Apr 282012

Computer monitor manufacturers quickly jumped on the widescreen technology bandwagon as soon as it appeared, not only because it was in the spirit of then new HDTV fashion, but also because widescreen displays have almost 12% less surface area than the (ex) standard 4:3 screens of same diagonal size. Profits increased due to initially higher prices and higher demand for widescreen monitors, but also because of less pixels required, and most manufacturers and consumers never looked back. Nobody blamed manufacturers because they were following the trend and everybody thought it was a win-win, except for the few of us who did the math to reveal how widescreen monitors of seemingly “same” screen size actually give less.

Monitor Screen Area Math

To calculate the screen area we need to first calculate the angle of the diagonal for each ratio so that we can use it in trigonometric formulas:

at 4:3 aspect ratio, the diagonal angle A = arctan (3/4) = 37.87°
at 16:10 ratio, the angle A = arctan (10/16) = 32.01°
at 16:9, the angle A is arctan (9/16) = 29.36°
(rounded to the second decimal)

since sin A = H / D (where H is screen height and D is screen diagonal),
and cos A = W / D (where W is screen width and D is screen diagonal),

we get:
H (screen height) = sin A * D, and
W (screen width) = cos A * D

Area = (H * W) or (sin A * D) * (Cos A * D), or thus
Area = D² * sin A * cos A.

The latter is my favorite if I have the diagonal size and the aspect ratio, so I don’t need to calculate the sides. Ultimately you can calculate theoretical constants for each ratio so you only have to multiply the applicable constant with the squared diagonal, in which case the theoretical formula for the monitor screen area can be expressed as

Area = D² * RC

where D is the monitor diagonal and RC is the screen aspect ratio constant which is for the above listed angles and formulas equal to 0.427 (for 16:9 screens), 0.449 (for 16:10) and 0.485 (for 4:3 screens), and thus

Area for 4:3 monitor is A = 0.485 * D²

Area for 16:10 monitor is A = 0.449 * D²

Area for 16:9 monitor is A = 0.427 * D².

These constants reveal that a 16:9 widescreen monitor of same diagonal size has close to 12% less real estate than the old-fashioned 4:3 (academy format) screen. The 16:10 monitor is a bit better with only 7.4% less area surface than the 4:3 screen. However, if you look at screen height, the experience is much worse than what the math is showing, because at 16:9 ratio and lower resolution (like in 1366 x 768 widescreen laptops as opposed to 1600 x 900 on 20″ monitors, or 1920 x 1080 on larger widescreen sets) you virtually always have to scroll down to see the full text, webpage or document.

20″ Monitors of Different Screen Ratio Compared

The screens with 20″ diagonal will have the following dimensions:

at 4:3 aspect ratio:
Height = 12.28″
Width = 15.79″
Area = 194 square inch

at 16:10 aspect ratio:
Height = 10.60″
Width = 16.96
Area = 180 square inch

at 16:9 aspect ratio
Height = 9.81″
Width = 17.43″
Area = 171 square inch

Clearly, the widescreen trend is a loss for consumers except for the ones who watch a lot of movies and work on wide spreadsheets. You can read about that and how to avoid some limitations of widescreen monitors in my widescreen rant post.

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