second for the return swing, a frequency of 1/2 Hz....

 to create a unit of length, a meter is approximately two kuš3, a liter
- External links :*...

 2 sila3, and a kilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

 is 2 ma-na.

See also

  • Historical weights and measures
  • Weights and measures
  • Babylonian mathematics
    Babylonian mathematics
    Babylonian mathematics refers to any mathematics of the people of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC. Babylonian mathematical texts are plentiful and well edited...

External links

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