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I bought an nice laptop with a HD 1920x1080 screen. The problem is text is almost unreadable, it is tiny. So I scaled the DPI (dots per inch) up to make the text readable.

What is the recommend setting for DPI? How do I calculate it myself?

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Watch out for some software that does not account for extra large text when you increase the font size by increasing the DPI. I've encountered fixed-sized windows (w/o scroll capability) that crop the text and push buttons. The only way to view the cropped info is to reduce the DPI. –  sawdust Sep 30 '11 at 10:21

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Regular computer displays are around 100 pixel per inch usually, with some of them, especially Laptop screens, going up to 150.

If you want to have all elements and text on the screen as large as a regular 100 dpi screen would show them*, look up your screen resolution / display size and adjust your software accordingly.

Or calculate yourself using the Pythagorean Theorem:

sqrt(pixelwidth*pixelwidth + pixelheight*pixelheight)/inches

This is about 116 for your screen, so that's what you need to tell your software.

* and this is an entirely personal preference — I like my screen elements smaller, so more stuff fits on the screen

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The DPI that is right for each individual is the one that looks right to them. Whatever you have it set to is correct and the recommended value.

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A suitable setting for DPI depends on screen resolution, screen size, distance between screen and eyes, your eyesight (which changes with age) and the strength of any glasses you are wearing.

I don't know of a rigorous quantitative well-tested formula that takes all these factors into account.

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