Length
Overview

In geometric measurements, length most commonly refers to the longest dimension
Dimension
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

of an object.

In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire
Wire
A wire is a single, usually cylindrical, flexible strand or rod of metal. Wires are used to bear mechanical loads and to carry electricity and telecommunications signals. Wire is commonly formed by drawing the metal through a hole in a die or draw plate. Standard sizes are determined by various...

which is shorter than wire thickness
Thickness
Thickness may refer to:Thickness may refer to:* Thickness in graph theory* Thickness of layers in Geology* Thickness The difference in height between two atmospheric pressure levels* Thickness planer a woodworking machine...

. Another example is FET
Fet
Fet is a municipality in Akershus county, Norway. It is part of the Romerike traditional region. The administrative centre of the municipality is the village of Fetsund.Fet was established as a municipality on 1 January 1838...

transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...

s, in which the channel width may be larger than channel length.

Length may be distinguished from height
Height
Height is the measurement of vertical distance, but has two meanings in common use. It can either indicate how "tall" something is, or how "high up" it is. For example "The height of the building is 50 m" or "The height of the airplane is 10,000 m"...

, which is vertical extent, and width or breadth, which are the distance from side to side, measuring across the object at right angles to the length.

Length is a measure of one dimension, whereas area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...

is a measure of two dimensions (length squared) and volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

is a measure of three dimensions
Dimensions
Dimensions is a French project that makes educational movies about mathematics, focusing on spatial geometry. It uses POV-Ray to render some of the animations, and the films are release under a Creative Commons licence....

(length cubed).
Discussions
Encyclopedia
In geometric measurements, length most commonly refers to the longest dimension
Dimension
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

of an object.

In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire
Wire
A wire is a single, usually cylindrical, flexible strand or rod of metal. Wires are used to bear mechanical loads and to carry electricity and telecommunications signals. Wire is commonly formed by drawing the metal through a hole in a die or draw plate. Standard sizes are determined by various...

which is shorter than wire thickness
Thickness
Thickness may refer to:Thickness may refer to:* Thickness in graph theory* Thickness of layers in Geology* Thickness The difference in height between two atmospheric pressure levels* Thickness planer a woodworking machine...

. Another example is FET
Fet
Fet is a municipality in Akershus county, Norway. It is part of the Romerike traditional region. The administrative centre of the municipality is the village of Fetsund.Fet was established as a municipality on 1 January 1838...

transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...

s, in which the channel width may be larger than channel length.

Length may be distinguished from height
Height
Height is the measurement of vertical distance, but has two meanings in common use. It can either indicate how "tall" something is, or how "high up" it is. For example "The height of the building is 50 m" or "The height of the airplane is 10,000 m"...

, which is vertical extent, and width or breadth, which are the distance from side to side, measuring across the object at right angles to the length.

Length is a measure of one dimension, whereas area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...

is a measure of two dimensions (length squared) and volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

is a measure of three dimensions
Dimensions
Dimensions is a French project that makes educational movies about mathematics, focusing on spatial geometry. It uses POV-Ray to render some of the animations, and the films are release under a Creative Commons licence....

(length cubed). In most systems of measurement, the unit of length is a fundamental unit
Fundamental unit
A set of fundamental units is a set of units for physical quantities from which every other unit can be generated.In the language of measurement, quantities are quantifiable aspects of the world, such as time, distance, velocity, mass, momentum, energy, and weight, and units are used to describe...

, from which other units are defined.

## History

Measurement has been important ever since man settled from his nomadic lifestyle and started using building materials; occupying land and trading with his neighbours. As society has become more technologically oriented much higher accuracies of measurement are required in an increasingly diverse set of fields, from micro-electronics to interplanetary ranging.

One of the oldest units of length measurement used in the ancient world was the 'cubit
Cubit
The cubit is a traditional unit of length, based on the length of the forearm. Cubits of various lengths were employed in many parts of the world in Antiquity, in the Middle Ages and into Early Modern Times....

' which was the length of the arm from the tip of the finger to the elbow. This could then be subdivided into shorter units like the foot, hand (which at 4 inches is still used today for expressing the height of horses) or finger, or added together to make longer units like the stride. The cubit could vary considerably due to the different sizes of people. As early as the middle of the tenth century it is believed that the Saxon king Edgar kept a "yardstick" at Winchester as the official standard of measurement. A traditional tale tells the story of Henry I
Henry I of England
Henry I was the fourth son of William I of England. He succeeded his elder brother William II as King of England in 1100 and defeated his eldest brother, Robert Curthose, to become Duke of Normandy in 1106...

(1100–1135) who decreed that the yard should be "the distance from the tip of the King's nose to the end of his outstretched thumb".

After Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

's Special Relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

, length can no longer be thought of being constant in all reference frames. Thus a ruler that is one meter long in one frame of reference will not be one meter long in a reference frame that is travelling at a velocity relative to the first frame. This means length of an object is variable depending on the observer.

## Units

In the physical sciences and engineering, when one speaks of "units of length", the word "length" is synonymous with "distance
Distance
Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...

". There are several units
Units of measurement
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...

that are used to measure
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...

length. Units of length
Unit of length
Many different units of length have been used across the world. The main units in modern use are U.S. customary units in the United States and the Metric system elsewhere. British Imperial units are still used for some purposes in the United Kingdom and some other countries...

may be based on lengths of human body parts, the distance travelled in a number of paces, the distance between landmarks or places on the Earth, or arbitrarily on the length of some fixed object.

In the International System of Units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

(SI), the basic unit
SI base unit
The International System of Units defines seven units of measure as a basic set from which all other SI units are derived. These SI base units and their physical quantities are:* metre for length...

of length is the meter and is now defined in terms of the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

. The centimeter and the kilometer, derived from the meter, are also commonly used units. In U.S. customary units, English or Imperial system of units, commonly used units of length are the inch
Inch
An inch 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...

, the foot, the yard
Yard
A yard is a unit of length in several different systems including English units, Imperial units and United States customary units. It is equal to 3 feet or 36 inches...

, and the mile
Mile
A mile is a unit of length, most commonly 5,280 feet . The mile of 5,280 feet is sometimes called the statute mile or land mile to distinguish it from the nautical mile...

.

Units used to denote distances in the vastness of space, as in astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

, are much longer than those typically used on Earth and include the astronomical unit
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....

, the light-year
Light-year
A light-year, also light year or lightyear is a unit of length, equal to just under 10 trillion kilometres...

, and the parsec
Parsec
The parsec is a unit of length used in astronomy. It is about 3.26 light-years, or just under 31 trillion kilometres ....

.

• Dimension
Dimension
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

• Distance
Distance
Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...

• Orders of magnitude (length)
• Reciprocal length
Reciprocal length
Reciprocal length or inverse length is a measurement used in several branches of science and mathematics. As the reciprocal of length, common units used for this measurement include the reciprocal metre or inverse metre , the reciprocal centimetre or inverse centimetre , and, in optics, the...

• Smoot
Smoot
The smoot is a nonstandard unit of length created as part of an MIT fraternity prank. It is named after Oliver R. Smoot, a fraternity pledge to Lambda Chi Alpha, who in October 1958 lay on the Harvard Bridge , and was used by his fraternity brothers to measure the length of the bridge.-Unit...

• Unit of length
Unit of length
Many different units of length have been used across the world. The main units in modern use are U.S. customary units in the United States and the Metric system elsewhere. British Imperial units are still used for some purposes in the United Kingdom and some other countries...