# How to calculate your video screen area



## twilyth (Feb 15, 2011)

Often it is very helpful to compare the area of a video monitor's display.  For example, if you go from a 22" to a 24" screen, how much bigger is that in terms of total area.

The calculation requires several steps and application of the Pythagorean Theorem, but it is all basic algebra.  I have a spreadsheet set up on Google docs so I can access this information whenever I need to.

Here are the steps I use in my spreadsheet to do the calculation.  Each step corresponds to a column as you will see in the screen shot at the end.

*Methodology:*

First you need to know the aspect ratio.  This will usually be 16:9 but in some cases might be 16:10.

The aspect ratio tells us the relative values of the width and height since it is basically saying that for every 16 units of width, there will be 9 units of height.

However you can't directly compare the absolute values of the aspect ration which has no units of measurement associated with it to the measurement of the diagonal which does.  You can however compare the relative ratios.


*Calculations:*

So, using the Pythagorean Theorem, you know that if you add the squares of the width (16) and height (9), you will get the value of the hypotenuse (diagonal) squared.  For a ratio of 16:9, 16^2 + 9^2 = 337.  The square root of this is about 18.4.

In other words, when the width is 16 units and the height is 9 units, the diagonal will be 18.4 units.

Since 2 screens with the same aspect ratio will always have the same ratios between their diagonals, height and width, it's easy now to calculate the precise dimensions based on the length of the diagonal.

First, calculate the ratio of the diagonal in inches (or other unit of measurement) to the aspect ratio diagonal - which in the case of an aspect ratio of 16:9 and a 22" screen will be 22/18.4 = 1.198

Now, use this number, 1.198, to directly calculate the the height and width in inches.

So the width will be 16 x 1.198 = 19.17.  And the height will be 9 x 1.198 = 10.78.

Finally, multiply the height in inches by the width in inches to get the area in square inches.  In this case the area of a screen with a 22" diagonal will be 19.17 x 10.78 = 206.8 sq. in.

As you can see, the calculations do involve a few steps but are not at all difficult to do.

*Example:*
Here is how I have my spreadsheet set up.







Let me know if I have made any serious errors.  I have checked the calculations against a few monitors and they seem to work.  Thanks


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## Maban (Feb 15, 2011)

I just use this: http://www.silisoftware.com/tools/screen.php


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## TheLaughingMan (Feb 15, 2011)

I use this to compare two displays together:  http://www.displaywars.com/


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## twilyth (Feb 15, 2011)

Maban said:


> I just use this: http://www.silisoftware.com/tools/screen.php





TheLaughingMan said:


> I use this to compare two displays together:  http://www.displaywars.com/



It never really occurred to me to find a web site that would do the calculations for me since the math is so basic.  

Also, having this in a spread sheet let's you do other calculations that may be useful.  For example, I often modify my spread sheet to calculate percentage change from one monitor size to another.  I can also add cells to calculate cost per square inch and many other parameters that I find useful.  This will be more difficult to do with a canned application that only lets you do certain things directly.

And while you may be able to do simple comparisons between 2 monitors, it may not always be so simple to do other calculations that the site designer may not have considered.

Finally, don't you get a greater sense of satisfaction from knowing how to do something yourself rather than relying upon a black box type of application.  I certainly do.


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## Maban (Feb 15, 2011)

twilyth said:


> Finally, don't you get a greater sense of satisfaction from knowing how to do something yourself rather than relying upon a black box type of application.  I certainly do.



In America? Surely you jest.


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## twilyth (Feb 15, 2011)

Maban said:


> In America? Surely you jest.



Of course.  We are a country of gear heads and do-it-youselfers.  Those attributes just don't tend to apply to more theoretical types of problems.  But as a people, I think we are known all over the world for being independent and self-sufficient.


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## TheLaughingMan (Feb 15, 2011)

twilyth said:


> For example, I often modify my spread sheet to calculate percentage change from one monitor size to another.  I can also add cells to calculate cost per square inch and many other parameters that I find useful.  This will be more difficult to do with a canned application that only lets you do certain things directly.
> 
> Finally, don't you get a greater sense of satisfaction from knowing how to do something yourself rather than relying upon a black box type of application.  I certainly do.



Well the percentage of difference is on Display wars for each aspect ratio a movie may be formated it when you watch it, but I digress.  While you are right that would be able to add more calculations, you would not be able to do cost per square inch.  A figure like that would depend on too many factors such as brand, sales, location where it was purchased, and the type of display.

I didn't say I could do the calculations, as I have done them before.  We both just decided that it was easier to check the interwebs first to see if anyone already did it.


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## twilyth (Feb 15, 2011)

TheLaughingMan said:


> Well the percentage of difference is on Display wars for each aspect ratio a movie may be formated it when you watch it, but I digress.  While you are right that would be able to add more calculations, you would not be able to do cost per square inch.  A figure like that would depend on too many factors such as brand, sales, location where it was purchased, and the type of display.
> 
> I didn't say I could do the calculations, as I have done them before.  We both just decided that it was easier to check the interwebs first to see if anyone already did it.



My only point was that you have a lot more flexibility by creating your own spreadsheet.  If you don't need that flexibility or don't want the hassle, that's certainly a valid personal choice.


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## TheLaughingMan (Feb 15, 2011)

twilyth said:


> My only point was that you have a lot more flexibility by creating your own spreadsheet.  If you don't need that flexibility or don't want the hassle, that's certainly a valid personal choice.



Incidentally, I used completely different math than you did.  I used more calculus, but I was in cal 3 at the time and this model was a test I was conducting.


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## douglatins (Feb 15, 2011)

I would use (sin(atan(9/16))*diag) x (cos(atan(9/16))*diag) whoops... damn it must be ok, i have been working for a long time

Yep, tried, same results, you could make the formula more fancy, like =SIN(ATAN(9/16))*COS(ATAN(9/16))*DIAG^2

22	206,8130564
24	246,1246291
26	288,8545994
28	335,0029674
30	384,5697329
32	437,5548961
34	493,958457
36	553,7804154
38	617,0207715
40	683,6795252
42	753,7566766
44	827,2522255
46	904,1661721
48	984,4985163
50	1068,249258
52	1155,418398
54	1246,005935
56	1340,011869

LOL there 1 step


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## twilyth (Feb 15, 2011)

TheLaughingMan said:


> Incidentally, I used completely different math than you did.  I used more calculus, but I was in cal 3 at the time and this model was a test I was conducting.





douglatins said:


> I would use (sin(atan(9/16))*diag) x (cos(atan(9/16))*diag) whoops... damn it must be ok, i have been working for a long time
> 
> Yep, tried, same results, you could make the formula more fancy, like =SIN(ATAN(9/16))*COS(ATAN(9/16))*DIAG^2
> {snip}
> ...


I've taken calculus and analytical geometry, trig, matrix algebra, etc.  I'm sure there are any number of ways to do this but I wanted to use the method that made the most intuitive sense to people and would be the easiest to follow and replicate.  

If I just toss a formula at someone and they have no idea what it means or how it works, then it impairs their ability to make their own additions - which in some cases may require an understanding of how each measurement is derived.

But thanks for posting alternative methods for the people who will understand them and be interested in utilizing them.


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