Inch

"Inches" redirects here. For other uses, see Inch (disambiguation).

The inch (symbol: in or ″) is a unit of length in the British imperial and the United States customary systems of measurement. It is equal to 1/36 yard or 1/12 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.

Inch
Unit system	Imperial/US units
Unit of	Length
Symbol	in or ″ (the double prime)^[1]
Conversions
1 in in ...	... is equal to ...
Imperial/US units	1/36 yd or 1/12 ft
Metric (SI) units	25.4 mm

Measuring tape with inches

A fire hydrant marked as 3-inch

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 the inch has been based on the metric system and defined as exactly 25.4 mm.

Name

The English word "inch" (Old English: ynce) was an early borrowing from Latin uncia ("one-twelfth; Roman inch; Roman ounce").^[2] The vowel change from Latin /u/ to Old English /y/ (which became Modern English /ɪ/) is known as umlaut.^{[citation needed]} 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]). In the Dutch language a term for inch is engelse duim (english thumb).^[5][6] Examples 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").

Usage

The inch is a commonly used customary unit of length in the United States,^[7] Canada,^[8][9] and the United Kingdom.^[10] 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)^[11] and may continue to be used as a secondary or supplementary indication following a metric measurement for other purposes.^[10]

Inches are commonly used to specify the diameter of vehicle wheel rims, and the corresponding inner diameter of tyres in tyre codes.^{[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 a double quote symbol, 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, and also the first and second cuts of the degree.)

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.^[12][13]

 

Measuring tape calibrated in 32nds of an inch

Equivalents

1 international inch is equal to:

• 10,000 'tenths'^[a]
• 1,000 thou^[b] or mil^[c]
• 100 points^[d] or gries^[e]
• 72 PostScript points^[f]
• 10,^[g][e] 12,^[h] or 40^[i] lines
• 6 computer picas^[j]
• 3 barleycorns^[k]
• 25.4 millimetres exactly (1 millimetre ≈ 0.03937008 inches)
• 0.999998 US Survey inches
• 1/3 or 0.333 palms
• 1/4 or 0.25 hands^[l]
• 1/12 or 0.08333 feet
• 1/36 or 0.02777 yards

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, the Textus Roffensis from 1120.^[16] Paragraph LXVII sets out the fine for wounds of various depths: one inch, one shilling; two inches, two shillings, etc.^[m]

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.^[19] 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".^[19]

Similar definitions are recorded in both English and Welsh medieval law tracts.^[20] 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".^[21]

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.^[22] However, the oldest surviving manuscripts date from the early 14th century and appear to have been altered with the inclusion of newer material.^[23]

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.^[24] John Bouvier similarly recorded in his 1843 law dictionary that the barleycorn was the fundamental measure.^[25] 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.^[24]

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 case 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.^[26]

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.^[27] 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.^[28]

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,^[29][30] with other manufacturers of gauge blocks following Johansson's definition by producing blocks designed to be equivalent to his.^[31]

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,^[32][33] effectively endorsing Johansson's pragmatic choice of conversion ratio.^[29]

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;^[34][35] the United States on 1 July 1959;^[36][37][38] Australia in 1961,^[39] effective 1 January 1964;^[40] and the United Kingdom in 1963,^[41] effective on 1 January 1964.^[42] 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.^[43][44]

Related units

US survey inches

The United States retains the 1/39.37-metre definition for surveying, producing a 2 millionth part difference between standard and US survey inches.^[44] This is approximately 1/8 inch per mile; 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 "be phased out" on 1 January 2023 and be superseded by the International foot (also known as the foot) equal to 0.3048 metres exactly, for all further applications.^[45] and by implication, the survey inch with it.

Continental inches

Main articles: Roman inch and French inch

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.^[46]

Scottish inch

The now obsolete Scottish inch (Scottish Gaelic: òirleach), 1/12 of a Scottish foot, was about 1.0016 imperial inches (about 25.44 mm).^[47]

See also

• English units
• Square inch, Cubic inch, and Metric inch
• International yard and pound
• Anthropic units
• Pyramid inch
• Digit and Line

Notes

1. A tenth of a thou, used in machining.
2. Used in machining and papermaking.
3. Formerly used in American English but now often avoided to prevent confusion with millimetres.
4. Used by the Australian Bureau of Meteorology for measuring rainfall until 1973^[14]
5. Part of John Locke's proposal for decimalization of English measures^[15]
6. The typographic point was originally 1/9 of the height of a (capital) letter (cap height) but later acquired a number of different absolute definitions; see Point (typography) § History for details.
7. Used in gunmaking.
8. Used in botany.
9. Used in button manufacturing.
10. Used in typography.
11. Used in American and British shoe sizes.
12. Used in measuring the height of horses.
13. 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.^[17][18]

References

Citations

1. Unicode Consortium (2019). "The Unicode Standard 12.1 — General Punctuation ❰ Range: 2000—206F ❱" (PDF). Unicode.org.
2. "inch, n.¹", Oxford English Dictionary, Oxford: Oxford University Press.
3. "ounce, n.¹", Oxford English Dictionary, Oxford: Oxford University Press.
4. "Inch | unit of measurement". Encyclopedia Britannica. Retrieved 28 March 2019.
5. "duim - lengtemaat". Genootschap Onze Taal. Retrieved 22 October 2022.
6. "duim". Retrieved 22 October 2022.
7. "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).
8. "Weights and Measures Act" (PDF). Canada. 1985. p. 37. Retrieved 11 January 2018 – via Justice Laws Website.
9. "Weights and Measures Act". Canada. 1 August 2014. p. 2. Retrieved 18 December 2014 – via Justice Laws Website. 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).
10. (PDF). UK: Department for Business Innovation and Skills. 2007. Archived from the original (PDF) on 4 July 2011. Retrieved 12 December 2014.
11. "The Traffic Signs Regulations and General Directions 2002 - No. 3113 - Schedule 2 - Regulatory Signs". UK: The National Archives. 2002. Retrieved 25 April 2013.
12. Flatchet, E; Petiet, J (1849). The student's guide to the locomotive engine. John Williams and Co. p. xi. One Metre is equal to ... 30.371 inches"
13. Parkinson, A C (1967). Intermediate Engineering Drawing (sixth ed.). p. 11. The basic major dia is actually 1.309 in.
14. "Climate Data Online – definition of rainfall statistics". Australia: Bureau of Meteorology. Retrieved 10 June 2012.
15. "Of Human Understanding", The Works of John Locke Esq., Vol. I, London: John Churchill, 1714, p. 293.
16. 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.
17. 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.
18. Duncan, Otis Dudley (1984). Notes on social measurement: historical and critical. US: Russell Sage Foundation. p. 87. ISBN 978-0-87154-219-9.
19. Klein, H. Arthur (1974). The world of measurements: masterpieces, mysteries and muddles of metrology. New York, US: Simon and Schuster. ISBN 9780671215651.
20. Hawkes, Jane; Mills, Susan (1999). Northumbria's Golden Age. UK: Sutton. p. 310. ISBN 978-0-7509-1685-1.
21. Williams, John (1867). "The civil arts – mensuration". The Traditionary Annals of the Cymry. Tenby, UK: R. Mason. pp. 243–245.
22. Swinton, John (1789). A proposal for uniformity of weights and measures in Scotland. printed for Peter Hill. p. 134.
23. 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.
24. Butler, Charles (1814). An Easy Introduction to the Mathematics. Oxford, UK: Bartlett and Newman. pp. 61.
25. 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.
26. 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.
27. 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. 10–11.
28. T. C. Mendenhall, Superintendent of Standard Weights and Measures (5 April 1893). (PDF). Archived from the original (PDF) on 30 September 2012.
29. "The History of Gauge Blocks" (PDF). mitutoyo.com. Mitutoyo Corporation. 2013. p. 8. Retrieved 1 February 2020.
30. Gaillard, John (October 1943). Industrial Standardization and Commercial Standards Monthly. p. 293. Retrieved 1 February 2020.
31. Cochrane, Rexmond C. (1966). Measures for Progress. NIST Special Publication, isue 275. U.S. Government Printing Office. p. 200. LCCN 65-62472.
32. Lewis, Herbert B. (1936). The Viewpoint of industry concerned with interchangeable manufacturing toward the proposal to standardize the inch. National Twenty-Eight Conference on Weights and Measures. US: National Bureau of Standards. p. 4. Retrieved 2 August 2012.
33. 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.
34. Howlett, L. E. (1 January 1959). "Announcement on the International Yard and Pound". Canadian Journal of Physics. 37 (1): 84. Bibcode:1959CaJPh..37...84H. doi:10.1139/p59-014.
35. 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.
36. 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.
37. 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.
38. Lewis Van Hagen Judson; United States. National Bureau of Standards (1976). Weights and measures standards of the United States: a brief history. Dept. of Commerce, National Bureau of Standards : for sale by the Supt. of Docs., U.S. Govt. Print. Off. pp. 30–1. Retrieved 16 September 2012.
39. Statutory Rule No. 142.
40. Australian Government ComLaw Weights and Measures (National Standards) Regulations - C2004L00578
41. Weights and Measures Act of 1963.
42. "Thoburn v Sunderland City Council [2002] EWHC 195 (Admin)". England and Wales High Court. 18 February 2002 – via British and Irish Legal Information Institute.
43. . National Physical Laboratory. 25 March 2010. Archived from the original on 26 January 2013. Retrieved 5 April 2013.
44. 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)
45. Materese, Robin (26 July 2019). "U.S. Survey Foot". NIST. Retrieved 1 February 2020.
46. *de Gelder, Jacob (1824). Allereerste Gronden der Cijferkunst [Introduction to Numeracy] (in Dutch). The Hague: de Gebroeders van Cleef. p. 166. Retrieved 10 April 2022.
47. "Dictionary of the Scots Language". Edinburgh: Scottish Language Dictionaries. Retrieved 22 January 2020.

Bibliography

• Attenborough, F. L. (1922), The Laws of the Earliest English Kings (Llanerch Press Facsimile Reprint 2000 ed.), Cambridge: Cambridge University Press, ISBN 978-1-86143-101-1, retrieved 11 July 2018