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 resolution — 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).
Basic principles Since most digital hardware devices use dots or pixels, the size of the media (in inches) and the number of pixels (or dots) are directly related by the pixels per inch. The following formula gives the number of pixels, horizontally or vertically, given the physical size of a format and the pixels per inch of the output:
Number of Pixels = Size in Inches ∗ PPI {\displaystyle {\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 100 × 100 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.
Outputting to a different device When moving images between devices, such as printing an image that was created on a monitor, it is important to understand the pixel density of both devices. Consider a 23″ HD monitor (20″ wide), that has a known, native resolution of 1920 pixels (horizontal). Let us assume an artist created a new image at this monitor resolution of 1920 pixels, possibly intended for the web without regard to printing. Rewriting the formula above can tell us the pixel density (PPI) of the image on the monitor display:
PPI (monitor) = Number of Pixels Size in Inches = 1920 20 = 96 ppi {\displaystyle {\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:
PPI (poster) = Number of Pixels Size in Inches = 1920 48 = 40 ppi {\displaystyle {\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.
Printing on paper Printing on paper is accomplished with different technologies. Newspapers and magazines were traditionally printed using a halftone screen, which would print dots at a given frequency, the screen frequency, in lines per inch (LPI) by using a purely analog process in which a photographic print is converted into variable sized dots through interference patterns passing through a screen. Modern inkjet printers can print microscopic dots at any location, and don't require a screen grid, with the metric dots per inch (DPI). These are both different from pixel density or pixels per inch (PPI) because a pixel is a single sample of any color, whereas an inkjet print can only print a dot of a specific color either on or off. Thus, a printer translates the pixels into a series of dots using a process called dithering. The dot pitch, the smallest size of each dot, is also determined by the type of paper the image is printed on. An absorbent paper surface, uncoated recycled paper for instance, lets ink droplets spread — so has a larger dot pitch. Often one wishes to know the image quality in pixels per inch (PPI) that would be suitable for a given output device. If the choice is too low, then the quality will be below what the device is capable of—loss of quality—and if the choice is too high then pixels will be stored unnecessarily—wasted disk space. The ideal pixel density (PPI) depends on the output format, output device, the intended use and artistic choice. For inkjet printers measured in DPI it is generally good practice to use half or less than the DPI to determine the PPI. For example, an image intended for a printer capable of 600 dpi could be created at 300 ppi. When using other technologies such as AM or FM screen printing, there are often published screening charts that indicate the ideal PPI for a printing method. Using the DPI or LPI of a printer remains useful to determine PPI until one reaches larger formats, such as 36" or higher, as the factor of visual acuity then becomes more important to consider. If a print can be viewed close up, then one may choose the printer device limits. However, if a poster, banner or billboard will be viewed from far away then it is possible to use a much lower PPI.
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