Here's how to manually calculate the pixel density of your smartphone's display


Color reproduction and overall properties aside, the pixel density is one of the more vital aspects of a display, regardless of the gadget it is "attached" to. It's an area in which our smartphones have witnessed a staggering growth in the past few years and it seems that the resolution bumps won't stop anytime soon. Let's talk about pixel density a bit, shall we?

Now, in case you're a smartphone geek, you certainly know what's the pixel density of your phone's screen. In case you don't (which we highly doubt, but still), there's an easy way to get around and calculate it on your own. Actually, there are two ways to do so, and have in mind that we're not taking a regular Google search as a viable option, since it's trivial and mainstream!

The more mundane and harder way is the old school manual one, which requires you to do some math. How long has it been since you've last exercised your algebra, hmm? Let's do it now. You need to know the resolution of the display as well as its diagonal. Provided that you have both in hand, you can apply them in the following formula, which is a slightly modified variation of the Pythagorean theorem:


With the above equation in mind, let's manually calculate the pixel density of a 5.3-inch 1080p display. As its resolution is 1080 by 1920 pixels and its diagonal 5.3 inches, we input these into the formula:


We square the width and the height of the display, then we add them to one another, and finally, find the square root of the sum in question. The outcome is the diagonal resolution of the display.


Finally, we divide by the screen diagonal and we get the sought pixel density number.


So, this is how the pixel density of a given display is usually found. That's the formula which is used in most cases. Of course, it's rather cumbersome and we doubt that anyone would actually use this in a real-life scenario. Still, it's curious to see what lies beneath the numerous PPI calculators available on the interwebs. Yes, these are extremely useful and we are used by just everyone. One of our favorite ones is made by Sven Neuhaus and can be found at https://www.sven.de/dpi/. It's as straightforward as it gets: you input the resolution, the display diagonal, and voila, the tool calculates the pixel density straight away. Here is it in action:


Of course, it's not the only PPI calculator available out there. What's your favorite one?

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20 Comments

1. B-power

Posts: 258; Member since: Feb 22, 2014

like I'm going to remember that.

3. Brewski

Posts: 691; Member since: Jun 05, 2012

That's why they made this article. So you can refer back to it if you need it. Or you can write the formula down. Or you can look up the phone in question on PhoneArena and it will tell you what it is. But really, if you're that bad at maths that you can't figure this out then maybe you shouldn't be concerning your little head with such big ideas as screen pixel density...

5. B-power

Posts: 258; Member since: Feb 22, 2014

that makes sense.

4. zeeBomb

Posts: 2318; Member since: Aug 14, 2014

Phonearena SLOWLY becoming anandtech. Nice guide i must say!

9. hellbread

Posts: 309; Member since: Nov 21, 2014

Or you can download first photo on your phone and keep it...

2. tedkord

Posts: 17356; Member since: Jun 17, 2009

It's just the Pythagorean theorem. The sum of the square of each side of a right triangle equals the square of the hypotenuse. So just take the sum of the two squares. Then take its square root. That gives you the number of pixels diagonally. Divide that by the number of inches diagonally, and you have pixels per inch. It's easy because the resolution of any display is advertised, and so is it's diagonal measurement in inches. You can also use it to calculate the two sides of the display in inches.

6. Ruturaj

Posts: 1484; Member since: Oct 16, 2014

You should look at how everyone messes up when it comes to circular display, when size is not a diagonal.

7. zeeBomb

Posts: 2318; Member since: Aug 14, 2014

I took my Nexus 4 and got 300.24. That's with the on screen buttons. With the full screen I get 317.8 PPI. Pretty handy I must say!

8. PeterK.

Posts: 314; Member since: Nov 13, 2013

Your algebra teacher likes this! Probably.

12. zeeBomb

Posts: 2318; Member since: Aug 14, 2014

Hey, peter you never know man.

19. Paella

Posts: 35; Member since: Aug 08, 2015

The PPI don't change. It is always 318 PPI.

11. amasog

Posts: 552; Member since: Aug 22, 2013

this is just a simple trigonometry. Pythagorean theorem, anyone?

13. roldefol

Posts: 4744; Member since: Jan 28, 2011

I've been doing these calculations for years, because I am a giant nerd. Come to think of it, this may be the only application for the Pythagorean Theorem I've encountered since high school.

15. PeterK.

Posts: 314; Member since: Nov 13, 2013

True, me either.

14. t184256

Posts: 14; Member since: Aug 28, 2015

The one that I wrote myself 6 years ago. It also gives me the size of the diaplay in mm and the area of it in cm2.

16. PeterK.

Posts: 314; Member since: Nov 13, 2013

Mind sharing?

18. t184256

Posts: 14; Member since: Aug 28, 2015

gist.github.com/t184256/a54ca203e7fbfcc69416

20. PeterK.

Posts: 314; Member since: Nov 13, 2013

Neat-o!

17. t184256

Posts: 14; Member since: Aug 28, 2015

gist.github.com/t184256/a54ca203e7fbfcc69416

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