Firstly, this isn’t your typical blog. There are no pictures included as all of the following is pure math. Leave a comment if you don’t understand and I’ll see if I can draw the formulae and scan them sometime. Alright, so you want to buy a new 30″ monitor but you’d like to know the exact height and width of the panel to get a feel for the viewable are on your desk before you buy it. How do you do it? Simple. You need the following:

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- Horizontal size (hypotenuse) of screen
- Aspect ratio

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For my example, I’m going to use a 19″ 16:9 aspect ratio screen. We are going to be using the formulae

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- sin(tan-1 height/width aspect ratio)*diagonal for height, and
- cos(tan-1 height/width aspect ration)*diagonal for width

- Fistly, 9/16 to get a decimal aspect ratio: 0.5625
- Using tan-1, we can work out the diagonal angle of the screen. tan-1 0.5625 = 29.358 , meaning the angle is 29.358° from horizontal.
- Use the following formula: sin (tan-1 result) * (diagonal size, hypotenuse) : sin 29.358 * 19: sin 29.358 = (0.49067565355234651434427338183771) * 19 = 9.3228374174945837725411942549166 = 9.32″ high
- Use the following formula: cos (tan-1 result) * (diagonal size, hypotenuse) : cos 29.358 * 19: cos 29.358 = 0.87157342826278517733892936862199 * 19 = 16.559895136992918369439658003818 = 16.56″ wide

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So we can see that the HxW of a 19″ 16:9 widescreen monitor is 9.32″ x 16.56″

How often do you see people referring to 2 x 19″ monitors side by side as an effective 38″? This is incorrect, to get 38″ diagonal you have to QUADRUPLE the area – i.e. double the 9.32″ height to 18.64″ as well as the width from 16.56″ to 33.12″. To calculate the actual diagonal of two monitors (using the specifications from the above example), we use the following formula, otherwise known as Pythagoras’ Theorem:

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- a² + b² = c² , where c is the hypotenuse

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For two 19″ monitors side by side, we retain a height of 9.32″ and double our width to 33.12″

To work out our new hypotenuse, or diagonal size, we can do the following:

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- ((9.32²)+(33.12²))sqrt, or
- ((9.32² = 86.8624) + (33.12² = 1096.9344) = 1183.7968) sqrt = 34.406348251449179331286630792993 = 34.41″ = 34.5″

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I hope that clears things up for anyone interested. If you have any questions or other areas (pun intended) you’d like covered, feel free to leave a comment.

## 10 Comments

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GauravWonderful explanation you have here! Pity I still have a 19 inch wide display in this day and age of 22+ inchers

The DukeLOL! … Just bustin your balls OJ

It was very informative and nicely explained. It is tough to explain math not being in person and you did it very well!

carpo93nice blog, very usefull but i do this kind of calculation in physics every day at schoolxD

Oj101Well Duke, you’re going to need 10s and a tape measure anyway, but if you’re sitting at home wondering if your desk deep enough to have that new 30″ monitor without it being too close you can now picture its height and width before buying. Without having the diagonal angle to work out height and width you would only be able to guess

WezI was thinking more in the line of using it when shopping for new monitors, especially for mixed size multi monitor setups

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The Dukeso what do all these fancy numbers tell me that 10 seconds and a measuring tape will not?

WezVery nice, I’ll stick a bookmark on this