Aspect ratio
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The aspect ratio of a geometric shape is the
ratio In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
of its sizes in different dimensions. For example, the aspect ratio of a
rectangle In Euclidean geometry, Euclidean plane geometry, a rectangle is a Rectilinear polygon, rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that a ...
is the ratio of its longer side to its shorter side—the ratio of width to height, when the rectangle is oriented as a "
landscape A landscape is the visible features of an area of land, its landforms, and how they integrate with natural or human-made features, often considered in terms of their aesthetic appeal.''New Oxford American Dictionary''. A landscape includes th ...
". The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal
fraction A fraction (from , "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, thre ...
. The values x and y do not represent actual widths and heights but, rather, the proportion between width and height. As an example, 8:5, 16:10, 1.6:1, and 1.6 are all ways of representing the same aspect ratio. In objects of more than two dimensions, such as hyperrectangles, the aspect ratio can still be defined as the ratio of the longest side to the shortest side.


Applications and uses

The term is most commonly used with reference to: * Graphic / image ** Image aspect ratio ** Display aspect ratio ** Paper size ** Standard photographic print sizes ** Motion picture film formats ** Standard ad size **
Pixel aspect ratio A pixel aspect ratio (PAR) is a mathematical ratio that describes how the width of a pixel in a digital image compares to the height of that pixel. Most digital imaging systems display an image as a grid of tiny, square pixels. However, som ...
**
Photolithography Photolithography (also known as optical lithography) is a process used in the manufacturing of integrated circuits. It involves using light to transfer a pattern onto a substrate, typically a silicon wafer. The process begins with a photosensiti ...
: the aspect ratio of an etched, or deposited structure is the ratio of the height of its vertical side wall to its width. * HARMST High Aspect Ratios allow the construction of tall microstructures without slant * Tire code * Tire sizing *
Turbocharger In an internal combustion engine, a turbocharger (also known as a turbo or a turbosupercharger) is a forced induction device that is powered by the flow of exhaust gases. It uses this energy to compress the intake air, forcing more air into th ...
impeller sizing * Wing aspect ratio of an aircraft or bird * Astigmatism of an
optical lens A lens is a transmissive optics, optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a #Compound lenses, compound lens consists of several simple ...
* Nanorod dimensions * Shape factor (image analysis and microscopy) *
Finite Element Analysis Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical models, mathematical modeling. Typical problem areas of interest include the traditional fields of structural ...
* Flag design; see List of aspect ratios of national flags


Aspect ratios of simple shapes


Rectangles

For a rectangle, the aspect ratio denotes the ratio of the width to the height of the rectangle. A
square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...
has the smallest possible aspect ratio of 1:1. Examples: * 4:3 = 1.: Some (not all) 20th century computer monitors ( VGA,
XGA The eXtended Graphics Array (usually called XGA) is a graphics card manufactured by IBM and introduced for the IBM PS/2 line of personal computers in 1990 as a successor to the IBM 8514, 8514/A. It supports, among other modes, a display resol ...
, etc.),
standard-definition television Standard-definition television (SDTV; also standard definition or SD) is a television system that uses a resolution that is not considered to be either high or enhanced definition. ''Standard'' refers to offering a similar resolution to the ...
* \sqrt:1 = 1.414...: international paper sizes (
ISO 216 ISO 216 is an international standard for paper sizes, used around the world except in North America and parts of Latin America. The standard defines the "A", "B" and "C" series of paper sizes, which includes the A4, the most commonly availabl ...
) * 3:2 = 1.5: 35mm still camera film,
iPhone The iPhone is a line of smartphones developed and marketed by Apple that run iOS, the company's own mobile operating system. The first-generation iPhone was announced by then–Apple CEO and co-founder Steve Jobs on January 9, 2007, at ...
(until
iPhone 5 The iPhone 5 is a smartphone that was developed and marketed by Apple Inc. It is the List of iPhone models, 6th generation iPhone, succeeding the iPhone 4s, and preceding both the iPhone 5s and iPhone 5c. It was formally unveiled as part of ...
) displays * 16:10 = 1.6: commonly used
widescreen Widescreen images are displayed within a set of aspect ratio (image), aspect ratios (relationship of image width to height) used in film, television and computer screens. In film, a widescreen film is any film image with a width-to-height aspect ...
computer display A computer monitor is an output device that displays information in pictorial or textual form. A discrete monitor comprises a visual display, support electronics, power supply, housing, electrical connectors, and external user controls. T ...
s ( WXGA) * Φ:1 = 1.618...:
golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their summation, sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if \fr ...
, close to 16:10 * 5:3 = 1.: super 16 mm, a standard
film gauge Film gauge is a physical property of photographic film, photographic or Film stock, motion picture film stock which defines its width. Traditionally, the major movie film gauges are 8 mm film, 8 mm, 16 mm film, 16 mm, 35 mm movie film, 35 mm, an ...
in many European countries * 16:9 = 1.:
widescreen Widescreen images are displayed within a set of aspect ratio (image), aspect ratios (relationship of image width to height) used in film, television and computer screens. In film, a widescreen film is any film image with a width-to-height aspect ...
TV and most laptops * 2:1 = 2:
dominoes Dominoes is a family of tile-based games played with gaming pieces. Each domino is a rectangular tile, usually with a line dividing its face into two square ''ends''. Each end is marked with a number of spots (also called ''Pip (counting), pips ...
* 64:27 = 2.: ultra-widescreen, 21:9 * 32:9 = 3.: super ultra-widescreen


Ellipses

For an ellipse, the aspect ratio denotes the ratio of the
major axis In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the longe ...
to the minor axis. An ellipse with an aspect ratio of 1:1 is a circle.


Aspect ratios of general shapes

In
geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
, there are several alternative definitions to aspect ratios of general
compact set In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., i ...
s in a d-dimensional space: * The diameter-width aspect ratio (DWAR) of a compact set is the ratio of its diameter to its width. A circle has the minimal DWAR which is 1. A square has a DWAR of \sqrt. * The cube-volume aspect ratio (CVAR) of a compact set is the ''d''-th root of the ratio of the ''d''-volume of the smallest enclosing axes-parallel ''d''-cube, to the set's own ''d''-volume. A square has the minimal CVAR which is 1. A circle has a CVAR of \sqrt. An axis-parallel rectangle of width ''W'' and height ''H'', where ''W''>''H'', has a CVAR of \sqrt = \sqrt. If the dimension ''d'' is fixed, then all reasonable definitions of aspect ratio are equivalent to within constant factors.


Notations

Aspect ratios are mathematically expressed as ''x'':''y'' (pronounced "x-to-y"). Cinematographic aspect ratios are usually denoted as a (rounded) decimal multiple of width vs unit height, while photographic and videographic aspect ratios are usually defined and denoted by whole number ratios of width to height. In
digital image A digital image is an image composed of picture elements, also known as pixels, each with '' finite'', '' discrete quantities'' of numeric representation for its intensity or gray level that is an output from its two-dimensional functions f ...
s there is a subtle distinction between the ''display'' aspect ratio (the image as displayed) and the ''storage'' aspect ratio (the ratio of pixel dimensions); see Distinctions.


See also

* Axial ratio *
Ratio In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
* Equidimensional ratios in 3D * List of film formats *
Squeeze mapping In linear algebra, a squeeze mapping, also called a squeeze transformation, is a type of linear map that preserves Euclidean area of regions in the Cartesian plane, but is ''not'' a rotation (mathematics), rotation or shear mapping. For a fixed p ...
* Scale (ratio) * Vertical orientation


References

{{DEFAULTSORT:Aspect Ratio Ratios