Editing Pixel density (section)

== Computer displays ==
The PPI/PPCM of a [[computer display]] is related to the size of the display in [[inch]]es/[[centimetre]]s and the total number of [[pixel]]s in the horizontal and vertical directions. This measurement is often referred to as [[dots per inch]], though that measurement more accurately refers to the resolution of a [[computer printer]].

For example, a 15-inch (38&nbsp;cm) display whose dimensions work out to 12&nbsp;inches (30.48&nbsp;cm) wide by 9&nbsp;inches (22.86&nbsp;cm) high, capable of a maximum 1024×768 (or [[XGA]]) pixel resolution, can display around 85&nbsp;PPI, or 33.46{{nbsp}}PPCM, in both the horizontal and vertical directions. This figure is determined by dividing the width (or height) of the display area in pixels by the width (or height) of the display area in inches. It is possible for a display to have different horizontal and vertical PPI measurements (e.g., a typical 4:3&nbsp;ratio CRT monitor showing a 1280×1024 mode computer display at maximum size, which is a 5:4&nbsp;ratio, not quite the same as 4:3). The apparent PPI of a monitor depends upon the screen resolution (that is, the number of pixels) and the size of the screen in use; a monitor in 800×600 mode has a lower PPI than does the same monitor in a 1024×768 or 1280×960 mode.

The [[dot pitch]] of a computer display determines the absolute limit of possible pixel density.
Typical circa-2000 [[cathode-ray tube]] or [[liquid crystal display|LCD]] computer displays range from 67 to 130&nbsp;PPI, though desktop monitors have exceeded 200&nbsp;PPI, and certain smartphone manufacturers' flagship mobile device models have been exceeding 500&nbsp;PPI since 2014.

In January 2008, [[Kopin Corporation]] announced a 0.44&nbsp;inch (1.12&nbsp;cm) [[SVGA]] LCD with a pixel density of 2272&nbsp;PPI (each pixel only 11.25{{nbsp}}μm).<ref>{{cite web | url=http://optics.org/cws/article/industry/32411 | title=Kopin unveils smallest color SVGA display | publisher=optics.org | date=11 January 2008 | access-date=6 June 2008}}</ref><ref>
{{cite web| url=http://www.kopin.com/data/Mar%2008%20Med%20Products%20Manu.pdf| title=Company Debuts World's Smallest Color SVGA Display| publisher= SID, Information Display magazine May 2008 Vol. 24, No. 05| date=31 May 2008| access-date=6 June 2008| url-status=dead| archive-url=https://web.archive.org/web/20080514060809/http://www.kopin.com/data/Mar%2008%20Med%20Products%20Manu.pdf| archive-date=14 May 2008}}</ref> In 2011 they followed this up with a 3760-DPI 0.21-inch diagonal VGA colour display.<ref>{{cite web|title=Innovations|url=http://www.kopin.com/about/innovations|publisher=kopin corporation|access-date=22 May 2014}}</ref> The manufacturer says they designed the LCD to be optically magnified, as in high-resolution eyewear devices.

[[Holography]] applications demand even greater pixel density, as higher pixel density produces a larger image size and wider viewing angle. [[Spatial light modulator]]s can reduce pixel pitch to 2.5&nbsp;[[μm]], giving a pixel density of 10,160&nbsp;PPI.<ref>[http://144.206.159.178/ft/CONF/16427337/16427346.pdf Horizontally scanning holography to enlarge both image size and viewing zone angle] {{webarchive|url=https://web.archive.org/web/20130120084833/http://144.206.159.178/ft/CONF/16427337/16427346.pdf |date=2013-01-20 }} Naoya Okada and Yasuhiro Takaki, Proc. SPIE Vol. 7233 723309-1</ref>

Some observations indicate that the unaided human generally can't differentiate detail beyond 300 PPI.<ref>{{cite web | url=http://prometheus.med.utah.edu/~bwjones/2010/06/apple-retina-display/ | title=Apple Retina Display | publisher=Jonesblog | date=24 June 2010 | access-date=25 September 2011}}</ref> However, this figure depends both on the distance between viewer and image, and the viewer’s [[visual acuity]].  The human eye also responds in a different way to a bright, evenly lit interactive display from how it does to prints on paper.

High pixel density display technologies would make [[Supersampling|supersampled antialiasing]] obsolete, enable true [[WYSIWYG]] graphics and, potentially enable a practical “[[paperless office]]” era.<ref>{{cite web | url=http://www.research.ibm.com/journal/rd/443/wisnieff.html | title=Electronic displays for information technology | publisher=IBM Journal of Research and Development Volume 44, Number 3, 2000 | date=10 November 1999 | access-date=6 June 2008}}</ref> For perspective, such a device at 15&nbsp;inch (38&nbsp;cm) [[Visual display unit#Diagonal size|screen size]] would have to display more than four [[Full HD]] screens (or [[WQUXGA]] resolution).

The PPI pixel density specification of a display is also useful for calibrating a monitor with a printer. Software can use the PPI measurement to display a document at "actual size" on the screen.

=== Calculation of monitor PPI ===
[[File:Display resolution and pixel density.png|thumb]]
PPI can be calculated from the screen's diagonal size in inches and the resolution in pixels (width and height). This can be done in two steps:

# Calculate diagonal resolution in pixels using the [[Pythagorean theorem]]''':'''<br /><math>d_p = \sqrt{w_p^2 + h_p^2}</math>
# Calculate the PPI''':'''<br /><math>PPI = \frac{d_p}{d_i}</math>
where
# <math>w_p</math> is width resolution in pixels
# <math>h_p</math> is height resolution in pixels
# <math>d_p</math> is diagonal size in pixels.
# <math>d_i</math> is diagonal size in inches (this is the number advertised as the size of the display).

For example:
# For 15.6-inch screen with a 5120×2880 resolution you get <math>\frac{\sqrt{5120^2 + 2880^2}}{15.6}</math> = 376.57 PPI.
# For 50-inch screen with a 8192×4608 resolution you get <math>\frac{\sqrt{8192^2 + 4608^2}}{50}</math> = 188 PPI.
# For 27-inch screen with a 3840×2160 resolution you get <math>\frac{\sqrt{3840^2 + 2160^2}}{27}</math> = 163 PPI.
# For 32-inch screen with a 3840×2160 resolution you get <math>\frac{\sqrt{3840^2 + 2160^2}}{32}</math> = 138 PPI.
# For an old-school 10.1-inch [[netbook]] screen with a 1024×600 resolution you get <math>\frac{\sqrt{1024^2 + 600^2}}{10.1}</math> = 117.5 PPI.
# For 27-inch screen with a 2560×1440 resolution you get <math>\frac{\sqrt{2560^2 + 1440^2}}{27}</math> = 108.8 PPI.
# For a 21.5-inch (546.1&nbsp;mm) screen with a 1920×1080 resolution you get <math>\frac{\sqrt{1920^2 + 1080^2}}{21.5}</math> = 102.46 PPI;
These calculations may not be very precise. Frequently, screens advertised as “X inch screen” can have their real physical dimensions of viewable area differ, for example:
* [[Apple Inc.]] advertised their mid-2011 [[iMac]] as a "21.5&nbsp;inch (viewable) [...] display,"<ref>[https://www.apple.com/imac/specs.html Apple iMac Tech Specs] {{webarchive|url=https://web.archive.org/web/20121018210809/http://www.apple.com/imac/specs.html |date=2012-10-18 }}, [[Apple Inc.]] Accessed on 27 January 2012.</ref> but its actual viewable area is 545.22&nbsp;mm or 21.465 inches.<ref>[http://www.displayalliance.com/storage/1-spec-sheets/LM215WF3-SDA1.pdf LM215WF3 LCD Product Specification], [[LG Display]]. Accessed on 27 January 2012.</ref> The more precise figure increases the calculated PPI from 102.46 (using 21.5) to 102.63.
* The [[Hewlett-Packard|HP]] LP2065 20&nbsp;inch (50.8&nbsp;cm) monitor has an actual viewable area of 20.1&nbsp;inch (51&nbsp;cm).<ref>[http://h10010.www1.hp.com/wwpc/us/en/sm/WF06a/382087-382087-64283-72270-444767-1815933.html HP LP2065 20-inch (50.8&nbsp;cm) LCD Monitor - Specifications and Warranty] {{webarchive|url=https://web.archive.org/web/20080410202021/http://h10010.www1.hp.com/wwpc/us/en/sm/WF06a/382087-382087-64283-72270-444767-1815933.html|date=2008-04-10}} ([[Hewlett-Packard Company]] official website)</ref>
* In a more significant case, some monitors such as the [[Dell]] UltraSharp UP3216Q (3840×2160 px) are advertised as a 32-inch "class" monitor (137.68 PPI), but the actual viewing area diagonal is 31.5 inches, making the true PPI 139.87.<ref>{{Cite web|url=https://www.dell.com/en-us/work/shop/dell-ultrasharp-32-ultra-hd-4k-monitor-with-premiercolor-up3216q/apd/210-afln/monitors-monitor-accessories|title = Electronics & Accessories &#124; Dell USA}}</ref>

=== Calculating PPI of camera view screens ===
Camera manufacturers often quote view screens in 'number of dots'.  This is not the same as the number of pixels, because there are 3 'dots' per pixel – red, green and blue. For example, the Canon 50D is quoted as having 920,000&nbsp;dots.<ref>[http://www.dpreview.com/reviews/canoneos50d/ dpreview.com, Canon EOS 50d]</ref>  This translates as 307,200&nbsp;pixels (×3 = 921,600&nbsp;dots).  Thus the screen is 640×480 pixels.<ref>[https://techcrunch.com/2010/07/21/a-quick-psa-on-dots-versus-pixels-in-lcds/ Techcrunch.com, dots vs pixels]</ref>

This must be taken into account when working out the PPI. 'Dots' and 'pixels' are often confused in reviews and specs when viewing information about digital cameras specifically.