# Inch (unit)

Physical unit
Unit name inch
Unit symbol ${\ displaystyle \ mathrm {in, \, ^ {\ prime \ prime}}}$
Physical quantity (s) length
Formula symbol ${\ displaystyle l}$
dimension ${\ displaystyle {\ mathsf {L}}}$
system Anglo-American system of measurement
In SI units ${\ displaystyle \ mathrm {1 \, in = 1 ^ {\ prime \ prime} = 2 {,} 54 \, cm = 0 {,} 0254 \, m}}$
Named after english inch

The inch (from Middle High German  zol  for 'cut piece of wood') or thumb's width denotes a large number of old units of measurement in the range of two to three centimeters. Usually it is the twelfth part of a foot . The inch itself was divided into twelve lines , but the decimal division of ten lines per inch also occurred. In addition, partial information such as B. 34 , 12 , 14 , 18 inches common. Such subdivisions into fractions by powers of 2 reach down to 1128 (= 2 −7 ) inches in metalworking .

The inch is still used as a standard measure of length in the USA today. Since the changeover to the metric system in Great Britain is met with various opposition (e.g. from the citizens' initiative Metric Martyrs ) and the units of the Anglo-American system of measurement are still widespread, especially in everyday dealings among citizens, customs are still common there in use. The situation is similar in Ireland, Canada, India, Malaysia, Australia and New Zealand. Furthermore, in numerous countries, customs are primarily used for measurements in technology .

In the English-speaking world it is called an inch .

## history

For the first time in England the customs are found as inches (from the Latin uncia 'twelfth', here the twelfth of a foot) in the laws of King Æthelberht of Kent, dating from the early 7th century . King Edward II defined the inch as the length of three grains of barley placed one behind the other .

In the Upper German-speaking area, the term inch replaced the original terms thumb and finger from 1500 . The origin of the word is Old High German zollo 'roundabout', Middle High German zol 'cylindrical piece, toggle, block, pin'.

In many other languages, the inch unit of length still refers to the thumb, for example in Dutch (duim), in Scandinavian languages (tomme, tum), in Romance languages ​​( pouce , pollice or pollicaria , pulgada ), in Czech, Slovak ( palec ) and Hungarian ( hüvelyk ). Typologically similar units of measurement are the finger width , the hand width , the span (one hand wide), the cubit (from the elbow to the tip of the middle finger), the foot (one foot long), the step (one step long) and the fathom ( the distance between the outstretched arms of a grown man).

## definition

### Current definition

With the introduction of the metric system , customs largely fell out of use. In the English-speaking world ( Anglo-American measuring system ) as well as in various technical areas, for example with the non-metric inch thread , the inch, which was set in 1956 as an international or English inch , is exactly 25.4 mm. The unit symbol for inches is the sequence of letters "in" (inch, according to ISO 31-1 Annex A ) or "″", the customs symbol with a double prime , which is also used as the second symbol.

1 in = 1 ″
= 1000  Thou  = 1000  mil  = 112  ft  = 136  yd  = 25.4  mm  = 2.54  cm  = 0.254  dm  = 0.0254  m .

The corresponding area measure is the square inch (English square inch , si, = 6.4516 cm²), and similarly cubic inch (English cubic inch , ci, = 16.387064 cm³) the volume measure.

In America, the survey inch is still in use for surveying purposes , which is defined as follows:

• 3937 survey inch = 100 m
• 1 survey inch = 1003937  m ≈ 25.4000508 mm

The deviation is 2  ppm (3.937 × 254 = 999.998). It is therefore only relevant for precise measurements or long distances. The US survey foot and thus also the US survey inch should no longer be used after 2022.

### Customs in German standards

Already in the DIN standard 4890 sheet 1 "inch - millimeter. Standard temperature (reference temperature 20 ° C) "of February 1935, the following was recommended:" For industrial measurements, when using the rounded value 1 ″ engl. = 25,400,000 mm, the deviation of 0.044 µ compared to the exact comparison value can be neglected "(µ stands for µm .) The comparison value refers to the value legally established in England at the time, which is based on an announcement by the National Physical Laboratory, Teddington: 1" engl. = 25.399 956 mm. "For dimensions and measurements of the highest accuracy", the standard also gives the conversion for an American inch: 1 "American. = 25,400 051 mm.

## use

The international customs are still used as a standard measure of length in the USA (only in the US land survey there is a different definition) and for specified size specifications in technology.

### Outerwear

• Are common tariff especially for specifying the waist (ger .: waist ) and inner leg length ( English inseam ) of ( jeans -) pants : for example, W 32 "/ L 34".
• (as inches, ") spreads for specifying the heel height of women's shoes , especially high heels and the thickness of plateaus in platform shoes , especially in international trade.

### Electronic equipment

• For specifying the screen diagonal : 15-inch (381 mm) or 19-inch (482.6 mm) screen for computers or notebooks , around 40 inches (102 cm) for televisions
• for the display size of devices such as smartphones , navigation devices , tablet computers or e-book readers
• for specifying the diagonal of video picture tubes and semiconductor image sensors ( CCD and CMOS ) of digital cameras: 1 ″ picture tube (approx. 16 mm net) or 12.5 ″ sensor (0.4 ″, therefore 6.4 mm - in this context the inch is defined differently from the usual dimension of 16 mm due to the former difference between the total and usable size of analog video picture tubes)
• for specifying raster or image resolution such as 96 dpi ( dots per inch  = "dots per inch")
• for disk sizes : 3 12 ″ (89 mm, actually 90 mm), 5 14 ″ (133 mm) and 8 ″ (203 mm)
• For form factors for any drives (including hard drives or optical drives) that corresponds to the size of a floppy disk drive for floppy disks of this size: here, however, only giving the name (corresponds approximately to the actual size of the disk or data carrier)
• the width of many data magnetic tapes : "eighths of an inch" (0.15 ", compact cassette , DAT ), quarter of an inch ( QIC ), half of an inch ( DLT , LTO )
• for speaker diameters: 8 ″ (203 mm), 12 ″ (305 mm) and 15 ″ (381 mm)
• In event technology, standard threads for microphone stands and lamp plugs are roughly 38 ″ instead of 9.525 mm.
• for sound carrier sizes :
• 7 "(178 mm, actually 175 mm) " Single " , 10" (254 mm, actually 250 mm) "EP" and 12 "(305 mm, actually 300 mm)" LP "and" Maxi "for vinyl records
• unofficially 5 ″ (127 mm, actually metric: 120 mm) and 3 ″ (76 mm, actually: 80 mm) for CDs , which, however, were defined metrically from the beginning and
• 0.15 "(3.81 mm, for" Compact Cassettes "), 0.25" (6.35 mm, "Shoelace"), 0.5 "(12.7 mm), 1" (25.4 mm ) and 2 ″ (50.8 mm) width for audio and video tapes
• Tape speed 1 78 ″ (exactly 4.7625, nominally 4.75 cm, for "Compact Cassettes"), 3 34 ″ (9.5 cm), 7 12 "(19.05 cm) and 15 "(38.1 cm) per second
• Length of the tonearm and recording for the cartridge on turntables :
• Tonearm lengths: 9 ″, 10 ″ and 12 ″
• Pickup: 12
• for electronics housing (computer and hi-fi housing): 1  U  = 1 34 ″ = 44.45 mm, 1  TE  = 0.2 ″ = 5.08 mm, 19 ″ racks (483 mm)
• Closely related to magnetic tapes for audio and video recordings are data tapes for computers , e.g. B. as " Quarter-Inch Cartridge "
• for wafer diameters in the semiconductor industry: 2 ″ = 50.8 mm, 3 ″ = 76.2 mm, but only 4 ″ = 100 mm, 6 ″ = 150 mm, 8 ″ = 200 mm
• Grid dimensions on circuit boards , connectors , ribbon cables , IC housings and prototype boards , often 110 ″ = 2.54 mm
• Basic unit for calculating the AWG coding for the wire diameter of electrical cables, in many standards primarily of US origin ( e.g. USB ), a fixed wire cross-section for small-signal applications

### Optical equipment, photography, sound engineering

• For the opening of telescopes in the amateur astronomy (scientific instruments are used exclusively metric dimensioned). The dimensions are used as an approximate equivalent: 4 ″ (10 cm), 4 12 ″ (11.4 cm), 6 ″ (15 cm), classic eight-inch (20 cm) or 14 ″ (35.6 cm) ),
• the diameter of eyepieces ; Receptacles usually 1 14 ″ and 2 ″ (31.8 and 50.8 mm),
• the focal lengths of the earliest telescopes (later they were given in feet ),
• the tripod thread of photographic cameras and microphones (usually 14 ″ × 20 turns per inch UNC thread , with medium format cameras often also 38 ″ × 16 turns per inch UNC thread)

### mechanical engineering

• Threads in the gas, pneumatic and hydraulic sectors. Two types of threads are common:
• Whitworth pipe thread BSP (British Standard Pipe), pipe thread for connections not sealing in the thread (cylindrical)
• Tapered Whitworth pipe thread BSPT (British Standard Pipe Tapered), pipe thread with cylindrical internal thread and conical (1:16) external thread. Their dimensions for outside diameter differ from the simple inch-meter conversion. The external thread diameter of a G 1 ″ thread is not 2.54 cm, but 3.325 cm. For the corresponding tables see Whitworth thread .
• Threads of - not uniformly standardized - gas-specific valve connections and protective caps on compressed gas cylinders (diameter and / or pitch), as well as screw connections in the gas, pneumatic and hydraulic area, such as pressure gauges , as well as the outer diameter of the high-pressure cylinders themselves (from production by pulling and to fit in brackets),
• Thread for fastening screws , especially in the USA and for computer elements, such as connector fixing screws , for example on the D-Sub ,
• Drive of square socket wrenches ( ratchets , ratchets ): 14 ″, 38 ″, 12 ″ and larger,
• Drive of hexagonal bits : 14 ″ (6.35 mm), also micro bits 532 ″ (3.97 mm) and large bits with 516 ″ (7.94 mm),
• Pitch dimensions of drive chains in mechanical engineering as well as bicycles ( 12 ″), motorcycles and also early multi-lane vehicles,
• Ball size in ball bearings : in bicycle bottom brackets usually 14 ″,
• Diameter of frame tubes (1 ″), thread (bottom bracket, pedal), also frame heights on bicycles,
• Pitch for saw chains (distance between the drive links), 38 ″ are very common here ,
• Tooth pitches on elongated saw blades, about 24 teeth per inch of a metal hand saw,
• in many dimensions of printing technology (paper dimensions , line heights, font heights, character spacing - DTP point : 1 pt = 172 ″ ≈ 0.3528 mm, not to be confused with the typographic point = 0.376 mm);
so also with the design of forms , namely
• horizontally in 110 ″ steps (standard tab stop on typewriters ) (pica but 112 ″) and
• vertically in 16 ″ grid (standard line feed for continuous paper (with leporello folding and transport perforation at the edges in 12 ″ grid) and typewriters ), whereby it must be taken into account that typewriters of German origin in German customs ( = 26.1 mm) are calibrated.
• With agricultural machinery : cutting units, knife division (comparable to the division of chainsaw chains), sometimes also with seed drills and thus row spacing in arable farming

### Aircraft construction

In aircraft construction, the inch is the determining measure for the dimensions of components, threads and tools. This unit has also been adopted from the Anglo-American region in the European aircraft industry. This reduces the costs of the aeronautical engineering companies, among other things with regard to tool maintenance, but also spare parts stocks for standard components.

### Vehicle construction, sports and sports equipment

• For the diameter of car rims : usually 10 ″ to 20 ″,
• for bicycle rims 10 ″ -24 ″ and 26 ″ (66 cm, ETRTO dimension on the rim shoulder 559 mm) and 28 ″ (71 cm, ETRTO 622 mm), partly also for frame sizes (18 ″), tube diameter on the steering column , stem and Handlebars (1 ″, 1 18 ″ or 2 ″). Different types of inches or different reference diameters are used, some of which are based on the rim diameter and some on the tire diameter. 27 ″ (“27 inches”) can designate a larger format than 28 ″ (“28 inches”), recently also 27.5 ″ and 29 ″ for mountain bikes, travel unicycles sometimes 36 ″, high bikes around 52 ″,
• for the tire width of diagonal tires ; In the case of radial tires (radial tires), however, the width is given in metric dimensions (mm),
• Outer diameter 1 ″, 1 18 ″, 1 14 ″ of frame tubes made of steel for bicycles, especially those that are classically soldered with sleeves,
• as the size of skateboard decks, axles, rollers and other components,
• as a size specification for surfboards ,
• in archery as length specification for bows, arrows and distance measurement of the chord from the pivot point,
• when specifying the caliber of firearms or air guns as the nominal caliber,
• with the barrel lengths of revolvers,
• the height of the hurdles in hurdles , for example 42 ″ in the men's 110 m hurdles,
• the circumference of the tennis racket handle: grip strength L 1 corresponds to 4 18 ″,
• in golf club fitting .

### Metal processing industry

Pipes and matching threads deviate considerably from the above definition, they are defined according to Whitworth thread . In heating and sanitary engineering (for nominal pipe diameter, Whitworth thread), the customs values ​​no longer correspond to today's dimensions. At the beginning of the 19th century, they related to the inner diameter, which has increased over time as the wall thickness decreases. "Inch" pipe dimensions are thus defined metrically.

The custom often practiced in the electronics trade in Germany of specifying the sizes of screens in inches alone is controversial. Opponents see this formally as an administrative offense . It is a violation of Sections 1, Paragraphs 1, 2, 3 of the Units and Time Act in conjunction with Section 1 of the Implementing Ordinance on the Units and Time Act. According to this, sizes in units other than metric are only permitted if the information in the legal unit (often as centimeters) is highlighted. Proponents do not see the designations as dimensions, but as product classes, which would not apply the law.

### Others

• In the case of musical instruments , inches apply to the most varied of lengths : like the head diameter of percussion instruments ,
• to indicate the width of the seat of a riding saddle ,
• Balloon sizes: vertically measured nominal diameter of round balloons (9 ″, 11 ″) and giant balloons (165 cm = 65 ″), each inflated.
• The winding cores of adhesive tape rolls usually have an (inner) diameter with a smooth inch. 1 ″, 2 ″, 3 ″ ( gaffer tape ) and 4 ″ (packing tape) fitting just above the metacarpal are common.
• The dimension of 19 mm = 34 ″ often occurs with tape width and chipboard thickness . The distance between the contact pins of a Euro plug also has this value.
• Fluorescent tubes with increasingly smaller outer diameters with type designations corresponding to eighths of an inch, formerly T12, now T8 and T5 (≈ 16 mm).
• For the glove size, the hand circumference is measured in French inches ( Pouce ).
• There are typewriters that could optionally be equipped with a 10 or 12 inch wide platen in the car. In lever type typewriters , the font runs 1 inch for every 15, 12 or 10 characters. Ball-head typewriters could be switched manually, the distance 10 or 12 could be read on the head.
• Application balls in roll-on packs, e.g. for deodorant, have a diameter of 0.4, 0.75, 1.0 or 1.4 inches (10.16, 19.05, 24.4 or 35.56 mm).
• Aerosol cans have a valve plate that is usually 1.25 inches in diameter, especially small ones with a diameter of 1 inch.
• High-pressure gas bottles (200 or 300 bar) with a volume of 50 liters have an outside diameter of 229 mm = 9 inches - but variable height. The standard diameters of smaller-volume bottles are 204/178/140/115 mm, i.e. 8/7 / 5.5 / 4.5 inches.
• Halogen lamps with an integrated reflector often exhibit (low voltage, often 20 watts) or 51 ( high voltage 80 to 150 watts) 121 mm diameter, and bear the PAR light designations PAR16 and PAR38 (eighth inch).

In addition, there are some applications in which officially meter-based units are used, but many standard values ​​have an inch origin, so the calibres of many firearms come from inch dimensions, such as 7.62 mm ( H&K G3 ) exactly 0.3 "(according to Winchester. 308), usually numerals in hundredths of an inch (in this case caliber .30). Another application is the connection pitch of electronic components of 2.54 mm, which corresponds to 110 ″, or parts thereof. There are examples in which the meter-based value is rounded down to save cumbersome comma values. In fact, these are inch-based sizes, so the usual format of 10 cm × 15 cm photo paper is actually 10.16 cm × 15.24 cm, which corresponds to 4 ″ × 6 ″.

For international interchangeability of technical parts it is extremely hindering that there are metal screws and nuts for all purposes in mm and in inch sizes , with different threads and even in cross combinations (inch diameters with metric pitch or vice versa, as well as metric threads with inch hexagon socket head ) . The differences are sometimes so small that they cannot be easily seen with the naked eye, but lead to damage to the thread during assembly. However, 4mm is only + 0.78% from 5/32 inches. Multiples are: 8 mm = approx. 5/16 ", 16 mm = approx. 5/8", 32 mm = approx. 1 1/4 ".

## Old definitions

German inch sizes and international inch-like sizes
Surname country year meter Conversion, (exact)
imperial inch United Kingdom 1819 0.025 400 438 10,000393,694  m
imperial inch United Kingdom 1895 0.025 399 978
imperial inch United Kingdom 1922 0.025 399 956
imperial inch United Kingdom 1932 0.025 399 950
imperial inch United Kingdom 1947 0.025 399 931
imperial inch United Kingdom 1956 0.025 4 25410000  m
survey inch United States 1866 0.025 400 051 1003937  m
pouce France 0.027 069 949 37513853  m
inch to bathe 1810 0.03 3100  m
inch Switzerland 1835 0.03 3100  m
inch Hesse 1817/21 0.025 140  m
inch Palatinate 1810s 0.033 130  m
inch Bavaria 1869 0.024 321 6 243,216,00510,000,000,000  m = 1012  Bayr. Decimal inches
Decimal inches Bavaria 1869 0.029 185 92 291,859,20610,000,000,000  m = 1210  Bayr. inch
inch Prussia 1755 0.026 154 5
Decimal inches Prussia 1816 0.037 662 5
Viennese customs Austria 0.026 34 7,902,016300,000,000  m
inch Saxony 1869 0.023 599 28,3191,200,000  m
(Verk) Tum Sweden 1737 0.024 74
Decimal Sweden 1863 0.029 69
polegada Portugal 0.027 5 11400  m
cun China 0.033 333 333 130  m
sun Japan 0.030 303 030 133  m

## Individual evidence

1. Entry in Duden
2. inch sb. 1 . In: Oxford English Dictionary . Volume VII, p. 790.
3. inch, 2.). In: Jacob Grimm , Wilhelm Grimm (Hrsg.): German dictionary . tape 32 : Sable – cypress branch - (XVI). S. Hirzel, Leipzig 1954, Sp. 33 ff . ( woerterbuchnetz.de ). 2 inch In: Wolfgang Pfeifer : Etymological dictionary of German. 2nd Edition. Akademie-Verlag, Berlin 1993, p. 1622. ( online ). Inch 1 . In: Elmar Seebold : Kluge. Etymological dictionary of the German language. 25th edition Walter de Gruyter, Berlin / Boston 2011, p. 1014.
4. Measuring Unit Change Coming in 2022 , National Geodetic Survey, 2019-06-14.
5. Sensor and pixel sizes of CCD and CMOS cameras , vision-doctor.de, accessed on January 29, 2018
6. How big is the sensor really? digicam-experts.de; accessed on January 29, 2018
7. Note: In 1969 Olympus defined the speeds for the microcassette as 2.4 and 1.2 cm / s metric, but as about half or quarter of the value of the compact cassette. See: goughlui.com
8. Gas cylinder valve thread DIN 477 , gewinde-normen.de, accessed on January 29, 2018
9. How to Determine Your Glove Size , accessed April 10, 2018
10. Note Smith-Corona Electric 12 “Made in Belgium” from 1957–1958, typewriters.ch, August 28, 2010, accessed on July 1, 2018.
11. Roll-On Balls euro-matic.de, accessed on August 12, 2018.
12. Industrial Gas: Seamless Steel High Pressure Cylinders worthingtonindustries.com, 2018, accessed February 7, 2020.