# Pixel Density - Computer Displays - Calculation of Monitor PPI

Calculation of Monitor PPI

Theoretically, PPI can be calculated from knowing the diagonal size of the screen in inches and the resolution in pixels (width and height). This can be done in two steps:

1. Calculate diagonal resolution in pixels using the Pythagorean theorem:

2. Calculate PPI:

where

• is diagonal resolution in pixels
• is width resolution in pixels
• is height resolution in pixels
• is diagonal size in inches (this is the number advertised as the size of the display).

For example, for a 21.5 inch (54.61 cm) screen with a 1920×1080 resolution (in which = 1920, = 1080 and = 21.5), we get 102.46 PPI; for a typical 10.1 inch netbook screen with a 1024×600 resolution (in which = 1024, = 600 and = 10.1), we get 117.5 PPI.

Note that 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.'s Mid-2011 iMac is advertised 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).