Pixel density

Pixels per inch (ppi) and pixels per centimetre (ppcm or pixels/cm) are measurements of the pixel density of an electronic image device, such as a computer monitor or a television set's display, or image digitizing device such as a camera or image scanner. Horizontal and vertical density are usually the same, as most devices have square pixels, but differ on devices that have non-square pixels. Pixel density is not the same as where the former describes the amount of detail on a physical surface or device, the latter describes the amount of pixel information regardless of its scale. Considered in another way, a pixel has no inherent size or unit (a pixel is actually a sample), but when it is printed, displayed, or scanned, then the pixel has both a physical size (dimension) and a pixel density (ppi).

Pixels per inch (ppi) and pixels per centimetre (ppcm or pixels/cm) are measurements of the pixel density of an electronic image device, such as a computer monitor or a television set's display, or image digitizing device such as a camera or image scanner. Horizontal and vertical density are usually the same, as most devices have square pixels, but differ on devices that have non-square pixels. Pixel density is not the same as where the former describes the amount of detail on a physical surface or device, the latter describes the amount of pixel information regardless of its scale. Considered in another way, a pixel has no inherent size or unit (a pixel is actually a sample), but when it is printed, displayed, or scanned, then the pixel has both a physical size (dimension) and a pixel density (ppi). \text{Number of Pixels} = \text{Size in Inches} * \text{PPI} Pixels per inch (or pixels per centimetre) describes the detail of an image file when the print size is known. For example, a pixel image printed in a 2-inch square has a resolution of 50 pixels per inch. Used this way, the measurement is meaningful when printing an image. In many applications, such as Adobe Photoshop, the program is designed so that one creates new images by specifying the graphic output device and PPI (pixels per inch). Thus the output target is often defined upon creating the image. \text{PPI (monitor)} = \frac{\text{Number of Pixels}}{\text{Size in Inches}} = \frac{1920}{20} = 96\text{ ppi} Now, let us imagine the artist wishes to print a larger banner 48 inches horizontally. We know the number of pixels in the image and the size of the output, from which we can use the same formula again to give the PPI of the printed poster: \text{PPI (poster)} = \frac{\text{Number of Pixels}}{\text{Size in Inches}} = \frac{1920}{48} = 40\text{ ppi} This shows that the output banner will have only 40 pixels per inch. Since a printer device is capable of printing at 300 ppi, the resolution of the original image is well below what would be needed to create a decent quality banner, even if it looked good on a monitor for a website. We would say more directly that a 1920 × 1080 pixel image does not have enough pixels to be printed in a large format. Calculate diagonal resolution in pixels using the Pythagorean theorem: d_p = \sqrt{w_p^2 + h_p^2} Calculate the PPI: PPI = \frac{d_p}{d_i} where w_p is width resolution in pixels h_p is height resolution in pixels d_p is diagonal size in pixels. d_i 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 resolution you get \frac{\sqrt{5120^2 + 2880^2}}{15.6} = 376.57 PPI. For 50-inch screen with an resolution you get \frac{\sqrt{8192^2 + 4608^2}}{50} = 188 PPI. For 27-inch screen with a resolution you get \frac{\sqrt{3840^2 + 2160^2}}{27} = 163 PPI. For 32-inch screen with a resolution you get \frac{\sqrt{3840^2 + 2160^2}}{32} = 138 PPI. For an old-school 10.1-inch netbook screen with a resolution you get \frac{\sqrt{1024^2 + 600^2}}{10.1} = 117.5 PPI. For 27-inch screen with a resolution you get \frac{\sqrt{2560^2 + 1440^2}}{27} = 108.8 PPI. For a 21.5-inch (546.1 mm) screen with a resolution you get \frac{\sqrt{1920^2 + 1080^2}}{21.5} = 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 inch (viewable) [...] display," but its actual viewable area is 545.22 mm or 21.465 inches. The more precise figure increases the calculated PPI from 102.46 (using 21.5) to 102.63. The HP LP2065 20 inch (50.8 cm) monitor has an actual viewable area of 20.1 inch (51 cm). In a more significant case, some monitors such as the Dell UltraSharp UP3216Q ( 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. 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 dots. This translates as 307,200 pixels (×3 = 921,600 dots). Thus the screen is pixels. 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.

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