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 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. 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, 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
One official government standard of measurement of the archaic system was the Cubit of Nippur. It is a Euboic Mana + 1 Diesis. 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 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 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. Distance units were geodectic as distinguished from non-geodectic basic length units. Sumerian geodesy divided latitude into seven zones between equator and pole.
Area
The GAN2 system G counting system evolved into area measurements. A special unit measuring brick quantity by area was called the brick-garden which held 720 bricks.
Capacity or volume
Capacity was measured by either the ŠE system Š for dry capacity or the ŠE system Š* for wet capacity
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.
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 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 sidereal day.
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. The Classical Mesopotamian System also has a proportional relationship, by virtue of standardized commerce, to Bronze Age Harappan and Egyptian metrologies.