Last updated

Unit system Imperial/US units
Unit of Length
Symbolinor″ (the double prime) [1]
1 in in ...... is equal to ...
   Imperial/US units   1/36  yd
1/12  ft
    Metric (SI) units   25.4  mm
Measuring tape with inches Inch tape.jpg
Measuring tape with inches

The inch (abbreviation: in or ) is a unit of length in the (British) imperial and United States customary systems of measurement. It is equal to 136 yard or 112 of a foot. Derived from the Roman uncia ("twelfth"), the word inch is also sometimes used to translate similar units in other measurement systems, usually understood as deriving from the width of the human thumb.


Standards for the exact length of an inch have varied in the past, but since the adoption of the international yard during the 1950s and 1960s, it has been based on the metric system and defined as exactly 25.4  mm.


The English word "inch" (Old English :ynce) was an early borrowing from Latin uncia ("one-twelfth; Roman inch; Roman ounce") not present in other Germanic languages. [2] The vowel change from Latin /u/ to Old English /y/ (which became Modern English /ɪ/) is known as umlaut. The consonant change from the Latin /k/ (spelled c) to English /tʃ/ is palatalisation. Both were features of Old English phonology; see Phonological history of Old English § Palatalization and Germanic umlaut § I-mutation in Old English for more information.

"Inch" is cognate with "ounce" (Old English :ynse), whose separate pronunciation and spelling reflect its reborrowing in Middle English from Anglo-Norman unce and ounce. [3]

In many other European languages, the word for "inch" is the same as or derived from the word for "thumb", as a man's thumb is about an inch wide (and this was even sometimes used to define the inch [4] ). Examples[ citation needed ] include Catalan : polzada ("inch") and polze ("thumb"); Czech : palec ("thumb"); Danish and Norwegian : tomme ("inch") tommel ("thumb"); Dutch : duim (whence Afrikaans : duim and Russian : дюйм); French : pouce; Hungarian : hüvelyk; Italian : pollice; Portuguese : polegada ("inch") and polegar ("thumb"); ("duim"); Slovak : palec ("thumb"); Spanish : pulgada ("inch") and pulgar ("thumb"); and Swedish : tum ("inch") and tumme ("thumb").


The inch is a commonly used customary unit of length in the United States, [5] Canada, [6] [7] and the United Kingdom. [8] It is also used in Japan for electronic parts, especially display screens. In most of continental Europe, the inch is also used informally as a measure for display screens. For the United Kingdom, guidance on public sector use states that, since 1 October 1995, without time limit, the inch (along with the foot) is to be used as a primary unit for road signs and related measurements of distance (with the possible exception of clearance heights and widths) [9] and may continue to be used as a secondary or supplementary indication following a metric measurement for other purposes. [8]

Inches are commonly used to specify the diameter of vehicle wheel rims, and the corresponding inner diameter of tyres – the last number in a Car/Truck tire size such as 235/75 R16; the first two numbers give the width (normally expressed in millimetres for cars & Light trucks) and aspect ratio of the tyre (height 75% of width in this example), the R Designates a Radial Ply Construction. Wheel manufacturers commonly specify the wheel width in inches (typically 6.5, 7, 7.5, or 8 for 235/75 tire).[ citation needed ]

The international standard symbol for inch is in (see ISO 31-1, Annex A) but traditionally the inch is denoted by a double prime, which is often approximated by double quotes, and the foot by a prime, which is often approximated by an apostrophe. For example, three feet two inches can be written as 3 2. (This is akin to how the first and second "cuts" of the hour and degree are likewise indicated by prime and double prime symbols.)

Subdivisions of an inch are typically written using dyadic fractions with odd number numerators; for example, two and three eighths of an inch would be written as 2+3/8 and not as 2.375 nor as 2+6/16. However for engineering purposes fractions are commonly given to three or four places of decimals and have been for many years. [10] [11]

Measuring tape calibrated in 32nds of an inch Inch tape.jpg
Measuring tape calibrated in 32nds of an inch


1 international inch is equal to:


Mid-19th century tool for converting between different standards of the inch Inch converter.jpg
Mid-19th century tool for converting between different standards of the inch

The earliest known reference to the inch in England is from the Laws of Æthelberht dating to the early 7th century, surviving in a single manuscript, the Textus Roffensis from 1120. [14] Paragraph LXVII sets out the fine for wounds of various depths: one inch, one shilling, two inches, two shillings, etc. [lower-alpha 12]

An Anglo-Saxon unit of length was the barleycorn. After 1066, 1 inch was equal to 3 barleycorns, which continued to be its legal definition for several centuries, with the barleycorn being the base unit. [17] 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, defining it as "three grains of barley, dry and round, placed end to end, lengthwise". [17]

Similar definitions are recorded in both English and Welsh medieval law tracts. [18] One, dating from the first half of the 10th century, is contained in the Laws of Hywel Dda which superseded those of Dyfnwal, 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". [19]

King David I of Scotland in his Assize of Weights and Measures (c. 1150) is said to have defined the Scottish inch 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. [20] However, the oldest surviving manuscripts date from the early 14th century and appear to have been altered with the inclusion of newer material. [21]

In 1814, Charles Butler, a mathematics teacher at Cheam School, 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. [22] John Bouvier similarly recorded in his 1843 law dictionary that the barleycorn was the fundamental measure. [23] 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 [i.e. by 1843] kept in the Exchequer chamber, Guildhall, and that was the legal definition of the inch. [22]

This was a point also made by George Long in his 1842 Penny Cyclopædia , 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. [24]

Before the adoption of the international yard and pound, various definitions were in use. In the United Kingdom and most countries of the British Commonwealth, the inch was defined in terms of the Imperial Standard Yard. The United States adopted the conversion factor 1 metre = 39.37 inches by an act in 1866. [25] In 1893, Mendenhall ordered the physical realization of the inch to be based on the international prototype metres numbers 21 and 27, which had been received from the CGPM, together with the previously adopted conversion factor. [26]

As a result of the definitions above, the U.S. inch was effectively defined as 25.4000508 mm (with a reference temperature of 68 degrees Fahrenheit) and the UK inch at 25.399977 mm (with a reference temperature of 62 degrees Fahrenheit). When Carl Edvard Johansson started manufacturing gauge blocks in inch sizes in 1912, Johansson's compromise was to manufacture gauge blocks with a nominal size of 25.4mm, with a reference temperature of 20 degrees Celsius, accurate to within a few parts per million of both official definitions. Because Johansson's blocks were so popular, his blocks became the de facto standard for manufacturers internationally, [27] [28] with other manufacturers of gauge blocks following Johansson's definition by producing blocks designed to be equivalent to his. [29]

In 1930, the British Standards Institution adopted an inch of exactly 25.4 mm. The American Standards Association followed suit in 1933. By 1935, industry in 16 countries had adopted the "industrial inch" as it came to be known, [30] [31] effectively endorsing Johansson's pragmatic choice of conversion ratio. [27]

In 1946, the Commonwealth Science Congress recommended a yard of exactly 0.9144 metres for adoption throughout the British Commonwealth. This was adopted by Canada in 1951; [32] [33] the United States on 1 July 1959; [34] [35] [36] Australia in 1961, [37] effective 1 January 1964; [38] and the United Kingdom in 1963, [39] effective on 1 January 1964. [40] The new standards gave an inch of exactly 25.4 mm, 1.7 millionths of an inch longer than the old imperial inch and 2 millionths of an inch shorter than the old US inch. [41] [42]

US Survey inches

The United States retains the 1/39.37-metre definition for survey purposes, producing a 2 millionth part difference between standard and US survey inches. [42] This is approximately 1/8 inch per mile. In fact, 12.7 kilometres is exactly 500,000 standard inches and exactly 499,999 survey inches. This difference is substantial when doing calculations in State Plane Coordinate Systems with coordinate values in the hundreds of thousands or millions of feet.

In 2020, the U.S. NIST announced that the U.S. survey foot would become obsolescent on 1 January 2023 and be superseded by the International foot (also known as the foot) equal to 0.3048 meters exactly for all further applications. [43] and by implication, the survey inch with it.

Continental inches

Before the adoption of the metric system, several European countries had customary units whose name translates into "inch". The French pouce measured roughly 27.0 mm, at least when applied to describe the calibre of artillery pieces. The Amsterdam foot (voet) consisted of 11 Amsterdam inches (duim). The Amsterdam foot is about 8% shorter than an English foot.[ citation needed ]

Scottish inch

The now obsolete Scottish inch (Scottish Gaelic : òirleach), 1/12 of a Scottish foot, was about 1.0016 imperial inches (about 25.4406 mm). [44]

See also


  1. Used in machining.
  2. Used in machining and papermaking.
  3. Formerly used in American English but now often avoided to prevent confusion with millimeters.
  4. Used by the Australian Bureau of Meteorology for measuring rainfall until 1973 [12]
  5. 1 2 Part of John Locke's proposal for decimalization of English measures [13]
  6. Used in gunmaking.
  7. Used in botany.
  8. Used in button manufacturing.
  9. Used in typography.
  10. Used in American and British shoe sizes.
  11. Used in measuring the height of horses.
  12. Old English :Gif man þeoh þurhstingð, stice ghwilve vi scillingas. Gife ofer ynce, scilling. æt twam yncum, twegen. ofer þry, iii scill. Translation (taken from Attenborough 1922, p. 13): If a thigh is pierced right through, 6 shillings compensation shall be paid for each stab. For a stab over an inch [deep], 1 shilling; for a stab between 2 and 3 inches, 2 shillings; for a stab over 3 inches 3 shillings. [15] [16]

Related Research Articles

Acre Unit of area

The acre is a unit of land area used in the imperial and US customary systems. It is traditionally defined as the area of one chain by one furlong, which is exactly equal to 10 square chains, ​1640 of a square mile, or 43,560 square feet, and approximately 4,047 m2, or about 40% of a hectare. Based upon the International yard and pound agreement of 1959, an acre may be declared as exactly 4,046.8564224 square metres. One recognised symbol for the acre is ac, but the word "acre" is also used as the symbol.

Imperial units System of units that were implemented on 1 January 1826 in the British Empire

The imperial system of units, imperial system or imperial units is the system of units first defined in the British Weights and Measures Act 1824 and continued to be developed through a series of Weights and Measures Acts and amendments. The imperial units replaced the Winchester Standards, which were in effect from 1588 to 1825. The system came into official use across the British Empire in 1826. By the late 20th century, most nations of the former empire had officially adopted the metric system as their main system of measurement, but imperial units are still used in the United Kingdom, Canada and some other countries formerly part of the British Empire. The imperial system developed from what were first known as English units, as did the related system of United States customary units.

Litre Unit of volume

The litre or liter is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metre (m3). A cubic decimetre occupies a volume of 10 cm × 10 cm × 10 cm and is thus equal to one-thousandth of a cubic metre.

Metre SI unit of length

The metre or meter is the base unit of length in the International System of Units (SI). The SI unit symbol is m. The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 of a second. The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's circumference is approximately 40000 km. In 1799, the metre was redefined in terms of a prototype metre bar. In 1960, the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86. The current definition was adopted in 1983 and modified slightly in 2002 to clarify that the metre is a measure of proper length.

Mile Unit of length

The mile is an English unit of length of linear measure equal to 5,280 feet, or 1,760 yards, and standardised as exactly 1,609.344 metres by international agreement in 1959.

The pound or pound-mass is a unit of mass used in the imperial, United States customary and other systems of measurement. Various definitions have been used; the most common today is the international avoirdupois pound, which is legally defined as exactly 0.45359237 kilograms, and which is divided into 16 avoirdupois ounces. The international standard symbol for the avoirdupois pound is lb; an alternative symbol is lbm, #, and or ″̶.

United States customary units System of units of measurement commonly used in the United States

United States customary units are a system of measurements commonly used in the United States since it was formalized in 1832. The United States customary system developed from English units which were in use in the British Empire before the U.S. became an independent country. The United Kingdom's system of measures was overhauled in 1824 to create the imperial system, which was officially adopted in 1826, changing the definitions of some of its units. Subsequently, while many U.S. units are essentially similar to their imperial counterparts, there are significant differences between the systems.

Yard Unit of length

The yard is an English unit of length, in both the British imperial and US customary systems of measurement, that comprises 3 feet or 36 inches. Since 1959 it is by international agreement standardized as exactly 0.9144 meters. 1,760 yards is equal to 1 mile.

The foot (pl. feet), abbreviation and IEEE standard symbol: ft, is a unit of length in the British imperial and United States customary systems of measurement. The prime symbol, , is a customarily used alternative symbol. Since the International Yard and Pound Agreement of 1959, one foot is defined as 0.3048 meters exactly. In customary and imperial units, one foot comprises 12 inches and one yard comprises three feet.

The quart is an English unit of volume equal to a quarter gallon. Three kinds of quarts are currently used: the liquid quart and dry quart of the US customary system and the imperial quart of the British imperial system. All are roughly equal to one liter. It is divided into two pints or four cups. Historically, the exact size of the quart has varied with the different values of gallons over time and in reference to different commodities.

Shoe size Measurement scale indicating the fitting size of a shoe

A shoe size is an indication of the fitting size of a shoe for a person.

A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Systems of measurement in use include the International System of Units (SI), the modern form of the metric system, the British imperial system, and the United States customary system.

The following systems arose from earlier systems, and in many cases utilise parts of much older systems. For the most part they were used to varying degrees in the Middle Ages and surrounding time periods. Some of these systems found their way into later systems, such as the Imperial system and even SI. There were several types to measure that is

The link, sometimes called a Gunter’s link, is a unit of length formerly used in many English-speaking countries. In US customary units modern definition, the link is exactly ​66100 of a US survey foot, or exactly 7.92 inches or approximately 20.12 cm.

English units are the units of measurement used in England up to 1826, which evolved as a combination of the Anglo-Saxon and Roman systems of units. Various standards have applied to English units at different times, in different places, and for different applications.

Dutch units of measurement

The Dutch units of measurement used today are those of the metric system. Before the 19th century, a wide variety of different weights and measures were used by the various Dutch towns and provinces. Despite the country's small size, there was a lack of uniformity. During the Dutch Golden Age, these weights and measures accompanied the Dutch to the farthest corners of their colonial empire, including South Africa, New Amsterdam and the Dutch East Indies. Units of weight included the pond, ons and last. There was also an apothecaries' system of weights. The mijl and roede were measurements of distance. Smaller distances were measured in units based on parts of the body – the el, the voet, the palm and the duim. Area was measured by the morgen, hont, roede and voet. Units of volume included the okshoofd, aam, anker, stoop, and mingel. At the start of the 19th century the Dutch adopted a unified metric system, but it was based on a modified version of the metric system, different from the system used today. In 1869, this was realigned with the international metric system. These old units of measurement have disappeared, but they remain a colourful legacy of the Netherlands' maritime and commercial importance and survive today in a number of Dutch sayings and expressions.

History of measurement Aspect of history

The earliest recorded systems of weights and measures originate in the 3rd or 4th millennium BC. Even the very earliest civilizations needed measurement for purposes of agriculture, construction, and trade. Early standard units might only have applied to a single community or small region, with every area developing its own standards for lengths, areas, volumes and masses. Often such systems were closely tied to one field of use, so that volume measures used, for example, for dry grains were unrelated to those for liquids, with neither bearing any particular relationship to units of length used for measuring cloth or land. With development of manufacturing technologies, and the growing importance of trade between communities and ultimately across the Earth, standardized weights and measures became critical. Starting in the 18th century, modernized, simplified and uniform systems of weights and measures were developed, with the fundamental units defined by ever more precise methods in the science of metrology. The discovery and application of electricity was one factor motivating the development of standardized internationally applicable units.

Comparison of the imperial and US customary measurement systems

Both the British Imperial and United States customary systems of measurement derive from earlier English systems used in the Middle Ages, that were the result of a combination of the local Anglo-Saxon units inherited from German tribes and Roman units brought by William the Conqueror after the Norman Conquest of England in 1066.

The international yard and pound are two units of measurement that were the subject of an agreement among representatives of six nations signed on 1 July 1959, namely the United States, United Kingdom, Canada, Australia, New Zealand, and the Union of South Africa. The agreement defined the yard as exactly 0.9144 meters and the (avoirdupois) pound as exactly 0.45359237 kilograms.

Imperial and US customary measurement systems

The imperial and US customary measurement systems are both derived from an earlier English system of measurement which in turn can be traced back to Ancient Roman units of measurement, and Carolingian and Saxon units of measure.



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