Customary unit of length
The
foot
(
pl.
feet
; standard symbol:
ft
)
[1]
[2]
is a
unit
of
length
in the
British imperial
and
United States customary
systems of
measurement
. The
prime symbol
,
′
, is commonly used to represent the foot.
[3]
In both customary and imperial units, one foot comprises 12
inches
, and one
yard
comprises three feet. Since
an international agreement in 1959
, the foot is defined as equal to exactly 0.3048 meters.
Historically, the "foot" was a part of many local systems of units, including the
Greek
,
Roman
,
Chinese
,
French
, and
English
systems. It varied in length from country to country, from city to city, and sometimes from trade to trade. Its length was usually between 250 mm and 335 mm and was generally, but not always, subdivided into 12 inches or 16
digits
.
The United States is the only industrialized country that uses the (international) foot in preference to the meter in its commercial, engineering, and standards activities.
[4]
The foot is legally recognized in the United Kingdom; road distance signs
must
use imperial units (however, distances on road signs are always marked in miles or yards, not feet; bridge clearances are given in meters as well as feet and inches), while its usage is widespread among the British public as a measurement of height.
[5]
[6]
The foot is recognized as an alternative expression of length in Canada.
[7]
Both the UK and Canada have partially
metricated
their units of measurement. The measurement of
altitude
in international
aviation
(the
flight level
unit) is one of the few areas where the foot is used outside the English-speaking world.
Historical origin
[
edit
]
Historically, the human body has been used to provide the basis for units of length.
[8]
The foot of an adult European-American male is typically about 15.3% of his height,
[9]
giving a person of 175 cm (5 ft 9 in) a foot-length of about 268 mm (10.6 in), on average.
Archaeologists believe that, in the past, the people of
Egypt
,
India
, and
Mesopotamia
preferred the
cubit
, while the people of
Rome
,
Greece
, and
China
preferred the foot. Under the Harappan linear measures, Indus cities during the Bronze Age used a foot of 13.2 inches (335 mm) and a cubit of 20.8 inches (528 mm).
[10]
The
Egyptian
equivalent of the foot?a measure of four palms or 16 digits?was known as the
djeser
and has been reconstructed as about 30 cm (11.8 in).
The Greek foot (
πο??
,
pous
) had a length of
1
/
600
of a
stadion
,
[11]
one stadion being about 181.2 m (594 ft);
[12]
therefore a foot was, at the time, about 302 mm (11.9 in). Its exact size varied from city to city and could range between 270 mm (10.6 in) and 350 mm (13.8 in), but lengths used for temple construction appear to have been about 295 mm (11.6 in) to 325 mm (12.8 in); the former was close to the size of the Roman foot.
The standard
Roman foot
(
pes
) was normally about 295.7 mm (11.6 in) (97% of today's measurement),
[13]
but in some provinces, particularly
Germania Inferior
, the so-called
pes Drusianus
(foot of
Nero Claudius Drusus
) was sometimes used, with a length of about 334 mm (13.1 in). (In reality, this foot predated Drusus.)
[14]
[15]
Originally both the Greeks and the Romans subdivided the foot into 16
digits
, but in later years, the Romans also subdivided the foot into 12
unciae
(from which both the English words "inch" and "
ounce
" are derived).
After the fall of the Roman Empire, some Roman traditions were continued but others fell into disuse. In AD 790
Charlemagne
attempted to reform the units of measure in his domains. His units of length were based on the
toise
and in particular the
toise de l'Ecritoire
, the distance between the fingertips of the outstretched arms of a man.
[16]
The
toise
has 6
pieds
(feet) each of 326.6 mm (12.9 in).
He was unsuccessful in introducing a standard unit of length throughout his realm: an analysis of the measurements of
Charlieu Abbey
shows that during the 9th century the Roman foot of 296.1 mm (11.66 in) was used; when it was rebuilt in the 10th century, a foot of about 320 mm (12.6 in)
[Note 1]
was used. At the same time, monastic buildings used the Carolingian foot of 340 mm (13.4 in).
[Note 1]
[17]
The procedure for verification of the foot as described in the 16th century posthumously published work by
Jacob Kobel
in his book
Geometrei. Von kunstlichem Feldmessen und absehen
is:
[18]
[19]
Stand at the door of a church on a Sunday and bid 16 men to stop, tall ones and small ones, as they happen to pass out when the service is finished; then make them put their left feet one behind the other, and the length thus obtained shall be a right and lawful
rood
to measure and survey the land with, and the 16th part of it shall be the right and lawful foot.
England
[
edit
]
The
Neolithic
long foot
, first proposed by archeologists
Mike Parker Pearson
and Andrew Chamberlain, is based upon calculations from surveys of
Phase 1 elements at Stonehenge
. They found that the underlying diameters of the stone circles had been consistently laid out using multiples of a base unit amounting to 30
long feet
, which they calculated to be 1.056 of a modern
international foot
(thus 12.672 inches or 0.3219 m). Furthermore, this unit is identifiable in the dimensions of some stone
lintels
at the site and in the diameter of the "southern circle" at nearby
Durrington Walls
. Evidence that this unit was in widespread use across southern Britain is available from the
Folkton Drums
from
Yorkshire
(
neolithic
artifacts, made from chalk, with circumferences that exactly divide as
integers
into ten long feet) and a similar object, the
Lavant drum
, excavated at
Lavant
, Sussex, again with a circumference divisible as a whole number into ten long feet.
[20]
The measures of
Iron Age Britain
are uncertain and proposed reconstructions such as the
Megalithic Yard
are controversial. Later
Welsh legend
credited
Dyfnwal Moelmud
with the establishment of
their units
, including a foot of 9 inches. The Belgic or North German foot of 335 mm (13.2 in) was introduced to England either by the
Belgic Celts
during their invasions prior to the Romans or by the
Anglo-Saxons
in the 5th and 6th century.
Roman units
were introduced following
their invasion
in AD 43. Following the
Roman withdrawal
and
Saxon invasions
, the Roman foot continued to be used in the construction crafts while the Belgic foot was used for land measurement. Both the Welsh and Belgic feet seem to have been based on multiples of the
barleycorn
, but by as early as 950 the English kings seem to have (ineffectually) ordered measures to be based upon an iron yardstick at
Winchester
and then
London
.
Henry I
was said to have ordered a new standard to be based upon the length of his own arm and, by the
c.
1300
Act concerning the
Composition of Yards and Perches
[21]
traditionally credited to
Edward I
or
II
, the statute foot was a different measure, exactly
10
/
11
of the old (Belgic) foot. The
barleycorn
,
inch
,
ell
, and
yard
were likewise shrunk, while
rods
and
furlongs
remained the same.
[22]
The ambiguity over the state of the
mile
was resolved by the 1593
Act against Converting of Great Houses into Several Tenements and for Restraint of Inmates and Inclosures in and near about the City of London and Westminster
, which codified the
statute mile
as comprising 5,280 feet. The differences among the various physical standard yards around the world, revealed by increasingly powerful
microscopes
, eventually led to the 1959 adoption of the
international foot
defined in terms of the meter.
Definition
[
edit
]
The
international yard and pound
agreement of July 1959 defined the length of the international yard in the United States and countries of the
Commonwealth of Nations
as exactly 0.9144
meters
. Consequently, since a foot is one third of a yard, the international foot is defined to be equal to exactly 0.3048 meters. This was 2
ppm
shorter than the previous US definition and 1.7 ppm longer than the previous British definition.
[23]
The 1959 agreement concluded a series of step-by-step events, set off in particular by the
British Standards Institution
's adoption of a scientific standard inch of 25.4
millimeters
in 1930.
Symbol
[
edit
]
The IEEE standard symbol for a foot is "ft".
[1]
In some cases, the foot is denoted by a
prime
, often approximated by an
apostrophe
, and the inch by a double prime; for example, 2
feet 4 inches is sometimes denoted 2′
4″.
[24]
Imperial units
[
edit
]
In
Imperial units
, the foot was defined as
1
/
3
yard, with the yard being realized as a physical standard (separate from the standard meter). The yard standards of the different
Commonwealth
countries were periodically compared with one another.
[25]
The value of the United Kingdom primary standard of the yard was determined in terms of the meter by the
National Physical Laboratory
in 1964 to be
0.914
3969
m
,
[26]
implying a pre-1959 UK foot of
0.304
7990
m
.
The UK adopted the international yard for all purposes through the
Weights and Measures Act 1963
, effective January 1, 1964.
[27]
When the international foot was defined in 1959, a great deal of survey data was already available based on the former definitions, especially in the United States and in
India
. The small difference between the survey foot and the international foot would not be detectable on a survey of a small parcel, but becomes significant for mapping, or when the
state plane coordinate system
(SPCS) is used in the US, because the origin of the system may be hundreds of thousands of feet (hundreds of miles) from the point of interest. Hence the previous definitions continued to be used for surveying in the United States and India for many years, and are denoted
survey feet
to distinguish them from the international foot. The United Kingdom was unaffected by this problem, as the
retriangulation of Great Britain
(1936?62) had been done in meters.
In the United States, the foot was defined as 12 inches, with the inch being defined by the
Mendenhall Order
of 1893 via 39.37 inches = 1 m (making a US foot exactly
1200
/
3937
meters, approximately
0.304
800
61
m
).
[28]
[29]
On December 31, 2022, the
National Institute of Standards and Technology
, the
National Geodetic Survey
, and the
United States Department of Commerce
deprecated use of the US survey foot and recommended conversion to either the meter or the
international foot
(0.3048 m).
[30]
[31]
[28]
However, the historic relevance of the US survey foot persists, as the
Federal Register
notes:
[32]
The date of December 31, 2022, was selected to accompany the modernization of the National Spatial Reference System (NSRS) by
NOAA
's National Geodetic Survey (NGS). The reason for associating the deprecation of the U.S. survey foot with the modernization of the NSRS is that the biggest impact of the uniform adoption of the international foot will be for users of the NSRS, due to very large coordinate values currently given in U.S. survey feet in many areas of the U.S. Impacts related to the change to international feet will be minimized if a transition occurs concurrently with others [
sic
] changes in the NSRS. ...
The difference in timelines will have no effect on users of the existing NSRS (National Spatial Reference System), because NGS (
NOAA
's National Geodetic Survey)
will continue to support the U.S. survey foot for components of the NSRS where it is used now and in the past
[emphasis added]. In other words, to minimize disruption in the use of U.S. survey foot for existing NSRS coordinate systems, the change will apply only to the modernized NSRS.
State legislation is also important for determining the conversion factor to be used for everyday land surveying and real estate transactions, although the difference (two
parts per million
) is of no practical significance given the precision of normal surveying measurements over short distances (usually much less than a mile). Out of 50 states and six other jurisdictions, 40 have legislated that surveying measures should be based on the US survey foot, six have legislated that they be made on the basis of the international foot, and ten have not specified.
[33]
The Indian survey foot is defined as exactly
0.304
7996
m
,
[34]
presumably derived from a measurement of the previous Indian standard of the yard. The current National Topographic Database of the
Survey of India
is based on the metric
WGS-84
datum
,
[35]
which is also used by the
Global Positioning System
.
Historical use
[
edit
]
An
ISO 2848
measure of 3 basic modules (30 cm) is called a "
metric foot
",
[
citation needed
]
but there were earlier distinct definitions of a metric foot during
metrication
in France and Germany.
France
[
edit
]
In 1799 the meter became the official unit of length in
France
. This was not fully enforced, and in 1812
Napoleon
introduced the system of
mesures usuelles
which restored the traditional French measurements in the retail trade, but redefined them in terms of metric units. The foot, or
pied metrique
, was defined as one third of a meter. This unit continued in use until 1837.
[37]
Germany
[
edit
]
In southwestern Germany in 1806, the
Confederation of the Rhine
was founded and three different
reformed feet
were defined, all of which were based on the metric system:
[38]
- In
Hesse
, the
Fuß
(foot) was redefined as 25 cm.
- In
Baden
, the
Fuß
was redefined as 30 cm.
- In the
Palatinate
, the
Fuß
was redefined as being
33
+
1
/
3
cm (as in France).
Other obsolete feet
[
edit
]
Prior to the introduction of the metric system, many European cities and countries used the foot, but it varied considerably in length: the
voet
in
Ypres
, Belgium, was 273.8 millimeters (10.78
in) while the
piede
in Venice was 347.73 millimeters (13.690
in). Lists of conversion factors between the various units of measure were given in many European reference works including:
Many of these standards were peculiar to a particular city, especially in Germany (which, before
German unification
in 1871, consisted of many kingdoms, principalities, free cities and so on). In many cases the length of the unit was not uniquely fixed: for example, the English foot was stated as 11
pouces
2.6
lignes
(
French inches and lines
) by
Picard
, 11
pouces
3.11
lignes
by
Maskelyne
, and 11
pouces
3
lignes
by
D'Alembert
.
[46]
Most of the various feet in this list ceased to be used when the countries adopted the metric system. The Netherlands and modern Belgium adopted the metric system in 1817, having used the
mesures usuelles
under Napoleon
[47]
and the newly formed
German Empire
adopted the metric system in 1871.
[48]
The
palm
(typically 200?280 mm) was used in many Mediterranean cities instead of the foot. Horace Doursther, whose reference was published
[
clarification needed
]
in Belgium which had the smallest foot measurements, grouped both units together, while J. F. G. Palaiseau devoted three chapters to units of length: one for linear measures (palms and feet); one for cloth measures (ells); and one for distances traveled (miles and leagues).
[
citation needed
]
Obsolete feet details
[
edit
]
In the table below, arbitrary cut-off points of 270 mm and 350 mm have been chosen.
[
citation needed
]
In Belgium, the words
pied
(French) and
voet
(Dutch) would have been used interchangeably.
[
citation needed
]
Notes
[
edit
]
- ^
a
b
c
d
The source document used pre-metric French units (
pied
,
pouce
and
ligne
).
- ^
The original meter was computed using pre-metric French units.
- ^
The Norwegian
fot
was defined in 1824 as the length of a (theoretical) pendulum that would have a period of
12
/
38
seconds at 45° from the equator.
- ^
Prior to 1835, the
pe
or foot was not used in Portugal; instead a palm was used. In 1835 the size of the palm was increased from 217.37 mm (according to Palaiseau) to 220 mm.
- ^
The Scots foot ceased to be legal after the
Act of Union
in 1707.
Present day uses
[
edit
]
International ISO-standard and other intermodal shipping containers
[
edit
]
International Standards Organisation
(ISO)-defined
intermodal containers
for efficient global freight/cargo shipping, were defined using feet rather than meters for their leading outside (corner) dimensions. All ISO-standard containers to this day are eight feet wide, and their outer heights and lengths are also primarily defined in, or derived from feet.
Quantities of global shipping containers are still primarily counted in
Twenty-foot Equivalent Units
, or TEUs.
Aviation
[
edit
]
Everyday global (civilian) air traffic / aviation continues to be controlled in
flight levels
(flying altitudes) separated by thousands of feet (although typically read out in hundreds ? e.g. flight level 330 actually means 33,000 feet, or about 10 kilometres in altitude).
Relation to shoe size
[
edit
]
The length of the (international) foot corresponds to a human foot with
shoe size
of 13 (UK), 14 (US male), 15.5 (US female) or 48 (EU sizing).
[58]
[
better source needed
]
Dimension
[
edit
]
In measurement, the term "linear foot" (sometimes incorrectly referred to as "lineal foot") refers to the number of feet in a length of material (such as lumber or fabric) without regard to the width; it is used to distinguish from
surface area
in
square foot
.
[59]
See also
[
edit
]
Notes
[
edit
]
- ^
a
b
The original reference was given in a round number of centimeters.
References
[
edit
]
- ^
a
b
"Recommended Unit Symbols, SI Prefixes, and Abbreviations"
(PDF)
. Retrieved
April 7,
2021
.
- ^
BS350:Part 1:1974 Conversion factors and tables Part 1. Basis of tables. Conversion factors
. British Standards Institution. 1974. pp. 5, 91.
- ^
Chicago Manual of Style
(17th ed.). University of Chicago Press. 2017. ¶ 10.66.
- ^
"Appendix G ? Weights and Measures"
.
The World Factbook
. Washington:
Central Intelligence Agency
. January 17, 2007.
Archived
from the original on February 23, 2011
. Retrieved
February 4,
2007
.
- ^
Kelly, Jon (December 21, 2011).
"Will British people ever think in metric?"
. BBC.
Archived
from the original on April 24, 2012.
- ^
Alder, Ken (2002). The Measure of all Things?The Seven-Year-Odyssey that Transformed the World. London: Abacus.
- ^
Weights and Measures Act
Archived
December 28, 2014, at the
Wayback Machine
, accessed January 2012, Act current to January 18, 2012. Basis for units of measurement 4.(1) All units of measurement used in Canada shall be determined on the basis of the International System of Units established by the General Conference of Weights and Measures. (...) Canadian units (5) The Canadian units of measurement are as set out and defined in Schedule II, and the symbols and abbreviations therefore are as added pursuant to subparagraph 6(1)(b)(ii).
- ^
Oswald Ashton Wentworth Dilke
(May 22, 1987).
Mathematics and measurement
. University of California Press. p.
23
.
ISBN
978-0-520-06072-2
. Retrieved
February 2,
2012
.
- ^
Fessler, Daniel M; Haley, Kevin J; Lal, Roshni D (January?February 2005).
"Sexual dimorphism in foot length proportionate to stature"
(PDF)
.
Annals of Human Biology
.
32
(1): 44?59.
doi
:
10.1080/03014460400027581
.
PMID
15788354
.
S2CID
194735
. Archived from
the original
(PDF)
on June 8, 2011.
- ^
Kenoyer JM (2010) "Measuring the Harappan world," in Morley I & Renfrew C (edd) The Archaeology of Measurement, 117;
"Archived copy"
(PDF)
. Archived from
the original
(PDF)
on June 26, 2015
. Retrieved
January 11,
2015
.
{{
cite web
}}
: CS1 maint: archived copy as title (
link
)
- ^
Herodotus; Rawlinson, George (May 14, 1861).
"History of Herodotus : a new English version"
. New York D. Appleton – via Internet Archive.
- ^
"Epidauros, Stadium (Building)"
.
www.perseus.tufts.edu
.
Archived
from the original on May 10, 2017.
- ^
Hosch, William L. (ed.) (2010)
The Britannica Guide to Numbers and Measurement
New York, NY: Britannica Educational Publications, 1st edition.
ISBN
978-1-61530-108-9
, p.206
- ^
Oswald Ashton Wentworth Dilke
(May 22, 1987).
Mathematics and measurement
. University of California Press. p.
26
.
ISBN
978-0-520-06072-2
. Retrieved
February 2,
2012
.
- ^
Duncan-Jones, R. P. (1980).
"Length-Units in Roman Town Planning: The Pes Monetalis and the Pes Drusianus"
.
Britannia
.
11
: 127?133.
doi
:
10.2307/525675
.
JSTOR
525675
.
S2CID
164149478
.
- ^
Russ Rowlett.
"How Many? A Dictionary of Units of Measurement"
. Center for Mathematics and Science Education,
University of North Carolina at Chapel Hill
.
Archived
from the original on December 24, 2012
. Retrieved
February 28,
2011
.
- ^
Sutherland, Elizabeth R (May 1957). "Feet and dates at Charlieu".
Journal of the Society of Architectural Historians
.
16
(2): 2?5.
doi
:
10.2307/987740
.
JSTOR
987740
.
- ^
Jacob Koebel
(1535).
Geometrei. Von kunstlichem Feldmessen und absehen
(in German).
Archived
from the original on November 16, 2011.
- ^
"Geometrey"
.
digital.slub-dresden.de
(in German). Saxon State Library
. Retrieved
February 22,
2019
.
- ^
Teather, Anne; et al. (February 8, 2019). "Getting the Measure of Stonehenge".
British Archaeology
(165): 48?51.
- ^
Great Britain (1762).
The statutes at large: from the Magna Charta, to the end of the eleventh Parliament of Great Britain, anno 1761 (continued to 1807)
. Vol. 1. Printed by J. Bentham. p. 400
. Retrieved
November 30,
2011
.
- ^
Zupko, Ronald Edward
(1977).
British Weights and Measures: A History from Antiquity to the Seventeenth Century
. University of Wisconsin Press. pp. 6, 10, 20.
ISBN
978-0-299-07340-4
.
- ^
"On what basis is one inch exactly equal to 25.4 mm? Has the imperial inch been adjusted to give this exact fit and if so when?"
.
National Physical Laboratory
. Archived from
the original
on August 7, 2012
. Retrieved
July 24,
2012
.
- ^
Chicago Manual of Style
(17th ed.). University of Chicago Press. 2017. ¶ 10.66.
- ^
See, for example,
Report on the Comparisons of the Parliamentary Copies of the Imperial Standards with the Imperial Standard Yard and the Imperial Standard Pound and with each other during the Years 1947 to 1948
(H.M.S.O., London, 1950).
Report on the Comparisons of the Parliamentary Copies of the Imperial Standards with each other during the Year 1957
(H.M.S.O., London, 1958).
- ^
Bigg, P. H.; Anderton, Pamela (March 1964).
"The United Kingdom standards of the yard in terms of the meter"
.
British Journal of Applied Physics
.
15
(3): 291?300.
Bibcode
:
1964BJAP...15..291B
.
doi
:
10.1088/0508-3443/15/3/308
. Archived from
the original
on August 3, 2012
. Retrieved
May 16,
2009
.
- ^
Thoburn v Sunderland City Council [2002] EWHC 195 (Admin) (18 February 2002)
- ^
a
b
Mitchell, Alanna (August 18, 2020).
"America Has Two Feet. It's About to Lose One of Them"
.
The New York Times
.
ISSN
0362-4331
. Retrieved
August 19,
2020
.
- ^
A. V. Astin & H. Arnold Karo (1959).
"Refinement of values for the yard and the pound"
.
Archived
August 21, 2006, at the
Wayback Machine
. Washington DC: National Bureau of Standards. Republished on National Geodetic Survey web site and the Federal Register (Doc. 59-5442, filed June 30, 1959)
- ^
"U.S. Survey Foot"
.
National Institute of Standards and Technology
. January 4, 2023
. Retrieved
April 4,
2024
.
- ^
"Measuring Unit Change Coming in 2022"
, National Geodetic Survey, June 14, 2019.
- ^
"Deprecation of the United States (U.S.) Survey Foot"
.
Federal Register
. October 5, 2020.
- ^
"State Plane Coordinate System"
, National Geodetic Survey, May 4, 2019.
- ^
Schedule to the
Standards of Weights and Measures Act, 1976
.
- ^
Survey of India
,
"National Map Policy ? 2005"
Archived
March 31, 2010, at the
Wayback Machine
.
- ^
Dr. Franz Mozhnik:
Lehrbuch des gesammten Rechnens fur die vierte Classe der Hauptschulen in den k.k. Staaten.
Im Verlage der k.k. Schulbucher Verschleiß-Administration bey St. Anna in der Johannisgasse ? Wien 1848
- ^
Denis Fevrier.
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(in French). Ministere de l'Economie, des Finances et de l'Industrie.
Archived
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. Retrieved
March 10,
2011
.
- ^
a
b
c
d
e
f
g
h
i
j
k
l
m
"Amtliche Maßeinheiten in Europa 1842"
[Official measures in Europe 1842] (in German).
Archived
from the original on July 23, 2013
. Retrieved
September 22,
2012
.
- ^
a
b
c
d
e
d'Anville, Jean Baptiste Bourguignon (1769).
Traite des mesures itineraires anciennes et modernes
[
Treatise of ancient and modern measures of distance
] (in French). Paris: de l'Imprimerie Royale
. Retrieved
October 24,
2011
.
- ^
Palaiseau, JFG (October 1816).
Metrologie universelle, ancienne et moderne: ou rapport des poids et mesures des empires, royaumes, duches et principautes des quatre parties du monde
. Bordeaux
. Retrieved
October 30,
2011
.
- ^
a
b
c
d
e
f
g
h
Jacob de Gelder (1824).
Allereerste Gronden der Cijferkunst
[
Introduction to Numeracy
] (in Dutch). 's-Gravenhage (The Hague) and Amsterdam: de Gebroeders van Cleef. pp.
163
?176
. Retrieved
March 2,
2011
.
- ^
a
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c
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"Units: L"
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.
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Area
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Volume
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Speed
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Mass
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Pressure
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Other units and measures
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Length
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Area
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Volume
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Cooking
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Wood
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Other
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Speed
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Mass
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Force
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Pressure
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Other units and measures
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