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DCCMT » Metrology

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.

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.

1 anzam |

1 sila = 6 anzam |

1 shekel = 4 sila |

1 barizu = 2 1/2 shekels |

1 gubar = 2 barizu |

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 |

Ancient units | Modern values |
---|---|

1(diš) | One |

1(u) | Ten |

1(geš_{2}) |
Sixty |

1(geš'u) | Six hundred |

1(šar_{2}) |
Three thousand, six hundred |

1(šar'u) | Thirty-six thousand |

1(šargal)^{gal} |
Two hundred and sixteen thousand |

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**.

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.

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

Ancient units | Approx. modern values |
---|---|

1 area = 1 rod squaresar |
36 m^{2} |

1 volume = 1 area sarsar x 1 cubit |
18 m^{3} |

1 (ubu) = 50 sar |
1800 m^{2} or 900 m^{3} |

1 (iku) = 2 ubu = 1 40 sar |
3600 m^{2} or 1800 m^{3} |

1 (eše) = 6 iku |
2.16 ha or 108,000 m^{3} |

1 (bur) = 3 eše |
6.48 ha or 324,000 m^{3} |

1 (bur'u) = 10 bur |
64.8 ha or 3,240,000 m^{3} |

1 (šar) = 6 bur'u |
388.8 ha |

1 (šar'u) = 10 šar |
3,888 ha |

1 (šargal) = 6 šar'u |
23,328 ha |

The * sila* could be divided into 60 shekels and the shekel into 180 grains. Multiples of the

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 |

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 |

Ancient units | (Approx.) modern values |
---|---|

1 brick = 12 00 brickssar |
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.

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 m^{2} |

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 |

Ancient units | Approx. modern values |
---|---|

1 qû |
270 m^{2} |

1 sūtu = 10 qû |
0.27 ha |

1 pānu = 6 sūtu = 2 ikû |
1.62 ha |

1 kurru = 5 pānu = 10 ikû |
8.1 ha |

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 m^{2} |

1 chain = 5 rods = 50 cubits | 30 m | ||

1 cable = 2 chains = 10 rods | 60 m | 1 cable x 1 cable = 25 mušaru |
900 m^{2} |

1 ikû = 1 40 mušaru |
0.36 ha |

Ancient units | Approx. modern values |
---|---|

1 grain | 70 cm^{2} |

1 akalu = 18 00 grains |
7.5 m^{2} |

1 qû = 10 akalu |
75 m^{2} |

1 sūtu = 6 qû |
450 m^{2} |

1 pānu = 6 sūtu |
0.27 ha |

1 kurru = 5 pānu |
1.35 ha |

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 cm^{2} |

1 cubit = 24 fingers | 0.5 m | 1 cubit x 1 finger = 1 grain | 100 cm^{2} |

1 cubit x 1 cubit = 1 small cubit | 0.25 m^{2} |
||

1 reed = 7 cubits | 3.5 m | 1 reed x 1 finger = 1 area finger | 730 cm^{2} |

1 reed x 1 cubit = 1 area cubit | 1.75 m^{2} |
||

1 reed x 1 reed = 1 area reed | 12.25 m^{2} |
||

1 rod = 2 reeds = 14 cubits | 7 m |

Eleanor Robson

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

http://oracc.iaas.upenn.edu/dccmt/metrology/