PPI & DPI Calculator for Screens

Pixel density is a ratio between a pixel count and a physical measurement, which is why the diagonal is used: the Pythagorean diagonal in pixels divided by the advertised diagonal in inches gives pixels per inch without needing to know the panel width and height separately. Dot pitch is the same information expressed as a distance, 25.4 millimetres divided by the PPI, so a 27-inch 3840 by 2160 monitor works out at about 163 PPI and a 0.156mm pitch, while a 24-inch 1920 by 1080 panel gives roughly 92 PPI and 0.28mm. Print resolution is a separate calculation with the same shape, dividing each pixel dimension by the intended print dimension in inches and taking the smaller of the two so neither axis is stretched. The reason no single number is correct everywhere is viewing distance: human visual acuity resolves roughly one arcminute, so the density needed for a print or panel to look continuous falls in proportion to how far away it is viewed. That is why 300 DPI is the norm for photographs and magazines held at arm length, 150 to 200 DPI satisfies wall posters, and billboards are output at a few tens of DPI. Two distinctions cause most of the confusion in practice. First, PPI and DPI are not the same physical thing. An inkjet or offset press addresses ink dots at 1200 to 2400 dpi and builds continuous tone out of halftone cells measured in lines per inch, typically 133 to 175 lpi for commercial offset, so a 300 PPI image is not asking the press for 300 dots. Second, the PPI figure stored in an image file is only a metadata tag; changing it rescales the intended print size but does not add or remove a single pixel. On screens there is a third layer, since CSS works in a reference pixel defined by W3C as the visual angle of one ninety-sixth of an inch at arm length, and operating systems map that to hardware pixels through a device pixel ratio, so a browser reporting 96 CSS pixels per inch says nothing about the panel underneath it.

The numbers built into modern displays are inherited from typesetting. The printer point of roughly one seventy-second of an inch meant that a display drawn at 72 pixels per inch could show a point of type as one pixel, and the original Macintosh of 1984 used a 512 by 342 screen at approximately that density so that on-screen layout matched printed output at one to one. Adobe PostScript, released in 1984, and the Apple LaserWriter of 1985 at 300 dots per inch turned that correspondence into the desktop publishing workflow. Microsoft chose a 96 dpi logical density for Windows instead, which is the direct ancestor of the 96 dpi assumption still baked into CSS and the W3C reference pixel. Print resolution conventions are older still and come from halftone reproduction, the process of rendering continuous tone as variably sized dots, which Frederic Ives developed in Philadelphia in 1881 and which reached commercial newspapers over the following two decades. Prepress practice settled on scanning at roughly twice the halftone screen ruling, and that quality factor is where the familiar 300 PPI target for a 150 lpi screen originates. Display density became a consumer marketing category much later, when Apple applied the term Retina to the iPhone 4 in 2010 at 326 PPI, arguing that pixels became individually indistinguishable at normal holding distance. The claim was a restatement of the same arcminute acuity limit that had governed halftone screen selection for a century.