Main Difference
The main difference between Length and Dimension is that the Length is a measured dimension of an object and Dimension is a minimum number of independent coordinates needed to specify any point within a mathematical space.
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Length
In geometric measurements, length is the most extended dimension of an object. In the International System of Quantities, length is any quantity with dimension distance. In other contexts, length is a measured dimension of an object. Length may be distinguished from height, 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. For example, it is possible to cut a length of wire shorter than the wire’s width. In most systems of measurement, the unit of length is a base unit, from which other units are derived.
Length is a measure of one dimension, whereas area is a measure of two dimensions (length squared) and volume is a measure of three dimensions (length cubed).
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Dimension
In physics and mathematics, the dimension of a mathematical 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 – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces.
In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. Ten dimensions are used to describe string theory, eleven dimensions can describe supergravity and M-theory, and the state-space of quantum mechanics is an infinite-dimensional function space.
The concept of dimension is not restricted to physical objects. High-dimensional spaces frequently occur in mathematics and the sciences. They may be parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space we live in.
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Length (noun)
The distance measured along the longest dimension of an object.
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Length (noun)
duration
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Length (noun)
The length of a horse, used to indicate the distance between horses at the end of a race.
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Length (noun)
Distance between the two ends of a line segment.
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Length (noun)
The distance down the pitch that the ball bounces on its way to the batsman.
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Length (noun)
Total extent.
“the length of a book”
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Length (noun)
Part of something that is long; a physical piece of something.
“a length of rope”
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Length (verb)
To lengthen.
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Dimension (noun)
A single aspect of a given thing.
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Dimension (noun)
A measure of spatial extent in a particular direction, such as height, width or breadth, or depth.
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Dimension (noun)
A construct whereby objects or individuals can be distinguished.
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Dimension (noun)
The number of independent coordinates needed to specify uniquely the location of a point in a space; also, any of such independent coordinates.
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Dimension (noun)
The number of elements of any basis of a vector space.
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Dimension (noun)
One of the properties that are regarded as fundamental measures of a physical quantity, such as mass, length and time.
“The dimension of velocity is length divided by time.”
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Dimension (noun)
Any of the independent ranges of indices in a multidimensional array.
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Dimension (noun)
An alternative universe or plane of existence.
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Dimension (verb)
To mark, cut or shape something to specified dimensions.
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Length (noun)
the measurement or extent of something from end to end; the greater of two or the greatest of three dimensions of an object
“the fish reaches a length of 10 inches”
“the delta is twenty kilometres in length”
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Length (noun)
the quality of being long
“the length of the waiting list”
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Length (noun)
the length of a swimming pool as a measure of the distance swum
“fifty lengths of the pool”
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Length (noun)
the length of a horse, boat, etc., as a measure of the lead in a race
“the mare won the race by seven lengths”
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Length (noun)
the extent of a garment in a vertical direction when worn
“the length of her skirt”
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Length (noun)
the full distance that a thing extends for
“the muscles running the length of my spine”
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Length (noun)
the full extent of one’s body
“he awkwardly lowered his length into the small car”
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Length (noun)
the metrical quantity or duration of a vowel or syllable
“the length of the syllable is isomorphic with the length of the syllabic vowel”
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Length (noun)
the amount of time occupied by something
“delivery must be within a reasonable length of time”
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Length (noun)
a piece or stretch of something
“the surviving length of track”
“a length of brown satin”
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Length (noun)
an extreme to which a course of action is taken
“they go to great lengths to avoid the press”
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Length (noun)
the distance from the batsman at which a well-bowled ball pitches
“Lewis tended to bowl short of a length”
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Length (noun)
(in bridge or whist) the number of cards of a suit held in one’s hand, especially when five or more
“to open one heart with equal length in hearts and spades is in the modern Acol style”
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Dimension (noun)
a measurable extent of a particular kind, such as length, breadth, depth, or height
“the drawing must be precise in dimension”
“the final dimensions of the pond were 14 ft x 8 ft”
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Dimension (noun)
a mode of linear extension of which there are three in space and two on a flat surface, which corresponds to one of a set of coordinates specifying the position of a point.
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Dimension (noun)
an expression for a derived physical quantity in terms of fundamental quantities such as mass, length, or time, raised to the appropriate power (acceleration, for example, having the dimension of length × time⁻²).
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Dimension (noun)
an aspect or feature of a situation
“we must focus on the cultural dimensions of the problem”
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Dimension (verb)
cut or shape (something) to particular measurements.
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Dimension (verb)
mark (a diagram) with measurements.