# Inch

"Inches" redirects here. For other uses, see Inch (disambiguation).
Inch
Unit system imperial/US units
Unit of length
Symbol in
Unit conversions
1 in in ...... is equal to ...
imperial/US units    1/36 yd
1/12 ft
metric (SI) units    25.4 mm

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,[1] Canada,[2][3] and the United Kingdom.[4] It is also used in Japan for electronic parts, especially 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)[5] and may continue to be used as a secondary or supplementary indication following a metric measurement for other purposes.[4]

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)
• 1/36 = 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.[6]

## 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: pollice 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.[7] 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."[8][9]

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.[10] 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".[10]

Similar definitions are recorded in both English and Welsh medieval law tracts.[11] 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".[12]

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

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.[15] John Bouvier similarly recorded in his 1843 law dictionary that the barleycorn was the fundamental measure.[16] 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.[15] 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.[17]

### 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).[18] 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.[19] (The ell, equal to 37 inches (about 94 cm), was in use in England until 1685.)[20] 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,[21] 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 old US inch.[22]

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.[23] 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.[24]

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.[25][26]

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.[27] 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.[28] 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.[29] This is approximately 1/8-inch in a mile.

## References

1. "Corpus of Contemporary American English". Brigham Young University. US. Retrieved 5 December 2011. lists 24,302 instances of inch(es) compared to 1548 instances of centimeter(s) and 1343 instances of millimeter(s).
2. "Weights and Measures Act". Justice Laws Website. Canada. 1 August 2014. p. 15. Retrieved 18 December 2014.
3. "Weights and Measures Act". Justice Laws Website. Canada. 1 August 2014. p. 2. Retrieved 18 December 2014. 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).
4. "Guidance Note on the use of Metric Units of Measurement by the Public Sector" (PDF). UK: Department for Business Innovation and Skills. 2007. Retrieved 12 December 2014.
5. "The Traffic Signs Regulations and General Directions 2002 - No. 3113 - Schedule 2 - Regulatory Signs". UK: The National Archives. 2002. Retrieved 25 April 2013.
6. "Climate Data Online – definition of rainfall statistics". Australia: Bureau of Meteorology. Retrieved 10 June 2012.
7. Goetz, Hans-Werner; Jarnut, Jörg; Pohl, Walter (2003). Regna and Gentes: The Relationship Between Late Antique and Early Medieval Peoples and Kingdoms in the Transformation of the Roman World. BRILL. p. 33. ISBN 978-90-04-12524-7. Retrieved 14 May 2012.
8. Wilkins, David (1871). Councils and Ecclesiastical Documents Relating to Great Britain and Ireland: English church during the Anglo-Saxon period: A.D. 595-1066. Oxford, UK: Clarendon Press. p. 48. Retrieved 18 December 2014.
9. Duncan, Otis Dudley (1984). Notes on social measurement: historical and critical. US: Russell Sage Foundation. p. 87. ISBN 978-0-87154-219-9. Retrieved 27 November 2011.
10. Klein, H. Arthur (1974). The world of measurements: masterpieces, mysteries and muddles of metrology. New York, US: Simon and Schuster.
11. Hawkes, Jane; Mills, Susan (1999). Northumbria's Golden Age. UK: Sutton. p. 310. ISBN 978-0-7509-1685-1.
12. Williams, John (1867). "The civil arts mensuration". The Traditionary Annals of the Cymry. Tenby, UK: R. Mason. pp. 243245.
13. Swinton, John (1789). A proposal for uniformity of weights and measures in Scotland. printed for Peter Hill. p. 134. Retrieved 27 February 2012.
14. Gemmill, Elizabeth; Mayhew, Nicholas (22 June 2006). Changing Values in Medieval Scotland: A Study of Prices, Money, and Weights and Measures. UK: Cambridge University Press. p. 113. ISBN 978-0-521-02709-0. Retrieved 27 February 2012.
15. Butler, Charles (1814). An Easy Introduction to the Mathematics. Oxford, UK: Bartlett and Newman. p. 61.
16. Bouvier, John (1843). "Barleycorn". A Law Dictionary: With References to the Civil and Other Systems of Foreign Law. Philadelphia, US: T. & J. W. Johnson. p. 188.
17. Long, George (1842). "Weights & Measures, Standard". The Penny Cyclopædia of the Society for the Diffusion of Useful Knowledge. London, UK: Charles Knight & Co. p. 436.
18. "Dictionary of the Scots Language". Edinburgh: Scottish Language Dictionaries. Retrieved 21 May 2011.
19. Heywood, John (1546). A dialogue conteinying the nomber in effect of all the prouerbes in the englishe tongue, compacte in a matter concernyng two maner of mariages, etc. London: Thomas Berthelet. Full text of 1874 reprint
20. Gibson, A. J. S.; Smout, T. C. (19 July 2007). Prices, Food and Wages in Scotland, 1550-1780. Cambridge University Press. p. 371. ISBN 978-0-521-03780-8. Retrieved 11 March 2012.
21. Astin, A.V.; Karo, H. A.; Mueller, F.H. (25 June 1959). "Refinement of Values for the Yard and the Pound" (PDF). US Federal Register.
22. "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. 25 March 2010. Retrieved 5 April 2013.
23. Judson, Lewis V (October 1963). Weights and Measures Standards of the United States - a brief history - NBS publication 447. United States Department of Commerce. p. 1011.
24. National Conference on Weights and Measures; United States. Bureau of Standards; National Institute of Standards and Technology (US) (1936). Report of the ... National Conference on Weights and Measures. US Department of Commerce, Bureau of Standards. p. 4. Retrieved 2 August 2012.
25. Wandmacher, Cornelius; Johnson, Arnold Ivan (1995). Metric Units in Engineering--going SI: How to Use the International Systems of Measurement Units (SI) to Solve Standard Engineering Problems. ASCE Publications. p. 265. ISBN 978-0-7844-0070-8. Retrieved 2 August 2012.
26. National Conference on Weights and Measures; United States. Bureau of Standards; National Institute of Standards and Technology (US) (1957). Report of the ... National Conference on Weights and Measures. US Department of Commerce, Bureau of Standards. pp. 45–6. Retrieved 2 August 2012.
27. United States. National Bureau of Standards (1959). Research Highlights of the National Bureau of Standards. US Department of Commerce, National Bureau of Standards. p. 13. Retrieved 3 August 2012.
28. A. V. Astin & H. Arnold Karo, (1959), Refinement of values for the yard and the pound, Washington DC: National Bureau of Standards, republished on National Geodetic Survey web site and the Federal Register (Doc. 59-5442, Filed, 30 June 1959, 8:45 am)
• 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)