Overview of Metrological Systems

This is a short outline of the most important metrological systems attested in cuneiform mathematics, as used in the translations presented here. For a more comprehensive description, see M. A. Powell, "Masse und Gewichte" [in English], in D. O. Edzard (ed.), Reallexicon der Assyriologie, vol. 7 (1987-90), Berlin: Walter de Gruyter, pp. 457-517.

Archaic metrologies are not given here. They are summarised most conveniently in H. Nissen, P. Damerow, and R. K. Englund, Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East, Chicago: University of Chicago Press, 1993, pp. 28-29.

Some third-millennium metrologies

Area, volume, and weight metrologies are identical to the Ur III and Old Babylonian periods (below). Compound metrological signs, which denote both number and unit, are represented in translation by the numerical value followed by the sign in parentheses, e.g. 2 (ban) 3 (sila) for 23 litres.

Capacity measures in Early Dynastic Ebla

1 anzam
1 sila = 6 anzam
1 shekel = 4 sila
1 barizu = 2 1/2 shekels
1 gubar = 2 barizu

Early Dynastic and Sargonic lengths

Ancient units Approx. modern values
1 finger 17 mm
1 double-hand = 10 fingers 17 cm
1 cubit = 3 double-hands 50 cm
1 seed-cubit = 2 cubits 1 m
1 reed = 3 seed-cubits 3 m
1 rod = 2 reeds 6 m

Early Dynastic to Old Babylonian discrete counting (in transliteration)

Ancient units Modern values
1(diš) One
1(u) Ten
1(geš2) Sixty
1(geš'u) Six hundred
1(šar2) Three thousand, six hundred
1(šar'u) Thirty-six thousand
1(šargal)gal Two hundred and sixteen thousand

Classic Ur III and Old Babylonian metrologies

During the Ur III period, scribes began to calculate with the Sexagesimal Place Value System (SPVS), in which numbers are divorced from commodities and metrologies. Measurements and quantifications continued to be recorded in traditional metrologies, however. The SPVS is transliterated purely numerically, with spaces separating the sexagesimal places, thus: 1 41 15. In translation, a semi-colon marks the integer-fraction boundary, and leading/trailing zeroes are used where appropriate to indicate absolute value, thus: 1 41;15 = 101 1/4 but 1 41 15 00 = 364,500 and 0;01 41 15 = 0.028125.

Standard units of calculation (which are often implicit within Old Babylonian word problems) are shown below in bold.

Length

Ancient units Approx. modern values
1 finger 17 mm
1 cubit = 30 fingers 0.5 m
1 half-reed (later: pace) = 3 cubits 1.5 m
1 reed = 6 cubits 3 m
1 rod = 12 cubits 6 m
1 chain = 1 00 cubits or 5 rods 30 m
1 cable = 1 00 rods 360 m
1 league = 30 00 rods or 30 cables 10.8 km

The cubit was the standard unit of height.

Area and volume

The sar could be divided into 60 shekels and the shekel into 180 grains.

Ancient units Approx. modern values
1 area sar = 1 rod square 36 m2
1 volume sar = 1 area sar x 1 cubit 18 m3
1 (ubu) = 50 sar 1800 m2 or 900 m3
1 (iku) = 2 ubu = 1 40 sar 3600 m2 or 1800 m3
1 (eše) = 6 iku 2.16 ha or 108,000 m3
1 (bur) = 3 eše 6.48 ha or 324,000 m3
1 (bur'u) = 10 bur 64.8 ha or 3,240,000 m3
1 (šar) = 6 bur'u 388.8 ha
1 (šar'u) = 10 šar 3,888 ha
1 (šargal) = 6 šar'u 23,328 ha

Capacity

The sila could be divided into 60 shekels and the shekel into 180 grains. Multiples of the gur were written with the sexagesimal place value system.

Ancient units Approx. modern values
1 sila 1 litre
1 (ban) = 10 sila 10 litres
1 (barig) = 6 ban 60 litres
1 gur = 5 barig 300 litres

Weight

Early Dynastic weight standards were much more variable, and heavier (with a mina of 0.55-0.68 kg), than later (Powell 1987-90, 508). Multiples of the talent were written with the sexagesimal place value system.

Ancient units Approx. modern values
1 grain 0.05 g
1 shekel = 3 00 grains 8.3 g
1 mina = 1 00 shekels 0.5 kg
1 talent = 1 00 minas 30kg

Bricks

Ancient units (Approx.) modern values
1 brick sar = 12 00 bricks 720 bricks
Small, unbaked brick = 15 x 10 x 5 fingers 25 x 17 x 8 cm
Number of small bricks in 1 volume sar
= 1 26 24 = 7;12 brick sar
5184 bricks
Square, baked brick = 20 x 20 x 5 fingers 33 x 33 x 8 cm
Number of square bricks in 1 volume sar
= 32 24 = 2;42 brick sar
1944 bricks

Multiples of the brick sar were written in the same way as large area and volume measures.

First-millennium metrologies

Arû measure for lengths and areas

Ancient length units Approx. modern values Ancient area units Approx. modern values
1 big finger 3.1 cm
1 arû cubit = 24 big fingers 75 cm
1 rod = 12 cubits 9 m 1 rod x 1 rod = 1 mušaru 81 m2
1 ubû = 50 mušaru 0.4 ha
1 ikû = 2 ubû 0.81 ha
1 eblu = 6 ikû 4.86 ha
1 būru = 3 eblu = 18 ikû 14.6 ha
1 šar = 60 būru 875 ha

Arû 'seed measure' for areas

Ancient units Approx. modern values
1 270 m2
1 sūtu = 10 0.27 ha
1 pānu = 6 sūtu = 2 ikû 1.62 ha
1 kurru = 5 pānu = 10 ikû 8.1 ha

Cable 'reed measure' for lengths and areas

Ancient units Approx. modern values Ancient area units Approx. modern values
1 finger 2 cm
1 cable-cubit = 24 fingers 0.5 m
1 rod = 12 cubits 6 m 1 rod x 1 rod = 1 mušaru 36 m2
1 chain = 5 rods = 50 cubits 30 m
1 cable = 2 chains = 10 rods 60 m 1 cable x 1 cable = 25 mušaru 900 m2
1 ikû = 1 40 mušaru 0.36 ha

Cable 'seed measure' for area

Ancient units Approx. modern values
1 grain 70 cm2
1 akalu = 18 00 grains 7.5 m2
1 = 10 akalu 75 m2
1 sūtu = 6 450 m2
1 pānu = 6 sūtu 0.27 ha
1 kurru = 5 pānu 1.35 ha

'Reed measure' for lengths and areas

Ancient length units Approx. modern values Ancient area units Approx. modern values
1 finger 2 cm 1 finger x 1 finger = 1 small finger 4 cm2
1 cubit = 24 fingers 0.5 m 1 cubit x 1 finger = 1 grain 100 cm2
1 cubit x 1 cubit = 1 small cubit 0.25 m2
1 reed = 7 cubits 3.5 m 1 reed x 1 finger = 1 area finger 730 cm2
1 reed x 1 cubit = 1 area cubit 1.75 m2
1 reed x 1 reed = 1 area reed 12.25 m2
1 rod = 2 reeds = 14 cubits 7 m
17 Jul 2014

Eleanor Robson

Eleanor Robson, 'Overview of Metrological Systems', The Digital Corpus of Cuneiform Mathematical Texts, Eleanor Robson, 2014 [http://oracc.museum.upenn.edu/dccmt/metrology/]

 
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