Inch - Unit of Measurement Definition

Q: How are inches expressed?

Inches are usually expressed using an abbreviation ( in ), or with a double prime symbol ( ″ ). For example: 3 inches = 3 in = 3″ They can be expressed in decimal form or in fraction form. For example: 0.5 in = 1/2 in

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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, as the denominators are all powers of 2.^[3]

$illustration showing the measurements for all fractions markings on a ruler$

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

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 allowed us to derive the length of an inch as being equal to 2.54 centimeters.^[4]

This is because there are 36 inches in a yard and 100 centimeters in a meter. Therefore,

1 inch = 100 cm/m ÷ 36 in/yd × 0.9144 m/yd = 2.54 cm/in

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 of an inch	1,000 thou
Ten-thousandths of an inch	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 (SI), 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 of an inch 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, thereby requiring 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.^[5]

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 a foot into 12 equal parts. That is, an inch equals 1/12 of a foot.

Even so, the actual length of the inch has varied over time in conjunction 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, and subsequently, 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.^[6]

For example, just 5 miles using the different foot definitions would result in a difference of 3.43 feet. This is a problem when conducting work with high-precision measurements.

The annoyances of 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.^[7] 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 (we use the decimal, or base-10 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 to the tip 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.

However, you can imagine how difficult it would be to build something together if everyone were trying to fit parts together that were measured with their own thumbs!

The number 12 also has 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.

Related Units of Measurement

There are several variations of the inch with varying amounts of 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.

In decimal form, 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 distances, it becomes 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, and as of December 31st, 2022, it has been phased out.^[8]

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 of a 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 of a 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 to 1/144 of a square foot.

Cubic Inch

When measuring a volume, the cubic inch is used. Abbreviated cu in or in³, it’s equal to a volume that is 1″ by 1″ by 1″.

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

As you can see, the importance of standardizing units and all agreeing to use the same measurements is extremely important. If we all used slightly different measurements, working together would be extremely frustrating and sometimes disastrous.

For example, in 1999, NASA lost its $125 million Mars Climate Orbiter satellite because engineers forgot to convert between feet and meters when exchanging data!

Frequently Asked Questions

How are inches expressed?

Inches are usually expressed using an abbreviation (in), or with a double prime symbol (″). For example:

3 inches = 3 in = 3″

They can be expressed in decimal form or in fraction form. For example:

0.5 in = 1/2 in

Is 1 inch exactly 2.54 cm?

Yes! 1 inch equals exactly 2.54 cm due to the July 1, 1959 yard and pound agreement, which defined 1 yard to be exactly 0.9144 meters, and therefore 1 inch equals exactly 2.54 cm.

How many inches are in a foot?

There are exactly 12 inches in 1 foot.

How do you calculate inches?

To calculate the number of inches in a measurement, it depends on what units were used to make the measurement. For example, if the measurements are in feet, multiply by 12 to find the number of inches.

If they are in centimeters, divide by 2.54 to find the number of inches. Common unit conversions can be found in the table above.

Is there a way to measure inches without a ruler?

If you want to measure the length of an object, in inches, without a ruler, find an object you know to be an inch long and use that to measure the object.

For example, a standard paperclip is about an inch long, so if your object is approximately 5.5 paperclips long, then it is approximately 5.5 inches long.

Inch – Unit of Measurement Definition