Pixels per Inch. Per inch?

Pixels per Inch. Per inch?

The physical properties of a screen, that is the number of pixels are not measured on a surface but as a line. Pixels per Inch (PPI)
Pixels per Inch. Per inch?
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.

Good old Pythagorean Theorem
  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 ereader

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 diagnal in inches gives a PPI of 300 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
PPI Calculator finds pixels per inch (PPI) and pixels per square inch (PPI^2). Calculate screen resolution and pixel density using width and height of display screen in pixels. Also find dot pitch and diagonal in pixels. Enter screen diagonal in inches or cm.