Inch – Unit of Measurement Definition

An inch is a unit of length commonly used in U.S. customary and imperial measurement systems. One inch is equal to 1/12 of a foot or 2.54 centimeters.

Usage of Inches

Inches are abbreviated in,[1] but are also often indicated with a double prime symbol ″. Usually a double-quote ” is used instead of a double-prime for convenience.

Portions of an inch are often represented either using decimal or fraction form. Inches are commonly divided into fractions of varying degrees of precision, including halves (1/2), quarters (1/4), eights (1/8), sixteenths (1/16), thirty-seconds (1/32), and sixty-fourths (1/64).[2]

These are known as dyadic fractions.

illustration showing the measurements for all fractions markings on a ruler

When more precision is needed, they are expressed using decimal form. In fields such as machining, inches are commonly expressed in thousandths (thou) or ten-thousandths (tenths).

Inches are often measured using a ruler, yardstick, architects or carpenter’s rule, or a tape measure.

Equivalent Length Measurements

The current length of an inch was defined in the July 1, 1959 yard and pound agreement, which redefined the inch in relation to metric units. The agreement defined one yard as being exactly equal to 0.9144 meters, which allows us to derive the length of an inch as being equal to 2.54 centimeters.[3]

1 inch is equal to:

Measurements in various units of length measurement equalling 1 inch.
Unit of Measure Amount Equaling 1 Inch
Feet 1/12 ft (0.0833)
Yards 1/36 yd (0.0277)
Centimeters 2.54 cm
Meters 0.0254 m
Thousandths 1,000 thou
Ten-thousandths 10,000 tenths

Use our inch conversion calculators to convert to even more length measurements.

Adoption Throughout the World

The inch is primarily used in the United States, as the rest of the world has mostly adopted the International System of Units, which is the modern version of the metric system.

In the U.S., an inch is commonly used for shorter measurements in many fields, including math, construction, and engineering, though many scientific fields have transitioned to using SI length units. Tenths, hundredths, and thousandths are used for very small measurements, often in fields such as machining.

Although Canada has adopted the metric system, Inches are also used mostly due to the close proximity and trade with the U.S. Many product imports and exports are denoted in inches, requiring limited use of the U.S. customary system.

The United Kingdom also still has limited use of the inch measurement, mostly in the public sector for signage.[4]

Origin & History of the Inch

One of the earliest definitions of the inch declares the length as being equal to three barleycorns. An inch is now the subdivision of 1/12 of a foot.

Even so, the actual length of the inch has varied with the variance in the true length of the foot. It wasn’t until the 1959 yard and pound agreement when the world agreed to the exact length of the national yard being equal to 0.9144 meters, that the definition of the inch was equal to 2.54 centimeters.

Before the 1959 agreement, there were actually multiple definitions of the inch, and the exact length varied throughout the world.

The U.S. was using a standard derived in 1893, defining the yard as being equal to 3600/3937 meters, or 0.914401828803658 meters. Britain, on the other hand, was using an 1824 definition of the yard as being equal to the length of a physical artifact.

The difference in definitions was subtle, as they were only off by 0.00013 of an inch. While the definitions were close, the slight variances caused issues as the precision requirements increased during the early 20th century.[5]

The annoyances with managing multiple varying definitions of various length and weight measurements throughout the world led to the need for an agreement on an international standard.

Why Are There 12 Inches in a Foot?

The early Romans subdivided the foot into 16 fingers and are credited with eventually dividing the foot into 12 inches.[6] But why did they choose to divide the foot into 12 inches?

The Romans used the duodecimal number system, which is a base-12 number system. They preferred to use halves and twelfths for subdivisions, and they used a notation system that used a dot, called an uncia, to indicate one-twelfth.

The word uncia later became the source for the word inch that we use today. This is the origin of the inch and the reason why there are 12 in a foot.

In addition to a preference for the number 12 with the number system of the period, the length of a thumb from the first joint is about an inch. The length of the thumb tip offers a convenient and semi-consistent form of measure, and subdividing the foot into these smaller units makes logistical sense for the time period.

The number 12 also more factors than other numbers such as the number 10, which makes it easier to work with mathematically. This makes it easy to handle fractions like 2/3 and 3/4, which are difficult to handle in a base-10 number system.

There are several variations of the inch with mixed usage today.

Survey Inch

The survey inch is used primarily in the United States for land survey purposes, as you may have guessed. It’s based on the survey foot, which is defined using the earlier 1893 definition of the yard. The survey foot is equal to 1200/3937 meters, and thus the survey inch is equal to 100/3937 meters.

The international foot is equal to 0.3048 meters, while the survey foot is equal to 0.304800609601219 meters. Though the difference in length is minute, over large differences is significant.

As you might have guessed, using two slightly different definitions of the inch in the U.S. continues to introduce confusion and the opportunity for error. Thankfully several government organizations have collaborated on deprecating the survey foot, and thus the survey inch, with the goal of completely phasing it out by 2022.[7]

Scottish Inch

Scotland used their own bespoke definitions for length measurement until they were officially replaced by English units in the 17th century. The Scottish units continued to be used unofficially for several centuries.

The Scottish inch is no longer used but was equal to 1/12 Scottish foot, or 1.0016 inches.

Roman Inch

As noted earlier, the modern inch is based on the Roman length system. The Roman uncia, or inch, is equal to 1/12 pes, or Roman foot.

The Roman inch is equal to 0.971 inches.

French Inch

The French inch, also known as the pouce or Paris inch, is based on the French system of measurement. The pouce is subdivided into 12 ligne.

Like other measurement systems, one pouce is equal to 1/12 French foot, or pied. One pouce is equal to 1.066 inches.

Metric Inch

A metric inch is 1/12 of a metric foot, which is occasionally used in the United Kingdom. Although the metric foot is not officially defined in an official standard, it is sometimes used in the lumber and construction industries.

One metric foot is equal to 30 centimeters, or 300 millimeters. Thus, one metric inch is equal to 2.5 centimeters or 25 millimeters.

Square Inch

When measuring an area, the square inch is used. Abbreviated sq in, it’s equal to an area that is 1″ by 1″.

One square inch is equal 1/144 of a square foot.

Cubic Inch

When measuring a volume, the cubic inch is used. Abbreviated cu in, it’s equal to a volume that is 1″ by 1″ by 1″.

One cubic inch is equal 1/1,728 of a cubic foot.

References

  1. International Organization for Standardization, ISO 31-1:1992, https://www.iso.org/standard/3623.html
  2. Arthur Gill, Stephen F. Krar, Machine Tool Technology Basics, https://books.google.com/books?id=ZVXjUc-BCbYC&ppis=_c&lpg=PA1147&ots=QTGOVJD9XW&pg=PA1141#v=onepage&q&f=false
  3. Ambler Thompson and Barry N. Taylor, Guide for the Use of the International System of Units (SI), National Institute of Standards and Technology, https://physics.nist.gov/cuu/pdf/sp811.pdf
  4. UK Department for Business, Energy & Industrial Strategy, Guidance Note on the use of Metric Units of
    Measurement by the Public Sector, https://webarchive.nationalarchives.gov.uk/20120306095713/http://www.bis.gov.uk/assets/bispartners/nmo/docs/legislation/legislation/units-of-measurement/gnotes-for-public-sector-on-use-of-metric.pdf
  5. Lewis Van Hagen Judson, United States. National Bureau of Standards, Weights and measures standards of the United States: a brief history, https://books.google.com/books?id=GXWfglKg11MC&lpg=PA8&pg=PA20#v=onepage&q&f=false
  6. National Institute of Standards and Technology, Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices, Handbook 44 - 2019 Edition, https://nvlpubs.nist.gov/nistpubs/hb/2019/NIST.HB.44-2019.pdf
  7. National Institute of Standards and Technology, Deprecation of the United States (U.S.) Survey Foot, https://www.federalregister.gov/documents/2019/10/17/2019-22414/deprecation-of-the-united-states-us-survey-foot