A Bit of Perspective

And math!

Everyone who sees it loves the iPhone’s Retina Display, but there are new 720p smartphones coming out that are getting some people to gabber joyously.

And so I asked myself the question, “What would the screen size need to be for a 720p Retina Display?”
First, what is Apple’s Retina Display? The screen is 960 x 640, and is 3.5 inches diagonally. As we’ve been taught by Pythagoras, the area of the square drawn on the hypotenuse of a right triangle is equal to the sums of the areas of the squares drawn on the other two sides, so we can find out how many pixels there are diagonally.
960 * 960 = 921600
640 * 640 = 409600
The root of 921600+409600 is ~1153.8

So, diagonally, we’re talking about 1153.8 pixels per 3.5 inches, or 329.65 pixels per inch.

Now we work backwards. If a phone had a screen of 1280×720, and had a resolution of 329.65 pixels per inch, what physical size would that be?

Pumped through the Pythagorean theorem, 1280×720 is 1468.60478 pixels diagonally.
That many pixels at 329.65 pixels per inch is about 4.4 inches diagonally.


A smartphone with a 720p display who wants to say it’s competing with Apple’s display must have a screen size of 4.4 inches or smaller. If a 4.5″ screen is touted the same way, they’re lying.

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