How this calculator works
A screen resolution gives pixels, and the diagonal gives a physical length. Converting the diagonal to inches and dividing the diagonal in pixels by it gives pixels per inch. The dot pitch is the inverse, converted to millimetres: a density of about 92 ppi has a dot pitch of 0.277 mm. The physical width and height follow from dividing each pixel count by the density. Because the density uses the diagonal, both axes are assumed to have the same density, which is true of nearly every consumer display. Printers use dots per inch, a separate measure of ink dots that can far exceed the pixel density of the image being printed.
Formula
diagonal in pixels = sqrt(horizontal^2 + vertical^2). PPI = diagonal in pixels / diagonal in inches. dot pitch (mm) = 25.4 / PPI. width (in) = horizontal pixels / PPI. height (in) = vertical pixels / PPI. To reverse, diagonal (in) = diagonal in pixels / PPI.
Worked example
A 1920 by 1080 monitor with a 24 inch diagonal has 2,202.9 pixels on the diagonal, so its density is 2,202.9 / 24 = 91.79 ppi. The dot pitch is 25.4 / 91.79 = 0.2767 mm. Its picture is 20.92 inches wide and 11.77 inches high. Asking for a 100 ppi screen of the same resolution gives a diagonal of 2,202.9 / 100 = 22.03 inches.
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Frequently asked questions
Is PPI the same as DPI?
No. PPI counts display or image pixels per inch, while DPI counts printer ink dots per inch. A printer may lay down several ink dots for each image pixel, so a 300 dpi printer is not the same thing as a 300 ppi image.
What density is considered sharp?
Around 110 ppi is comfortable at normal desktop viewing distance, and phones and laptops often exceed 300 ppi. Sharpness also depends on viewing distance, so a large television at several metres can look crisp at a much lower density.
Does PPI affect the physical size of an image?
Only when you also fix a physical size. The same 1920 pixel image is 6.4 inches wide at 300 ppi and 19.2 inches wide at 100 ppi; the pixels do not change, only the density at which they are shown or printed.
Why is my calculated PPI slightly different from the specification?
Manufacturers round the quoted diagonal and sometimes quote the viewable diagonal rather than the panel diagonal. A 23.8 inch panel sold as 24 inches gives a slightly different result.