Pixels per Inch (PPI). Measured as a line or a square?

For years, I tried to figure out screen resolution in relation to the physical properties of a screen. Only now I understood that the physical properties of a screen, that is the number of pixels, are not measured on a surface but as a line.

So when it says 300 pixels per inch, these are on a line an inch long. And there are many more on a square inch. There are 90,000 physical pixels on a square inch of such a screen. Of course, assuming the pixels are squares.

A bit one dimensional to mix up lines and surfaces when defining resolution 😉

Calculations

To have this figured out made me happy. This new knowledge gave me insight and input for calculations.

The PPI of a display can be derived from the diagonal size of a screen in inches and the resolution (horizontal and vertical) in pixels. The calculation is done in two steps.

1. Calculate the diagonal resolution in pixels, relying on the Pythagorean Theorem:
   
   dₒ = √(w² + h²)
   
   w = width and h = height
   
2. Calculation of the PPI is the total numbers of pixels divided by the diagonal size:
   
   PPI = dₒ/dᵢ

With these two simple formulas, I can plug in the numbers.

Outcome for my e-reader

So for the screen of six inches diagonal and resolution of 1072 by 1448 it is:

dₒ = 1801.6

It is six inches, and so I divide by six.

PPI = 300.27.

Close! Pretty, pretty close. And now the theory is clear, I also can use and understand this calculator:

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