This article was written by Don VanSyckel, the club president, as a part of "The President's Pen". This article appeared in the December 2020 WYSIWYG newsletter.
Monitor Sizes, What They Mean
by Don VanSyckel
For a little change of pace, I thought I'd present something for you to think about. The size of monitors (and TVs) are listed as a diagonal measurement. But what does a few extra inches actually get you. First a couple of definitions so we're all on the same page.
height (h) the distance vertically
width (w) the distance horizontally
diagonal (d) the distance from one corner to an opposite corner
area the height (h) times the width (w)
monitor ratio the width to height ratio
since monitors are rectangles d² = w² + h²
Today's computer monitor are mostly a ratio of 16:9. This means that if you take the width (no matter what it is), divide it by 16, multiply that answer by 9, and you get the height. You might have noticed that many monitors list their resolution as 1920 X 1080. (Note: using the previous 1920 / 16 = 120; then 120 X 9 = 1080.) Higher end monitors are generally 3840 X 2160, again the same 16:9 ratio.
The thing is monitors are not listed and sold by their width and height; they are sold by diagonal. So how do diagonals compare? How about a monitor that is 16" X 9" and a second that is 32" X 18". I trust you recognize that these two are both 16:9 ratio. The first has an area of 144 (16 X 9) in.² and the second an area of 576 (32 X 18) in.². The diagonal of the first is 18.36" and the second is 36.72". The second diagonal is exactly double the first just like the width and height. The area is 4 times as much (576 / 144). So you get 4 times the viewing area for double the diagonal.
Now here's the thinking part. Skip this if you want and jump down to the summary.
For all 16:9 ration monitors:
h/9 = w/16 becomes: h = (9/16) w
w² + h² = d²
w² + ( (9/16)w )² = d²
d² = (1 + (9/16)² )w²
d² = 1.316 w² ( actually 1.31640625 )
d = 1.147 w ( actually 1.1473474844178637061557324699192 )
w = d / 1.147
w = 0.872 d ( actually 0.87157553712454928420138727685257 )
h = (9/16) w
h = (9/16) (0.872 d)
h = (0.5625)(0.872 d)
h = 0.490 d ( actually 0.49026123963255897236328034322957 )
area = w X h = 0.872 d X 0.490 d
area = 0.428 d² ( actually 0.42729970326409495548961424332344 )
Summary:
I was looking on the web at 27" and 32" monitors, but how do the viewing areas compare?
27" area = 0.428 d² = 311 in sq ( actually 311.50148367952522255192878338279 )
32" area = 0.428 d² = 437 in sq ( actually 437.55489614243323442136498516321 )
The 32" diagonal is 18% (32 / 27) larger but the 32" area is 40% (437 / 311) larger.
So is the 32" monitor worth 18% or 40% more than the 27" monitor, today? Or just wait a few weeks and there will be another set of monitor prices.
End of Article