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

Demystify screen resolution with PPI: learn how to calculate pixels per inch and understand the physical properties of a screen.

Calculate Pixels per Inch on this e-reader with a six inch screen.

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.

Example of Pythagorean Theorem for Pixels per inch — Good old Pythagorean Theorem for Pixels per inch

Calculate the diagonal resolution in pixels, relying on the Pythagorean Theorem:

dₒ = √(w² + h²)

w = width and h = height
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.

1800 pixels in diagonal divided by the diagonal in inches gives a PPI of 300 pixels per inch.

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

Pixels Per Inch PPI Calculator