An inch (plural: inches; symbol or abbreviation: in or, sometimes, ″ – a double prime) is the name of a unit of length in a number of different systems, including Imperial units, and United States customary units. There are 36 inches in a yard and 12 inches in a foot. A corresponding unit of area is the square inch and a corresponding unit of volume is the cubic inch. The inch is usually the universal unit of measurement in the United States, and is widely used in the United Kingdom, and Canada, despite the introduction of metric to the latter two in the 1960s and 1970s, respectively. The inch is still commonly used informally, although less, in other Commonwealth nations such as Australia; an example being the long-standing tradition of measuring the height of newborn children in inches rather than centimeters.

International inch

Effective July 1, 1959, the United States and countries of the British Commonwealth defined the length of the international yard to be exactly 0.9144 meters. Consequently, the international inch is defined to be equal to exactly 25.4 millimeters.

The international standard symbol for inch is in (see ISO 31-1, Annex A). In some cases, 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.

Equivalence to other units of length

1 international inch is equal to:

• 1,000 thou (1 thou is 0.001 inches.)

• 1,000 mil (1 mil = 1 thou = 0.001 inches)

• 1,000,000 microinches (1 μin is one millionth of an inch.)

• ~0.02778 yards (1 yard is equal to 36 inches.)

• 2.54 centimeters (1 centimeter is equal to about 0.3937 international inches.)

Historical origin

The origin of the inch is disputed. Historically, in different parts of the world (even different cities within the same country) and at different points in time, the inch has referred to similar but different standard lengths.

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.

In some other languages, the word for "inch" is similar to or the same as the word for "thumb"; for example, inch/thumb; inch/thumb; inch, pulgar thumb; inch, polegar thumb; inch, tumme thumb; inch/thumb; inch, anguli finger; inch/thumb; inch/thumb.

Given the etymology of the word "inch", it would seem that the inch is a unit derived from the foot, but this was probably only so in Latin and in Roman times. In English, there are records of fairly precise definitions for the size of an inch (whereas the definitions for the size of a foot are probably anecdotal), so it seems that the foot was then defined as 12 times this length. For example, the old English ynche was defined (by King David I of Scotland in about 1150) 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. To account for the much larger length later called an inch, there are also attempts to link it to the distance between the tip of the thumb and the first joint of the thumb, but this may be speculation.

There are records of the unit being used circa AD 1000 (both Laws of Æthelberht and Laws of Ælfred).

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 mediæval law tracts. One, dating from the first half of the 10th century, is contained in the Laws of Hywel Dda (see Hywel Dda) which superseded those of Dyvnwal, 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".

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.

One source says that the inch was at one time defined in terms of the yard, itself supposedly defined as the distance between Henry I of England's nose and his thumb. This is unlikely as Henry was born in 1068.

Prior to the adoption of the international inch (see above), the United Kingdom and most countries of the British Commonwealth defined the inch in terms of the Imperial Standard Yard. But Canada had its own, different, definition of the inch, defined in terms of metric units. The Canadian inch was defined to be equal to 25.4 millimeters, the amount later accepted as the international inch.

Metric or decimal inch

A metric inch (25 mm instead of 25.4 mm) was the equivalent of an inch under a former proposal for the metrification and unification of the English system of measures. It is now considered to be a strange unit of measurement.

In Sweden, between 1855 to 1863, the existing Swedish "working inch" of ~24.74 mm was replaced by a "decimal inch" of ~29.69 mm which was one tenth of the Swedish foot. Proponents argued that a decimal system simplifies calculations. However, having two different Swedish inch measures (and the English inch on top of that) proved to be complicated. So in a transition period between 1878 and 1889 the metric units were introduced as the overall standard measures. However, the various inches survived some time in building and construction trades.