Inch
Encyclopedia
An inch is the name of a unit
Units of measurement
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...

of length
Length
In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...

in a number of different systems, including Imperial unit
Imperial unit
The system of imperial units or the imperial system is the system of units first defined in the British Weights and Measures Act of 1824, which was later refined and reduced. The system came into official use across the British Empire...

s, and United States customary units
United States customary units
United States customary units are a system of measurements commonly used in the United States. Many U.S. units are virtually identical to their imperial counterparts, but the U.S. customary system developed from English units used in the British Empire before the system of imperial units was...

. There are 36 inches in a yard
Yard
A yard is a unit of length in several different systems including English units, Imperial units and United States customary units. It is equal to 3 feet or 36 inches...

and 12 inches in a foot. Corresponding units of area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...

and volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

are the square inch
Square inch
A square inch is a unit of area, equal to the area of a square with sides of one inch. The following symbols are used to denote square inches:*square in*sq inches, sq inch, sq in*inches/-2, inch/-2, in/-2...

and the cubic inch
Cubic inch
The cubic inch is a unit of measurement for volume in the Imperial units and United States customary units systems. It is the volume of a cube with each of its 3 sides being one inch long....

.

## Usage

The inch is one of the most common units of length in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...

, and is also widely used in the United Kingdom
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...

Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...

, despite the introduction of metric to the latter two in the 1960s and 1970s, respectively. The inch is sometimes used informally in other Commonwealth nations, such as Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...

.

## International inch

From July 1, 1959, the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...

and countries of the British Commonwealth
Commonwealth of Nations
The Commonwealth of Nations, normally referred to as the Commonwealth and formerly known as the British Commonwealth, is an intergovernmental organisation of fifty-four independent member states...

defined the length of the international yard
Yard
A yard is a unit of length in several different systems including English units, Imperial units and United States customary units. It is equal to 3 feet or 36 inches...

to be exactly 0.9144 metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

s. Consequently, the international inch is defined as exactly 25.4 millimetre
Millimetre
The millimetre is a unit of length in the metric system, equal to one thousandth of a metre, which is the SI base unit of length....

s. This creates a slight difference between the international units and American surveyor's units which are described in the article on the foot.

The international standard symbol for inch is in (see ISO 31-1
ISO 31-1
ISO 31-1 is the part of international standard ISO 31 that defines names and symbols for quantities and units related to space and time.Its definitions include:Annex A of ISO 31-1 lists units of space and time based on the foot, pound and second...

, Annex A). In some cases, the inch is denoted by a double prime
Prime (symbol)
The prime symbol , double prime symbol , and triple prime symbol , etc., are used to designate several different units, and for various other purposes in mathematics, the sciences and linguistics...

, which is often approximated by double quotes
Quotation mark
Quotation marks or inverted commas are punctuation marks at the beginning and end of a quotation, direct speech, literal title or name. Quotation marks can also be used to indicate a different meaning of a word or phrase than the one typically associated with it and are often used to express irony...

, and the foot by a prime
Prime (symbol)
The prime symbol , double prime symbol , and triple prime symbol , etc., are used to designate several different units, and for various other purposes in mathematics, the sciences and linguistics...

, which is often approximated by an apostrophe.

## Equivalence to other units of length

1 international inch is equal to:
• 1,000 thou
Thou (unit of length)
A thou also known as a mil or point, is the verbalized abbreviation for "thousandth of an inch." It is a unit of length equal to 0.001 inch....

(also known as mil) (1 mil = 1 thou = 0.001 inches)
• 1,000,000 microinches (1 μin is one millionth of an inch.)

• ≈ 0.02778 yard
Yard
A yard is a unit of length in several different systems including English units, Imperial units and United States customary units. It is equal to 3 feet or 36 inches...

s (1 yard is equal to 36 inches.)
• 2.54 centimetre
Centimetre
A centimetre is a unit of length in the metric system, equal to one hundredth of a metre, which is the SI base unit of length. Centi is the SI prefix for a factor of . Hence a centimetre can be written as or — meaning or respectively...

s (1 centimetre ≈ 0.3937 international inches.)

## Historical origin

The origin of the inch is disputed. Historically, different parts of the world (even different cities within the same country) and at different points in time, used the word to refer to similar but different standard lengths.

The English word inch comes from Latin uncia
Uncia
Uncia can refer to:* Uncia , an ancient Roman bronze coin* Uncia , an ancient Roman unit of length* Uncia , a Bolivian tin mine...

meaning "one twelfth part" (in this case, one twelfth of a foot); the word ounce
Ounce
The ounce is a unit of mass with several definitions, the most commonly used of which are equal to approximately 28 grams. The ounce is used in a number of different systems, including various systems of mass that form part of the imperial and United States customary systems...

(one twelfth of a troy pound) has the same origin. The vowel change from u to i is umlaut
Germanic umlaut
In linguistics, umlaut is a process whereby a vowel is pronounced more like a following vowel or semivowel. The term umlaut was originally coined and is used principally in connection with the study of the Germanic languages...

; the consonant change from c to ch is palatalization
Palatalization
In linguistics, palatalization , also palatization, may refer to two different processes by which a sound, usually a consonant, comes to be produced with the tongue in a position in the mouth near the palate....

(see Old English phonology).

In some other languages, the word for "inch" is similar to or the same as the word for "thumb"; for example, inch/thumb; inch/thumb; inch, pulgar thumb; inch, polegar thumb; inch, tumme thumb; inch/thumb; inch, anguli finger; inch/thumb; inch/thumb, Danish
Danish language
Danish is a North Germanic language spoken by around six million people, principally in the country of Denmark. It is also spoken by 50,000 Germans of Danish ethnicity in the northern parts of Schleswig-Holstein, Germany, where it holds the status of minority language...

and / tommer inch/inches and tommel thumb.
Given the etymology of the word "inch", it would seem that the inch is a unit derived from the Foot unit, but this was probably only so in Latin and in Roman times. In English, there are records of fairly precise definitions for the size of an inch (whereas the definitions for the size of a foot are probably anecdotal), so it seems that the foot was then defined as 12 times this length. For example, the old English ynche was defined (by King David I of Scotland in about 1150) as the width of an average man's thumb at the base of the nail, even including the requirement to calculate the average of a small, a medium, and a large man's measures. To account for the much larger length later called an inch, there are also attempts to link it to the distance between the tip of the thumb and the first joint of the thumb, but this may be speculation.

The earliest known reference to the inch in England is from the Laws of Æthelberht dating to the early 7th century. Paragraph LXVII sets out the fine for wounds of various depths: one inch, one shilling, two inches, two shillings, etc. "Gif man þeoh þurhstingð, stice ghwilve vi scillingas. Gife ofer ynce, scilling. æt twam yncum, twegen. ofer þry, iii scill."

An Anglo-Saxon unit of length was the barleycorn. After 1066, 1 inch was equal to 3 barleycorn, which continued to be its legal definition for several centuries, with the barleycorn being the base unit. One of the earliest such definitions is that of 1324, where the legal definition of the inch was set out in a statute of Edward II of England
Edward II of England
Edward II , called Edward of Caernarfon, was King of England from 1307 until he was deposed by his wife Isabella in January 1327. He was the sixth Plantagenet king, in a line that began with the reign of Henry II...

, defining it as "three grains of barley
Barley
Barley is a major cereal grain, a member of the grass family. It serves as a major animal fodder, as a base malt for beer and certain distilled beverages, and as a component of various health foods...

, dry and round, placed end to end, lengthwise".

Similar definitions are recorded in both English and Welsh medieval law tracts. One, dating from the first half of the 10th century, is contained in the Laws of Hywel Dda
Hywel Dda
Hywel Dda , was the well-thought-of king of Deheubarth in south-west Wales, who eventually came to rule Wales from Prestatyn to Pembroke. As a descendant of Rhodri Mawr, through his father Cadell, Hywel was a member of the Dinefwr branch of the dynasty and is also named Hywel ap Cadell...

which superseded those of Dyvnwal, an even earlier definition of the inch in Wales. Both definitions, as recorded in Ancient Laws and Institutes of Wales (vol i., pp. 184,187,189), are that "three lengths of a barleycorn is the inch".

Charles Butler, a mathematics teacher at Cheam School
Cheam School
Cheam School is a preparatory school in Headley in the civil parish of Ashford Hill with Headley in the English county of Hampshire. It was founded in 1645 by the Reverend George Aldrich in Cheam, Surrey and has been in operation ever since....

, in 1814 recorded the old legal definition of the inch to be "three grains of sound ripe barley being taken out the middle of the ear, well dried, and laid end to end in a row", and placed the barleycorn, not the inch, as the base unit of the English Long Measure system, from which all other units were derived. John Bouvier
John Bouvier
John Bouvier , American jurist and legal lexicographer, was born in Codognan, France.In 1802 his family, who were Quakers , emigrated to America and settled in Philadelphia. In 1808, he began a printing business, and in 1810, he wed Elizabeth Widdifield, with whom he had one daughter, Hannah Mary...

similarly recorded in his 1843 law dictionary that the barleycorn was the fundamental measure. Butler observed, however, that "[a]s the length of the barley-corn cannot be fixed, so the inch according to this method will be uncertain", noting that a standard inch measure was now (by his time) kept in the Exchequer chamber, Guildhall, and that was the legal definition of the inch. This was a point also made by George Long in his 1842 Penny Cyclopædia
Penny Cyclopaedia
The Penny Cyclopædia of the Society for the Diffusion of Useful Knowledge was a multi-volume encyclopedia edited by George Long and published by Charles Knight alongside the Penny Magazine. The volumes were published from 1833 to 1843.-External links:...

, observing that standard measures had since surpassed the barleycorn definition of the inch, and that to recover the inch measure from its original definition, in the event that the standard measure were destroyed, would involve the measurement of large numbers of barleycorns and taking their average lengths. He noted that this process would not perfectly recover the standard, since it might introduce errors of anywhere between one hundredth and one tenth of an inch in the definition of a yard.

Before the adoption of the international inch (see above), the United Kingdom
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...

and most countries of the British Commonwealth
Commonwealth of Nations
The Commonwealth of Nations, normally referred to as the Commonwealth and formerly known as the British Commonwealth, is an intergovernmental organisation of fifty-four independent member states...

defined the inch in terms of the Imperial Standard Yard. But Canada
Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...

had its own, different, definition of the inch, defined in terms of metric units
Metric system
The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...

. The Canadian inch was defined to be equal to 25.4 millimetre
Millimetre
The millimetre is a unit of length in the metric system, equal to one thousandth of a metre, which is the SI base unit of length....

s, the amount later accepted as the international inch.

## Metric or decimal inch

A metric inch (25 mm instead of 25.4 mm) was the equivalent of an inch under a former proposal for the metrification and unification of the English system of measures.

In Sweden
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....

, between 1855 to 1863, the existing Swedish "working inch" of ≈24.74 mm was replaced by a "decimal inch" of ≈29.69 mm which was one tenth of the Swedish foot. Proponents argued that a decimal system simplifies calculations. However, having two different Swedish inch measures (and the English inch on top of that) proved to be complicated. So in a transition period between 1878 and 1889 the metric units were introduced as the overall standard measures. However, the various inches survived some time in building and construction trades.

## Scottish inch

A Scottish inch
Inch
An inch is the name of a unit of length in a number of different systems, including Imperial units, and United States customary units. There are 36 inches in a yard and 12 inches in a foot...

was a Scottish measurement of length. It equals 1/12 ft in Scottish measures
Obsolete Scottish units of measurement
Scotland had a distinct system of measures and weights until at least the late 18th century, based on the ell as a unit of length, the stone as a unit of mass and the boll and the firlot as units of dry measure...

, and 1.0016 inches in imperial units (about 1.0016 inches (2.5441 cm)). It was used in the popular expression , in English "Give him an inch and he'll take an ell", first published as "For when I gave you an inch, you tooke an ell," by John Heywood in 1546. (The ell, equal to 37 inches or about 94 cm, was in use in England until 1824.) A Scottish square inch was equivalent to 1.0256 imperial square inches and 6.4516 square centimetres.

Scottish measures were made obsolete, and English measurements made standard in Scotland, by act of parliament in 1824.

• Anthropic units
Anthropic units
Anthropic units are units of measurement which explicitly arose from human physiology or behavior. Some were derived directly from the dimensions of the human body, and as such, are commonly referred to as anthropomorphic...

• English units
• Gry
Gry (disambiguation)
Gry may refer to:* -gry, a word puzzle about words ending in "gry"* Gry, an obsolete unit of measurement equal to 1/10 of a line and 1/120 of an inch invented by the philosopher John Locke....

• Guz
Guz
A guz , also written as gaz, guzz, guj or gudge, is an obsolete unit of length used in parts of Asia. It is a regionally variable measurement, corresponding culturally to the yard in that it was often used for measuring textiles...

• Imperial unit
Imperial unit
The system of imperial units or the imperial system is the system of units first defined in the British Weights and Measures Act of 1824, which was later refined and reduced. The system came into official use across the British Empire...

• Pyramid inch
Pyramid inch
The pyramid inch is a unit of measure claimed by pyramidologists to have been used in ancient times. Supposedly it was one twenty-fifth of a "sacred cubit", 1.00106 imperial inches, or 2.5426924 centimetres.-History:...

• United States customary units
United States customary units
United States customary units are a system of measurements commonly used in the United States. Many U.S. units are virtually identical to their imperial counterparts, but the U.S. customary system developed from English units used in the British Empire before the system of imperial units was...