Editing Pixel density (section)

=== 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>