Oj0
03-11-2010, 03:08 AM
Alright, so you want to buy a new 30" monitor but you'd like to know the exact height and width of the panel. How do you do it? Simple. You need the following:
Horizontal size (hypotenuse) of screen
Aspect ratio
For my example, I'm going to use a 19" 16:9 aspect ratio screen.
We are going to be using the formulae
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
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:
a² + b² = c² , where c is the hypotenuse
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:
((9.32²)+(33.12²))sqrt, or
((9.32² = 86.8624) + (33.12² = 1096.9344) = 1183.7968) sqrt = 34.406348251449179331286630792993 = 34.41" = 34.5"
I hope that clears things up for anyone interested :)
Horizontal size (hypotenuse) of screen
Aspect ratio
For my example, I'm going to use a 19" 16:9 aspect ratio screen.
We are going to be using the formulae
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
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:
a² + b² = c² , where c is the hypotenuse
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:
((9.32²)+(33.12²))sqrt, or
((9.32² = 86.8624) + (33.12² = 1096.9344) = 1183.7968) sqrt = 34.406348251449179331286630792993 = 34.41" = 34.5"
I hope that clears things up for anyone interested :)