Inch

"Inches" redirects here. For other meanings of inch or inches, see Inch (disambiguation).

1 inch =

SI units
0.0254 m	25.4 mm
US customary/Imperial units
1/36 yd	1/12 ft

An inch (plural: inches; abbreviation or symbol: in or ″ – a double prime) is a unit of length in the imperial and United States customary systems of measurement. Historically an inch was also used in a number of other systems of units. Traditional standards for the exact length of an inch have varied in the past, but since July 1959 when the international yard was defined as 0.9144 metres, the international inch has been exactly 25.4 mm. There are 12 inches in a foot and 36 inches in a yard.

Usage

The inch is a commonly used customary unit of length in the United States, Canada, and the United Kingdom. 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) and may continue to be used as a secondary or supplementary indication following a metric measurement for other purposes.

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 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″.

Measuring tape calibrated in 32nds of an inch

Equivalence to other units of length

1 international inch is equal to:

• 1,000 thou (also known as mil) (1 mil = 1 thou = 0.001 inches)
• 0.027777... yards (1 yard is equal to 36 inches.)
• 2.54 centimetres exactly (1 centimetre ≈ 0.3937 international inches.)
• 72 PostScript Points (there are 72.27 traditional US printer points to the inch)
• 100 points (1 point = 0.01 inches), as used by the Australian Bureau of Meteorology for measuring rainfall before 1974.

Etymology

The English word inch comes from Latin uncia meaning "one-twelfth part" (in this case, one twelfth of a foot); the word ounce (one twelfth of a troy pound) has the same origin. The vowel change from u to i is umlaut; the consonant change from c (pronounced as k) to ch is palatalisation (see Old English phonology).

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); for example, Catalan: polzada inch, polze thumb; French: pouce inch/thumb; Italian: pollicecode: it is deprecated inch/thumb; Spanish: pulgada inch, pulgar thumb; Portuguese: polegada inch, polegar thumb; Dutch: duim inch/thumb; Afrikaans: duim inch/thumb; Swedish: tum inch, tumme thumb, Danish and Norwegian: tomme / tommer inch/inches and tommel thumb; Czech: palec inch/thumb; Slovak: palec inch/thumb; Hungarian: hüvelyk inch/thumb.

History

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 from 1120. 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, defining it as "three grains of barley, 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 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".

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. However, the oldest surviving manuscripts date from the early 14th century and appear to have been altered with the inclusion of newer material.

Charles Butler, a mathematics teacher at Cheam School, 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 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, 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.

Scottish inch

The now obsolete Scottish inch (Scottish Gaelic: òirleach), 1/12 of a Scottish foot, was about 1.0016 imperial inches (about 2.5441 cm). It was used in the popular expression Gie 'im an inch, an he'll tak an ell, 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 (about 94 cm), was in use in England until 1685.) The modern version of the saying is "Give him an inch and he'll take a mile".

Continental inches

Before the adoption of the metric system, several European countries had customary units whose name translates into "inch". The French pouce measured 2.70 cm, at least when applied to describe the calibre of artillery pieces (see also: Units of measurement in France). The Amsterdam foot (voet) consisted of 11 Amsterdam inches (duim) (see Dutch units of measurement). The Amsterdam foot is about 8% shorter than an English foot.

Modern standardisation

In 1959 the International yard and pound agreement defined the international yard as 0.9144 metres, and the imperial and US yards were redefined accordingly.

This resulted in the internationally accepted length of the imperial and US customary inch being exactly 25.4 millimetres. The international inch is 1.7 millionths of an inch longer than the old imperial inch, and 2 millionths of an inch shorter than the US inch.

Before the adoption of the international inch 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, and in 1893 Mendenhall ordered the physical realization of the inch 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.

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.

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. The United States, the United Kingdom, Canada, Australia, New Zealand and South Africa signed a treaty agreeing to the same standards on 1 July 1959. This gives an inch of exactly 25.4 mm. However, the United States retains the 1/39.37-metre definition for survey purposes creating a slight difference between the international and US survey inches; the difference is 2 millionths of the US survey inch. This is approximately 1/8-inch in a mile.

See also

• Anthropic units
• English units
• Square inch
• Cubic inch
• Gry
• Guz
• French inch (pouce)
• Pyramid inch
• Line & French line (ligne)
• UCUM
• International yard and pound

References

• Collins Encyclopedia of Scotland
• Weights and Measures, by D. Richard Torrance, SAFHS, Edinburgh, 1996, ISBN 1-874722-09-9 (NB book focusses on Scottish weights and measures exclusively)
• This article incorporates text from "Dwelly's [Scottish] Gaelic Dictionary" (1911).
• Scottish National Dictionary and Dictionary of the Older Scottish Tonguefy:Tomme (lingtemaat)