I was recently asked an interesting question about how the area of a widescreen compares with the area of a traditional display. Now, usually, one hears that you get to see additional parts of the picture on a widescreen, so that was my conditioned response. However, I decided to delve into the math a bit, to see if that proved to be true. As it turned out, you don’t get more area on a widescreen display.
A traditional display has a ratio (width:length) of 4:3, screen size is typically given as the diagonal (or if we are thinking triangles, the hypotenuse).
d represent the diagonal
w represent the width
h represent the height
A represent the area
We get two equations:
Using the Pythagorean theorem:
Using the ratio of length to width:
Equation 3, comes from substituting 2 into 1, we get:
Equation 4 comes from substituting 3 into 2 we get w, which we will use to find area:
Therefore, the area of the 4:3 display (equation 5) is:
Following the same procedure for the 16:9 display, we get:
The ratio of the area of the 4:3 display to the 16:9 display, therefore, is:
In other words, you get about 12% extra screen area on a traditional, 4:3 display, compared to a widescreen 16:9 display. Not exactly a revelation perhaps, not something that immediately springs to mind. The advantage (of the widescreen), perhaps comes in the form of usable area for an image displayed in widescreen, where the 4:3 display will likely have less usable area.