Ancient weights and measures

Contents 
Introduction
Many systems of weights and measures have existed throughout history in different civilisations. The definitions of some of these units are often regarded as vague and inaccurate. True enough, although the roots of many of the units were the same, the actual value of a unit differed from civilization to civilization, or epoch to epoch. That fact should not lead to a conclusion that historical units of measure were inaccurate in general. Many units were defined to a high precision, and standards of measurement and tracking were in many cases excellent. As a case in point, the Great Pyramid of Giza was built to a precision of 0.015 m over sides that are 235 meters, over four and a half thousand years ago.
Mesopotamian system
Mesopotamia includes a number of cultures. The Sumerian number system uses a base 60 positional notation, and is the origin for the division of 60 for hours and angles.
Length
 kù
 Cubit (Sumerian). Akkadian ammatu. The copper bar cubit of Nippur, the first known standard bar, defines the Sumerian cubit as about 518.5 mm, widely used in third millennium BC. It was split in 30 digits. The Babylonian (or Salamis) cubit was around 484 mm.
 foot
 Defined as 264.6 mm by Sumerian ruler Gudea of Lagash around 2575 BC, this is the oldest preserved standard of length.
 digit
 1/16 foot or 1/30 cubit
 stadion
 148.5 m
 parasang
 Babylonian league is 5.6 km
Area
 sar
 Garden plot (Sumerian)
 iku
 "Plot of land enclosed by a boundary dike/canal", 100 sar. Probably 120 · 120 cubit²
Volume
 log
 0.54 l
 homer
 720 log
Weight and monetary
 shekal
 8.36 g, introduced around 3000 BC
 mina
 60 shekal
Time
 year
 The Sumerians used a 360 day year by 2100 BC.
 week
 The Babylonians introduced the seven day week, due to the belief that seven brought bad luck, so they did not want to work the seventh day.
 hour
 The 12 hour day and 12 hour night originates from Mesopotamia. The length of these hours changed through the year, being equally spaced over the time of light and dark, respectively.
Persian system
Length
 finger
 ¼ palm
 palm
 ¼ foot
 zereth
 Foot, ½ cubit
 arsani
 Cubit, 52.0 up to 64.0 cm
 cane
 2 paces, 6 cubits
 chebel
 40 cubits
 parasang
 The distance a horse would walk for one hour, 250 chebel, approx. 6 km. (6.23 km in mid 19th century. In today's Iran as well as Turkey, a metric farsang of 10 km is commonly used. Forerunner for league.
 mansion
 Equivalent to stathmos, 4 parsang
Volume
 chenica
 1.32 l, probably derived from the Greek cheonix
Egyptian system
Much of the Egyptian system of measurement is based on the Mesopotamian. The Egyptian system in its turn formed the basis of the later Greek system. The Egyptians based their measurements on the Royal cubit, for which the pharaoh devised a standard (master) cut in granite. From these standards, it is clear that accuracies in measurements of at least 1/16 yeba (1 mm) were possible. The Egyptian system was also noteworthy in having units for volume derived from the standard for length. While the Royal cubit is a very well defined unit, uncertainty is connected to the units for land measurement, especially when the Greek stadion and schoinos units came in use.
Length
 meh nesut
 Royal cubit, 52.3 cm, varied by less than 0.5 cm through the times.
 shesep
 Width of palm, alt. shep, 1/7 Royal cubit. It is speculated that the fraction of 1/7 may have been so that a reasonable pi could be made of 22 shesep over 1 cubit.
 yeba
 Digit, also zebo, ¼ palm, logically enough
 thumb
 4/3 yeba, or 2.49 cm. Basis for the Roman uncia and later, the inch.
 meh scherer
 Forearm, basically 6 / 7 Royal cubit. Also known as the common cubit, used by commons and not as precise.
 double remen
 Approx. 72.3 cm, the length of the diagonal of a Royal cubit square. (Because the hypotenuse of a square is the side × the square root of 2 (an irrational number), an exact decimal value for the remen in terms of Royal cubits cannot be given.)
 remen
 ½ double remen
 remen digit
 1/20 remen
 khet, also jet, hayt
 Senus, 100 Royal cubit
 stadion
 400 Royal cubits, 209.2 m
 parasang
 10000 Royal cubits
 schoinos
 Presumably the "common atur", 12000 Royal kubits or 6.3 km.
 iter, also atur or ater
 Royal river measure (pl. iteru or itrw). 20000 Royal cubits, or 10.46 km. The units parasang, schoinos and ater seems to be often interchanged. The book of Herodotus clearly states the Egyptian mile as twice a Persian parasang, i.e. 20000 Royal cubits.
Area
 setat, also aura
 100 × 100 Royal cubit²
 jata
 100 setat, is said to be used to this day.
 remen
 ½ setat
 hebes
 ½ remen
 sa
 ½ hebes
Volume
 hekat
 1/30 Royal cubit³, 4.8 l, used for grain. Was divided into fractions of ½, ¼, 1/8, 1/16, 1/32 and 1/64 by an "Eye of Horus" rule.
 oipe, also ipet
 4 hekat
 jar
 5 oipe
 hinu
 1/10 hekat, used for perfume as well as grain.
 ro
 1/32 hinu
 des
 For liquids, approx. 0.5 l
 secha
 For beer
 hebenet
 For wine
Weight
 deben
 91 g, normally of copper, but also silver, gold and probably lead. Also used as money.
 qedety
 1/10 deben
Time
 year
 The 365 day year was introduced by 2773 BC
Miscellaneous
 seked
 Unit of inclination, also seqt. Indicates horizontal dimension measured in palms (and digits fractions as necessary) per vertical Royal cubit rise. E.g. 5 seked is 54.46°, 5¼ seked is 53.13°, 5½ seked is 51.84°.
 shaty
 1/6 silver deben or 1/3 lead deben
Indus Valley system
The people of the Indus Civilization (ca. 2600 BC) achieved great accuracy in measuring length, mass, and time. They were among the first to develop a system of uniform weights and measures. Their measurements were extremely precise. Their smallest division, which is marked on an ivory scale found in Lothal, was approximately 1.704mm, the smallest division ever recorded on a scale of the Bronze Age. The decimal system was used. Harappan engineers followed the decimal division of measurement for all practical purposes, including the measurement of mass as revealed by their hexahedron weights. Weights were based on units of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500, with each unit weighing approximately 28 grams, similar to the English ounce or Greek uncia, and smaller objects were weighed in similar ratios with the units of 0.871.
Greek system
The Greek system was built mainly upon the Egyptian, and formed the basis of the later Roman system.
Length
 pous
 Foot (pl. podes), 31.6 cm, said to be 3/5 Egyptian Royal cubit. There are variations, from an Ionic foot is 29.6 cm to a Doric foot that is 32.6 cm
 daktulos
 Digit (pl. daktuloi), 1 / 16 pous
 condulos
 1/8 pous
 palaiste
 Palm, ¼ pous
 dikhas
 ½ pous
 spithame
 Span, ¾ pous
 pugon
 Homeric cubit, 1¼ pous
 pechua
 Cubit, 1½ podes, 47.4 cm
 bema
 Pace, 2½ podes
 khulon
 4½ podes
 orguia
 Fathom, 6 podes
 akaina
 10 podes
 plethron
 Cord measure, (pl. plethra), 100 podes
 stadion
 (pl. stadia), 6 plethra, i.e. 600 podes. Usually stated as 185.4 m. For reference, the stadion at Olympus measures 192.3 m. With a widespread use throughout antiquity, there were many variants of a stadion, from as low as 157 m up to 211 m.
 diaulos
 (pl. diauloi), 2 stadia. Only used for the Olympic footrace introduced in 724 BC.
 dolikhos
 6 or 12 diauloi. Only used for the Olympic footrace introduced in 720 BC.
 parasanges
 Persian measure, 30 stadia, 5.5 km. Used by Xenophon, for instance.
 skhoinos
 Lit. "reefs" (pl. skhoinoi), based on Egyptian river measure iter or atur. Usually defined as 60 stadia or 11.1 km. There are variants, see Egyptian atur.
 stathmos
 One days journey, roughly 25 km. May have been variable, dependent on terrain.
Volume
 kotule
 Liquid measure, (pl. kotulai), ¼ kheonix
 kheonix, alsp khoinix
 (pl khoenikes), approx. 1.1 l. Initially used for wheat.
 modios
 Bushel, 8 kheonikes
 medimnos
 48 kheonikes
 kotule
 Dry measure, 6 kuathoi
 khous
 Dry measure, 12 kotulai
 metretes
 Dry measure, 12 choes, approx. 34 l
Weight and monetary
 Medimnos
 ~25 kg
 Talent
 60 minae
 Mina
 100 drachmae
 Decadrachm
 Coin only, 10 drachmae
 Tetradrachm
 Coin only, 4 drachmae
 Stater
 Coin only, also didrachmon, 2 drachmae
 Drachma
 Weight of silver coin, 4.5 to 6 g
 Diobolus
 (two oboloi) 1/3 drachmae
 Obolus
 1/6 drachma, silver
 Chalkos
 1/8 obolus, copper
Miscellaneous
 muriade
 10.000
Roman system
The Roman system of measurement was built on the Greek system with Egyptian influences. The Roman units were generally accurate and well documented.
Length
Roman unit  Latin name  Roman Feet  Metric Equivalence  Imperial Equivalence 

one digit  digitus  1/16  18.525 mm  0.72933 in 
one palm  palmus  ¼  7.41 cm  2.92 in 
one foot  pes  1  29.64 cm  11.67 in 
one cubit  cubitus  1½  44.46 cm  17.50 in 
one step  gradus  2½  0.741 m  2 ft 5 in 
one pace  passus  5  1.482 m  4 ft 10.3 in 
one perch  pertica  10  2.964 m  9 ft 8.7 in 
one arpent  actus  120  35.568 m  116 ft 8 in 
one stadion  stadium  625  185.25 m  607 ft 9 in 
one mile  milliarium  5000  1.482 km  0.9209 mi 
one league  leuga  7500  2.223 km  1.381 mi 
In Antiquity the Roman foot was not divided into inches, i.e. twelve shares.
Area
Roman unit  Latin name  Acres  Equivalence 

one square foot  pes quatratus  1/14 400  ~ 875 cm² 
one square perch  scripulum  1/144  ~ 8.75 m² 
one aune of furrows  actus minimus  1/30  ~ 42 m² 
one rood  clima  ¼  ~ 315 m² 
one acre  actus quadratus  1  ~ 1260 m² 
one yoke  iugerum  2  ~ 2520 m² 
one morn  heredium  4  ~ 5040 m² 
one centurie  centuria  400  ~ 50.4 ha 
one "quadruplex"  saltus  1600  ~ 201.6 ha 
The Roman acre is the squared Roman arpent. This equals 14 400 square feet or about 0.126 hectares, more exactly almost 1264.673 square metres.
Volume
Roman unit  Latin name  Sesters  Equivalence 

one spoonfull  ligula  1/48  ~ 11.2 mL 
one dose  cyathus  1/12  ~ 45 mL 
one sixthsester  sextans  1/6  ~ 90 mL 
one thirdsester  triens  1/3  ~ 180 mL 
one halfsester  hemina  ½  ~ 270 mL 
one double thirdsester  cheonix  2/3  ~ 360 mL 
one sester  sextarius  1  ~ 540 mL 
one congius  congius  6  ~ 3.25 L 
one urn  urna  24  ~ 13 L 
one jar  amphora  48  ~ 26 L 
one hose  culleus  960  ~ 520 L 
The Roman jar, socalled "amphora quadrantal" is the cubic foot. The congius is halfafoot cube. The Roman sester is the sixth of a congius.
Roman unit  Latin name  Pecks  Equivalence 

one drawingspoon  acetabulum  1/128  ~ 67.5 mL 
one quartersester  quartarius  1/64  ~ 135 mL 
one halfsester  hemina  1/32  ~ 270 mL 
one sester  sextarius  1/16  ~ 540 mL 
one gallon  semodius  ½  ~ 4.67; L 
one peck  modius  1  ~ 8.67 L 
one bushel  quadrantal  3  ~ 26 L 
Like the jar, the Roman bushel or "quadrantal" is one cubic foot. It's almost 26.027 liters. The third part of this quadrantal is the Roman peck.
Weight
The roman units of weight varied significantly throughout the times, since most of the standards were obtained from the weight of particular coins. The values listed are based on the gold aureus of Augustus which were in use from 27 BC to AD 296. The earliest bronze coins of Rome 338 BC to 268 BC were 0.273 kg.
Roman unit  Latin name  Drachms  Equivalence 

one chalcus  chalcus  1/48  0.071 g 
one siliqua  siliqua  1/18  0.189 g 
one obolus  obolus  1/6  0.57 g 
one scruple  scrupulum  1/3  1.14 g 
one drachm  drachma  1  3.4 g 
one shekel  sicilicus  2  6.8 g 
one ounce  uncia  8  27.25 g 
one pound  libra  96  327 g 
one mine  mina  128  436 g 
All the multiples of the Roman ounce have their proper names.
 uncia
 sextans
 quadrans
 trians
 quincunx
 semis
 septunx
 bes
 dodrans
 dextans
 deunx
 as
One and a half ounce was called by Romans sescuncia.
Time
 year
 The Julian calendar 365¼ day year was introduced in 45 BC.
Vedic system
Vedic measures were first used by the Indian Vedic civilization, and are still in use today – primarily for religious purposes in Hinduism and Jainism.
 See also: Vedic units of time
Chinese system
The traditional units used in Imperial China (市制 Pinyin: Shìzhì, "city standard") are used to this day, albeit now rounded and bound to SI units, and changed to a divisor of 10 instead of the traditional 16.
 See also: Chinese units
Arabic system
The Arabic system is based on the Persian system.
Length
 assbaa
 Finger, ¼ palm
 cabda
 Palm, ¼ foot
 foot
 Base unit, 0.32 m
 arsh
 Cubit, traditionally 2 feet, new definition 1½ feet
 orgye
 Pace, 6 feet
 qasab
 Cane, 12 feet
 seir
 Stadion, 600 feet
 ghalva
 720 feet
 farasakh
 League, from parasang, 18000 feet, 5.76 km.
 barid
 4 farasakh
 marhala
 8 farasakh
Hebrew
See Hebrew weights
See also
References
 Measure for Measure, Richard Young and Thomas Glover, ISBN 188979600X.
 Masse und Gewichte, Marvin A. Powell
 The Civilisation of Ancient Egypt, Paul Johnson
External links
Mesopotamia
 Mesopotation bibliograpy (http://www.dubsar.com/nippur/rrannex.html)
Egypt
 Measuring length in Ancient Egypt (http://www.petrie.ucl.ac.uk/digital_egypt/weights/lenght.html)
 Egyptian units (http://gopher.ulb.ac.be/~pcara/hobbies/egypres.pdf)
 Egypt unidades, pesos e medidas (http://www.educ.fc.ul.pt/docentes/opombo/seminario/rhind/medida.htm)
 Las Matemáticas en el Antiguo Egipto (http://www.egiptologia.org/ciencia/matematicas/unidades.htm)
 Irrational numbers and pyramids (http://www.thehallofmaat.com/maat/print.php?sid=39)
 Sekeds and the Geometry of the Egyptian Pyramids (http://www.kch42.dial.pipex.com/sekes.htm)
Greece
 Greek measure (http://www.tulane.edu/~august/H310/handouts/Coinage.htm)
 More on the schoinos (http://www.chufu.de/Strabon/2125.htm)
General
 Dictionary of Units of Measurement (http://www.unc.edu/~rowlett/units/)
 Units of measure (http://www.sizes.com/)
 Unit systems (http://unicon.netian.com/unitsys_e.html)
 Mile measurements (http://www.kb.nl/kb/resources/frameset_kb.html?/kb/skd/skd/mathemat.html)
 Old units of measure (http://www.du.edu/~jcalvert/tech/oldleng.htm)
 Measures from Antiquity and the Bible (http://members.aol.com/JackProot/met/antbible.html)
 Alte Längenmaße und ihre Bedeutung (http://www.jlorber.com/Texte/Masse.html)
 Projekt zur Erschliessung historisch wertvoller Altkartenbestände (http://ikar.sbb.spkberlin.de/werkzeugkasten/sonderregeln/4_3.htm)de:Alte Maße und Gewichte