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I'm quite confused by the nomenclature; what does DPI really mean?

The way I interpret it, it says how many pixels there are per inch of the display. Now naturally, you can't change this (not on LCDs, anyway). But operating systems have a setting to "change" the DPI... but what does that mean?

If I "change" my DPI from 96 to 110, shouldn't that make everything smaller, because I'm supposedly fitting more pixels to every inch on the display (by definition)? Why does everything get bigger instead?

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Text size is normally expressed in points (of which there is a fixed value of 72 per inch on digital displays), not pixels. Therefore 12-point text will take 12/72*96=16 pixels on a 96 DPI display, but 12/72*110=18.3 pixels on a 110 display. Unless your display is capable of changing its native resolution on the fly (which would be a very neat trick to see), your text will appear 110/96-1=14.6% larger.

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What you change isn't the physical number of dots per inch on the display, it changes the number of dots your system believes are in an inch. So for a 12 point font, that's 1/6 of an inch, so it's 1/6 of however many pixels your DPI number is.

The same is done with images in some contexts which have a 'native' DPI [or are assumed to be 96 dpi] which is scaled to your system's DPI.

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Dots per inch comes from printing the image out onto paper.

So an image that is 800x600 pixels at 100 dots per inch will print at 8 inches x 6 inches.

The display uses this as a basis for determining the size of text on the display (as per Ignacio's answer).

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