Stadia

Many systems of weights and measures have existed throughout history. The definitions of some of these units were often vague and inaccurate, and although the roots of many of the units were the same, the actual value of a unit differed from country to country, 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 were in many cases excellent. As a case in point, the Great Pyramid of Giza was built to a precision of 15 mm over sides that are 235 m, over four and a half thousand years ago.

The systems of antiquity

Main systems in antiquity

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. For reference, the inner square of the Tower of Babel measured 120 by 120 cubits.
• foot – Defined as 264.6 cm 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.

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. Note also the cubit and remen which has a ratio that constitutes an irrational number. 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.

The Egyptians were of fine geometers. They could not calculate the radix of two, but they could draw it. Discovering a good approximation in trigonometry: "Twenty times the radix of two, divided by 28, is very close to unit." So, they wanted to have a 28-digit cubit.

By the theoretical value of the Mesopotanian 30-digit Nippur Cubit equal :  518 616 µm.
<center> The Egyptian Remen (pygon)	<center> equal	<center> 20 / 28	<center> Nippur Cubit (ell)	<center> =	<center> 37.044 cm
<center> The Old Egyptian Royal Cubit	<center> equal	<center> 20√2 / 28	<center> Nippur Cubit (ell)	<center> ~	<center> 52.388 cm
<center> The Egyptian Royal Cubit	<center> equal	<center> 20√2 / 28	<center> Old Royal Cubit	<center> =	<center> 52.920 cm

• The Egyptians geometers divided the Nippur Cubit into 28 digits instead of 30 (= ½ × 60 ! in Mesopotamia, inventor of sexagesimal calculation.)  ?  Thus, Egyptians defined the later called "Roman digit".
• 20 (later called) Roman digits is the length the Egyptian construction Remen during the third millennium BC.  ?  The 20-digit measure is called "pygon" in Greek language.
• Centuries later, they used a construction Remen with 20 digits token from the Old Royal Cubit.  ?  Since, the foot of the new Royal Cubit (later called "Shaku" in Japan) and the (later called) Roman foot were related by the ratio: 100 to 98 exactly one.

Note, that the well-known "megalithic yard" (~ 83 cm) and the "Nippur cubit" are related by simple ratio 16 : 10.  The theoretical "length of Roman barleycorn" is exactly  8 252 µm.

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, 1 / 4 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
• remen – 1 / 2 double remen
• remen digit – 1 / 20 remen
• khet – Senus, 100 Royal cubit, also jet, hayt
• stadion – 400 Royal cubits, 209.2 m
• parasang – 10000 Royal cubits
• schoinos – Presumably the "common atur", 12000 Royal kubits or 6.3 km.
• iter – Royal river measure (pl. iteru or itrw), also atur or ater. 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 – 100 · 100 Royal cubit², also aura
• jata – 100 setat, is said to be used to this day.
• remen – 1 / 2 setat
• hebes – 1 / 4 setat
• sa – 1/8 setat

Volume

• hekat – 1 / 30 Royal cubit³, 4.8 l, used for grain. Was divided into fractions of 1/2, 1/4, 1/8, 1/16, 1/32 and 1/64 by an "Eye of Horus" rule.
• oipe – Alt. 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°, 5 1/4 seked is 53.13°, 5 1/2 seked is 51.84°.
• shaty – 1 / 6 silver deben or 1 / 3 lead deben

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, 1 / 4 pous
• dikhas – 1 / 2 pous
• spithame – Span, 3 / 4 pous
• pugon – Homeric cubit, 5 / 4 pous
• pechua – Cubit, 3 / 2 podes, 47.4 cm
• bema – Pace, 5 / 2 podes
• khulon – 9 / 2 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), 1 / 4 kheonix
• kheonix – Alt. 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 –
• talent – 60 mina
• mina – 100 drachma
• decadrachm – Coin only, 10 drachma
• tetradrachm – Coin only, 4 drachma
• stater – Coin only, also didrachm, 2 drachma
• drachma – Weight of silver coin, 4.5 to 6 g
• diobol – 1 / 3 drachma
• obolo – 1 / 6 drachma, silver
• khalkoi – 1 / 8 obolo, 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 accurate and well documented.
Distances may have been measured by odometers connected to carriage axles, for instance.

Length

<center> Roman unit	<center> Latin name	<center> Feet	<center> Equivalence
<center> one digit	<center> digitus	<center> 1 / 16	<center> 18.525 mm
<center> one palm	<center> palmus	<center> 1 / 4	<center> 7.41 cm
<center> one foot	<center> pes	<center> 1	<center> 29.64 cm
<center> one cubit	<center> cubitus	<center> 1½	<center> 44.46 cm
<center> one step	<center> gradus	<center> 2½	<center> 0.741 m
<center> one pace	<center> passus	<center> 5	<center> 1.482 m
<center> one perch	<center> pertica	<center> 10	<center> 2.964 m
<center> one arpent	<center> actus	<center> 120	<center> 35.568 m
<center> one stadion	<center> stadium	<center> 625	<center> 185.25 m
<center> one mile	<center> miliarius	<center> 5000	<center> 1.482 km
<center> one league	<center> leuga	<center> 7500	<center> 2.223 km
<center>The Roman foot is defined sixteen 28th of the Nippur cubit. The "theoretical" value of the Nippur ell is: 518 616 µm exactly. Therefore Romain foot is 296 352 µm. This is around 29.64 cm.</center>

• In Antiquity the Roman foot was not divided into inches, i.e. twelve shares.

Area

<center> Roman unit	<center> Latin name	<center> Acres	<center> Equivalence
<center> one square foot	<center> pes quatratus	<center> 1 / 14 400	<center> ~ 875 cm²
<center> one square perch	<center> scripulum	<center> 1 / 144	<center> ~ 8.75 m²
<center> one aune of furrows	<center> actus minimus	<center> 1 / 30	<center> ~ 42 m²
<center> one rood	<center> clima	<center> 1 / 4	<center> ~ 315 m²
<center> one acre	<center> actus quadratus	<center> 1	<center> ~ 1260 m²
<center> one yoke	<center> iugerum	<center> 2	<center> ~ 2520 m²
<center> one morn	<center> heredium	<center> 4	<center> ~ 5040 m²
<center> one centurie	<center> centuria	<center> 400	<center> ~ 50.4 ha
<center> one "quadruplex"	<center> saltus	<center> 1600	<center> ~ 201.6 ha
<center>The Roman acre is the squared arpent. (1 arpent = 12 ten feet perches) This egal 14 400 squared feet or about 0.126 hektar, more exactly one, almost: 1264.673 square metres.</center>

Volume

• Liquid measures :

<center> Roman unit	<center> Latin name	<center> Sesters	<center> Equivalence
<center> one egg-spoon	<center> ligula	<center> 1 / 48	<center> ~ 1⅛ cl
<center> one table-spoon	<center> cyathus	<center> 1 / 12	<center> ~ 4½ cl
<center> one sixth-sester	<center> sextans	<center> 1 / 6	<center> ~ 9 cl
<center> one third-sester	<center> triens	<center> 1 / 3	<center> ~ 18 cl
<center> one half-sester	<center> hemina	<center> 1 / 2	<center> ~ 27 cl
<center> one double third-sester	<center> cheonix	<center> 2 / 3	<center> ~ 36 cl
<center> one sester	<center> sextarius	<center> 1	<center> ~ 54 cl
<center> one congius	<center> congius	<center> 6	<center> ~ 3¼ l
<center> one urn	<center> urna	<center> 24	<center> ~ 13 l
<center> one jar	<center> amphora	<center> 48	<center> ~ 26 l
<center> one hose	<center> culleus	<center> 960	<center> ~ 520 l
<center>The Roman jar, so-called "amphora quadrantal" is the cubic foot. The congius is half-a-foot cube. The Roman sester is the sixth of a congius.</center>

• Dry measures :

<center> Roman unit	<center> Latin name	<center> Pecks	<center> Equivalence
<center> one drawing-spoon	<center> acetabulum	<center> 1 / 128	<center> ~ 6¾ cl
<center> one quarter-sester	<center> quartarius	<center> 1 / 64	<center> ~ 13½ cl
<center> one half-sester	<center> hemina	<center> 1 / 32	<center> ~ 27 cl
<center> one sester	<center> sextarius	<center> 1 / 16	<center> ~ 54 cl
<center> one gallon	<center> semodius	<center> 1 / 2	<center> ~ 4⅔ l
<center> one peck	<center> modius	<center> 1	<center> ~ 8⅔ l
<center> one bushel	<center> quadrantal	<center> 3	<center> ~ 26 l
<center>The Roman bushel, the quadrantal, is the cubic foot. Just like the jar. Its almost 26.027 liters. The third part of this quadrantal is the Roman peck.</center>

Weight

<center> Roman unit	<center> Latin name	<center> Drachms	<center> Equivalence
<center> one chalcus	<center> chalcus	<center> 1 / 48	<center> 71 mg
<center> one siliqua	<center> siliqua	<center> 1 / 18	<center> 189⅓ mg
<center> one obolus	<center> obolus	<center> 1 / 6	<center> 0.568 g
<center> one scruple	<center> scrupulum	<center> 1 / 3	<center> 1.136 g
<center> one drachm	<center> drachma	<center> 1	<center> 3.408 g
<center> one shekel	<center> sicilicus	<center> 2	<center> 6.816 g
<center> one ounce	<center> uncia	<center> 8	<center> 27.264 g
<center> one pound	<center> libra	<center> 96	<center> 327.168 g
<center> one mine	<center> mina	<center> 128	<center> 436.224 g
<center>There is no direct relationship between the lengths and the weights. But : The Roman pound is worth three quarters exactly of the Greek mine. Thus the Greek and Roman drachm is related by the ratio 32 to 25.</center>

• Others give 327.453 grams to the Roman pound, i.e. an additional 0.1 percent.

<center> All the multiples of the Roman ounce have their proper names.
<center>   1 ounce    =	<center> uncia	<center>   7 ounces  =	<center> septunx
<center>   2 ounces  =	<center> sextans	<center>   8 ounces  =	<center> bes
<center>   3 ounces  =	<center> quadrans	<center>   9 ounces  =	<center> dodrans
<center>   4 ounces  =	<center> trians	<center> 10 ounces  =	<center> dextans
<center>   5 ounces  =	<center> quincunx	<center> 11 ounces  =	<center> deunx
<center>   6 ounces  =	<center> semis	<center> 12 ounces  =	<center> as
<center> One and a half ounce was called by Romans :  "sescuncia". </center>

Time

• year – The Julian calendar 365 1/4 day year was introduced in 45 BC.

Other important systems of Antiquity

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

Persian system

The Persian system had influence on the Greek system, at least. The ghalva (stadion) and parasang were much used as a land measure. There are significant uncertainty, though.

Length

• finger – 1 / 4 palm
• palm – 1 / 4 foot
• zereth – Foot, 1 / 2 cubit
• arsani – Cubit, 52.0 up to 64.0 cm
• cane – 2 paces, 6 cubits
• chebel – 40 cubits
• stadion – Forerunner to Greek and Egyptian stadion, presumably around 264 m
• 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.
• schoinos – Origin of Greek and Egyptian measures
• mansion – Equivalent to "stathmos", 4 parsang

Volume

• chenica – 1.32 l, probably basis of the Greek cheonix

Arabic system

The Arabic system is based on the Persian system.

Length

• assbaa – Finger, 1 / 4 palm
• cabda – Palm, 1 / 4 foot
• foot – Base unit, 0.32 m
• arsh – Cubit, traditionally 2 feet, new definition 3 / 2 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

The systems of the Middle Age

Medieval systems still in use

English system

Before the Roman based measurement system was introduced from 1066 onwards, there existed a Anglo-Saxon system of measure based on the units of the barleycorn and the gyrd (rod). This presumably had Germanic origins. Later development of the British system continued by defining the units by law in the Magna Carta of 1215, and issuing measurement standards from the then capital Winchester. Standards were renewed in 1496, 1588 and 1758. The last Imperial Standard Yard in bronze was made in 1845. See: Imperial system of units

Length

• barleycorn – Basic Anglo Saxon unit, the length of a corn of barley. The unit survived after 1066, but now defined as 1/3 inch. Note the relation to the grain unit of weight.
• digit – 3 / 4 inch
• ynch – Anglo Saxon inch, 3 barleycorns. Based on the uncia from 1066.
• nail – 3 digits
• palm - 3 inches
• hand – 4 inches
• shaftment - Width of the hand and outstretched thumb, 6 1/2 ynches before 1066, 6 inches thereafter
• span – Width of the outstretched hand, from the tip of the thumb to the tip of the little finger, 3 palms
• foot – Usually 13 ynches but also other variants. Shortened by basing it on the Roman pes from 1066.
• cubit – Forearm, 18 inches
• ell – Elbow, 20 nails or 45 inches. Mostly for measuring clothing
• yard – Introduced after 1066, 3 feet.* fathom – From one fingertip to the other, 6 feet
• furlong – "Furrow long" (Saxon furrow is fuhr), based on the stadion, defined as 40 rods
• league – Usually three miles. Intended to be an hour's walk.
• mile – Introduced after 1066, originally the Roman mile at 5000 feet, in 1592 it was extended to 5280 feet to make it an even number of furlongs.
• rod – Saxon gyrd measuring stick, might have been from 20 "natural feet". Retained its length but redefined as 16 1/2 Roman feet after 1066.
• chain – Gunter's Chain, introduced in the 17th century, 66 foot alternative to the rod for land measurement.

Area

• acre – Saxon unit, meaning "field", one furlong by 4 rods. Probably meant to be "as much area as could be plowed in one day".

Weight

• 1 ton = 2240 lb exactly. (This amount is called a long ton in US customary units)
• 1 hundredweight = 112 lb exactly. (This amount is called a long hundredweight in US customary units )
• 1 ounce (oz) = 16 dr exactly = 437.5 gr exactly = 0.028 349 523 125 kg exactly
• 1 pound (lb) = 16 oz exactly = 7000 gr exactly = 0.453 592 37 kg exactly

• 1 grain (gr) = 64.79891 mg exactly
• 1 dram (dr) = 27.34375 gr exactly
• 1 scruple (s ap) = 20 gr exactly
• 1 pennyweight (dwt) = 24 gr exactly
• 1 dram apothecaries (dr ap) = 3 s ap exactly
• 1 ounce apothecaries (oz ap) or ounce troy (oz t) = 8 dr ap exactly = 480 gr exactly
• 1 pound apothecaries (lb ap) or pound troy (lb t)= 5760 gr

Miscellaneous

• score – 20

US system

The US system is based on the English system from the 1700s. See U.S. customary units.

Abandoned medieval systems

Scottish system

Length

• inch – 2.554 cm
• foot – 12 inches, 30.645 cm
• ell – Elbow, 37 Scots inches. 94.5 cm
• fall – 18 Scots feet
• mile – 320 falls, 1814.2 m

Spanish system

There were several variants, the Castilian is shown.

Length

• punto – Point, 1 / 12 linea
• linea – Line, 1 / 12 pulgada
• pulgada – Inch, 1 / 36 vara, 0.02322 m
• pie – Foot, 12 pulgadas, 0.2786 m
• vara – Yard, 0.8359 m
• paso – Pace, 60 pulgadas
• legua – League, 5000 varas, approx 4.2 km

French system

In France, again, there were many local variants. For instance, the lieue could vary from 3.268 km in Beauce to 5.849 km in Provence.

Length

• lieue commune – French land league, 4.452 km, 1/25 Equatorial degree
• lieue marine – French (late) sea league, 5.556 km, 3 nautical miles.
• lieue de poste – Legal league, 2000 toises, 3.898 km
• lieue metrique – Metric system adaptation, 4.000 km
• toise – Fathom, 6 pieds. Originally introduced by Charlemagne in 790, it is now considered to be 1.949 m.
• pied – Foot, varied through times, the Paris pied de roi is 32.48 cm. Used by Coulomb in manuscripts relating to the inverse square law of electrostatic repulsion. Isaac Newton used the "Paris foot" in his Philosophiae Naturalis Principia Mathematica.
• pouce – Inch, 1 / 12 pied
• ligne – 1 / 12 pouce

Volume

• litron –

Weight

• quintal

German system

Up to the introduction of the metric system, almost every town in Germany had their own definitions. It is said that by 1810, only in Baden there were 112 different Ellen.

Length

• Meile – A German geographische Meile or Gemeine deutsche Meile was defined as 7.420 km, but there were a wealth of variants:
  • Anhalt – 7532 m
  • Baden – 8889 m before 1810, 8944 m before 1871, 8000 m thereafter
  • Böhmen – 7498 m
  • Brabant – 5000 m
  • Bayern – 7415 m, connected to a 1/15 Equatorial degree as 25406 Bavarian feet.
  • Hamburg (Prussia) – In 1816, king Frederick William III of Prussia adopted the Danish mile at 7532 m, or 24000 Prussian feet. Also known as Landmeile
  • Hessen-Kassel – 9206 m
  • Lippe-Detmold – 9264 m
  • Oldenburg – 9894 m
  • Osnabrück – 5160 m
  • Pfalz – 4630 m
  • Rheinland – 4119 m
  • Sachsen – Postmeile, 7500 m. Also 9062 m or 32000 feet in Dresden
  • Schleswig-Holstein – 8803 m
  • Westfalen – 11100 m, but also 9250 m
  • Vienna – 7586 m
  • Wiesbaden – 1000 m
  • Württemberg – 7449 m
• Reichsmeile – New mile when the metric system was introduced, 7.5 km. Prohibited by law in 1908.
• Schainos – Uncertain use, between 10 and 12 km,
• Wegstunde – One hours travel, used up to the 18th century. In Germany 1 / 2 Meile or 3.71 km, in Switzerland 16000 feet or 4,8 km
• Stadion – Uncertain use
• Rute – Roman origin, use as land measure. Very differing definitions, 10, 12, 14, 15, 18 or 20 feet, varied between approx. 3 and 5 m.
• Klafter – Fathom, usually 6 feet. Regional changes from 1.75 m in Baden to 3 m in Switzerland.
• Elle – Distance between elbow and finger tip. In the North, often 2 feet, In Prussia 17 / 8 feet, in the South variable, often 2 1/2 feet. The smallest known German elle is 402.8 mm, the longest 811 mm.
• Fuss – The foot varied between 23.51 cm in Wesel and 40.83 cm in Trier.
• Rheinfuss – Rhine foot, used in the North, 31.387 cm
• Zoll – Inch. Usually 1 / 12 foot, but also 1 / 10.
• Linie – Usually 1 / 12 inch, but also 1 / 10.

Volume

• Klafter – For firewood, 2.905 m³

Dutch system

The Dutch system was not standardized until Napolean introduced the metric system so different towns measures with the same names but differing sizes.

Some common measures:

Weight

• Ons, Once – 1/16 pond =31 g
• Pond (Amsterdam) – 404.09 gram (other ponds were also in use
• Scheepslast – 4000 Amsterdam pond = 1976.4 kg = 2.18 US ton

Length

• duim –2.54 cm
• kleine palm –3 cm
• groete palm –9.6 cm, after 1820, 10 cm
• voet –12 duim = abt. 29.54 cm, many local variations
• el – about 70 cm

Volume

• Pint – 0.6 l

Danish system

From May 1 1683, king Christian V of Denmark introduced an office to oversee weights and measures, a justervæsen, to be led by Ole Rømer. The definition of the alen was set to 2 Rhine feet. Rømer later discovered that differing standards for the Rhine foot existed, and in 1698 an iron Copenhagen standard was made. A pendulum definition for the foot was introduced in 1820, and changed in 1835. The metric system was introduced in 1907.

Length

• mil – Danish mile. Towards the end of the 17th century, Ole Rømer connected the mile to the circumference of the earth, and defined it as 12000 alen. This definition was adopted in 1816 as the Prussian Meile. The coordinated definition from 1835 was 7.532 km. Earlier, there were many variants, the most commonplace the Sjællandsk miil of 17600 fod or 11.130 km.
• palme – Palm, for circumference, 8.86 cm
• alen – Forearm, 2 fod
• fod – Defined as a Rheinfuss 31.407 cm from 1683, before that 31.41 cm with variations.
• kvarter – Quarter, 1 / 4 alen
• tomme – Inch, 1 / 12 fod
• linie – Line, 1 / 12 tomme
• skrupel – Scruple, 1 / 12 linie

Volume

• potte – Pot, from 1863 1 / 32 fot³
• smørtønde – Barrel of butter, from 1683 136 potter
• korntønde – Barrel of corn, from 1683 144 potter

Weight

• pund – Pound, from 1863 the weight of 1 / 62 fot³ of water, 499.75 g

Miscellaneous

• dusin – 12
• snes – 20
• gross – 144

Norwegian system

Before 1541, there were no common definition for length measures in Norway, and local variants flourished. In 1541, an alen in Denmark and Norway was defined by law to be the Sjælland alen. Subsequently, the alen was defined by law as 2 Rhine feet from 1683. From 1824, the basic unit was defined as a fot being derived from astronomy as the length of a one second pendulum times 12/38 at a latitude of 45°. The metric system was introduced in 1887.

Length

• alen – Forearm, 62.748 cm from 1824, 62.75 cm from 1683, 63.26 cm from 1541. Before that, local variants.
• favn – Fathom (pl. favner), 1.882 m.
• fjerdingsvei – Quarter mile, alt. fjerding, 1/4 mil, i.e. 2.82375 km.
• fot – Foot, 1/2 alen. From 1824, 31.374 cm.
• kvarter – Quarter, 1/4 alen.
• linje – Line, 1/12 tomme or approx. 2.18 mm
• lås – 28.2 m
• landmil – Old land-mile, 11.824 km.
• mil – Norwegian mile, spelled miil prior to 1862, 18000 alen or 11.295 km. Before 1683, a mil was defined as 17600 alen or 11.13 km. The unit survives to this day, but in a metric 10 km adaptation
• rast –Lit. "rest", the old name of the mil. A suitable distance between rests when walking. Believed to be approx. 9 km before 1541.
• steinkast – Stones throw, perhaps 25 favner, used to this day as a very approximate measure.
• stang – Rod, 5 alen or 3.1375 m
• tomme – Thumb (inch), 1/12 fot, approx. 2.61 cm. This unit was commonly used for measuring timber until the 1970s. Nowadays, the word refers invariably to the Imperial inch, 2.54 cm.
• skrupel – Scruple, 1/12 linje or approx. 0.18 mm.

Area

• mål – 100 kvadrat rode, 984 m². The unit survives to this day, but in a metric 1000 m² adaptation.
• kvadrat rode – Square stang, 9.84 m²
• tønneland – "Barrel of land", 4 mål

Volume

• favn – 1 alen by 1 favn by 1 favn, 2.232 m³, used for measuring firewood to this day.
• skjeppe – 1/8 tønne, i.e. 17.4 l.
• tønne – Barrel, 139.2 l.

Weight

• bismerpund – 12 pund, 5.9808 kg
• laup – Used for butter, 17.93 kg (approx. 16.2 l). 1 laup is 3 pund or 4 spann or 72 merker.
• merke – From Roman pound, (pl. merker), 249.4 g, 218.7 g before 1683.
• ort – 0.9735 g
• pund – Pound, alt. skålpund, 2 merker 0.4984 kg, was 0.46665 kg before 1683
• skippund – Ships pound, 159.488 kg. Was defined as 151.16 kg in 1270.
• spann – Same as laup
• vette – 28.8 mark or 6.2985 kg.
• våg – 1/8 skippund, 17.9424 kg.

Nautical

• favn – Fathom (pl. favner), 3 alen, 1.88 m
• kabellengde – Cable length, 100 favner, 185.2 m
• kvartmil – Quarter mile, 10 kabellengder, 1852 m
• sjømil – Sea mile, 4 kvartmil, 7408 m, defined as 1/15 Equatorial degree.

Monetary

• ort – See riksdaler and speciedaler.
• riksdaler - Until 1813, Norwegian thaler. 1 riksdaler is 4 ort or 6 mark or 96 skilling.
• skilling – Shilling, see riksdaler and speciedaler.
• speciedaler – Since 1816. 1 speciedaler is 5 ort or 120 skilling. From 1876, 1 speciedaler is 4 kroner (Norwegian crown, NOK).

Miscellaneous

• tylft – 12, also dusin
• snes – 20
• stort hundre – Large hundred, 120
• gross – 144

Swedish system

In Sweden, a common system for weights and measures was introduced by law in 1665. Before that, there were a number of local variants. The system was slightly revised in 1735. In 1855, a decimal reform was instuted that defined a new Swedish inch as 1/10 foot. It did not last long, because the metric system was subsequently introduced in 1889. Up to the middle of the 19th century there was a death penalty for falsifying weights or measures.

Length

• aln – Forearm (pl. alnar). After 1863, 59.37 cm. Before that, from 1605, 59.38 cm as defined by king Carl IX of Sweden in Norrköping 1604 based on the Rydaholmsalnen.
• famn – Fathom, 3 alnar.
• kvarter – Quarter, 1 / 4 aln
• fot – Foot, 1/2 aln. Before 1863, the Stockholm fot was the commonly accepted unit, at 29.69 cm.
• linje – Line, after 1863 1/10 tum, 2.96 mm. Before that, 1/12 tum or 2.06 cm.
• mil – Mile, also lantmil. From 1699, defined as a unity mile of 18000 aln or 10.69 km. The unufied mile was meant to define the suitable distance between inns.
• nymil – New mile from 1889, 10 km exactly. Commonly used to this day, normally referred to as mil.
• kyndemil – The distance a torch will last, approx 16 km
• skogsmil – Also rast, distance between rests in the woods, approx 5 km.
• fjärdingsväg – 1 / 4 mil
• stenkast – Stone's throw, approx 50 m.
• ref – 160 fot, for land measurement, was 100 fot after 1855.
• stång – 16 fot, for land measurement
• tum – Thumb (inch), after 1863 1/10 fot, 2.96 cm. Before that, 1/12 fot or 2.474 cm.

Area

• kannaland – 1000 fot², or 88.15 m²
• kappland – 154.3 m².
• spannland – 16 kappland
• tunneland – 2 spannland
• kvadratmil – Square mil, 36 million square favnar, from 1739.

Volume

• pot – Pot (pl pottor), 0.966 l
• tunna – 2 spann
• ankare – Liquid measure, 39.26 l
• ohm – Also åm, 155 pottor
• storfavn – 3.77 m³
• kubikkfavn – 5.85 m³

Weight

• skeppspund – Ships pound, 20 lispund or 170.03 kg.
• bismerpund – 12 skålpund, 5.101 kg.
• lispund – 20 skålpund
• skålpund – Pound, 0.42507 kg
• mark – 1 / 2 skålpund or 212.5 g. Used from the Viking era, when it was approx 203 g.
• ort – 4.2508 g

Nautical

• kabellãngd – Initially 100 famnar or 178 m, Later, a distansminut or 1 / 10 nautical mile.
• kvartmil – Quarter mile, 1852 m, identical to nautical mile.
• sjõmil – Sea mile, 4 kvartmil, 7408 m

Monetary

• daler – From 1534, Swedish thaler. From 1873, replaced by the krona (Swedish crown, SEK).
• riksdaler – From 1624, 1 1/2 daler, from 1681 2 daler, from 1715 3 daler, from 1776 6 daler
• skilling – From 1776, 1 / 48 riksdaler
• mark – From 1534, 1 / 3 daler.From 1604, 1 / 4 daler.
• õre – From 1534, 1 / 8 mark. Subsequently replaced by the skilling, but from 1855 reintroduced as 1 / 100 riksdaler.

Finnish system

In Finland, approximate measures derived from body parts and were used for a long time, some being later standardised for the purpose of commerce. Some Swedish, and later some Russian units have also been used.

• vaaksa – The distance between the tips of little finger and thumb, when the fingers are fully extended.
• kyynärä – (c. 60 cm) The distance from the elbow to the fingertips.
• syli – Fathom, (c. 180 cm) the distance between the fingertips of both hands when the arms are raised horizontally on the sides.
• virsta – 2672 m (Swedish) 1068.84 m (Russian)
• peninkulma – (c. 10 km) The distance a barking dog can be heard in still air.
• poronkusema – (c. 7.5 km) The distance a reindeer walks between two spots it urinates on. This unit originates from Lapland.
• leiviskä – (8.5004 kg)
• kappa – (5.4961 l) Still in use at market places to measure potatoes.
• tynnyrinala – (4936.5 m²) The area (of field) that could be sown with one barrel of grain.
• kannu – (2,6172 l)
• kortteli – Used for both length (14.845 cm) and volume (3.2715 dl).

See also

• Weights and measures

References

• Measure for Measure, Richard Young and Thomas Glover, ISBN 1-889796-00-X.
• Masse und Gewichte, Marvin A. Powell
• The Civilisation of Ancient Egypt, Paul Johnson
• The Weights and Measures of England, R. A. Connor
• World Weights and Measures. Handbook for Statisticians, UN Department of Economic and Social Affairs
• Lexikon der Münzen, Maße, Gewichte, Zählarten und Zeitgrößen aller Länder der Erde, Richard Klimpert, 1896
• Grand dictionnaire universel du XIXe siècle, Pierre Larousse, 1874
• De gamle danske længdeenheder, N.E. Nørlund, 1944
• Mål og vægt, Poul Rasmussen, 1967.
• Med mått mätt - Svenska och utländska mått genom tiderna, Albert Carlsson, ISBN 91-36-03157-7.