# World widescreen web

Thinking of upgrading your conventional picture-tube TV to a fancy new flat-panel widescreen? But you’re on a budget and don’t want to go overboard? Confused about what size TV to buy? You’ve come to the right place.

The main criterion for choosing a screen size is one that I have not seen described in other TV buying guides: viewing area. The viewing area of a 32″ conventional TV is 492 square inches, whereas the viewing area of a 32″ widescreen TV is a mere 438 square inches! If you’re upgrading from a 32″ conventional TV you’ll want at least a 34″ widescreen to get the same viewing area.

Here’s how I arrived at those figures.

The advertised size of a TV display is the length of the diagonal. If from the diagonal we can determine the height of the display, h, and the width, w, then the viewing area is h×w. Thanks to Pythagoras we know that h2+w2 = 322. But this isn’t enough information to determine the viewing area: we also need the fact that the aspect ratio of most conventional TV displays is 4:3, which means the width of the display is four-thirds the height.

Substituting 4h/3 for w and then simplifying gives us:

h2+(4h/3)2 = 322
h2+16h2/9 = 322
25h2/9 = 322
h = √(9×322/25)
h = 3×32/5 = 19.2

Plugging that into the formula for viewing area (h×w) and recalling that w = 4h/3,

h×4h/3 = 19.2×4×19.2/3 = 491.52 square inches

Knowing that the aspect ratio of widescreen displays is 16:9 and using similar arithmetic gives a result of 438 square inches for a 32″ diagonal.

In fact, the math shows that for a given diagonal, the viewing area of a 16:9 display will always be about 11% less than the viewing area of a 4:3 display.

But wait! It’s not as simple as finding the widescreen TV that has at least the same viewing area as your conventional TV. You should also take into account the kinds of programming you watch.

Do you watch a lot of wide-format movies on your 4:3 TV? If so, you’ve certainly noticed the “letterboxing” needed to fit the wide aspect ratio of the film into the narrow one of the display. You’re not using the entire viewing area; some of it is wasted, as much as 32% of it for very wide format formats such as “CinemaScope.” With a 16:9 TV the need for letterboxing wide-format movies is decreased or eliminated.

Similarly, if you watch a lot of conventional TV programming (sitcoms, newscasts, etc.) on a widescreen TV, you’ll get “reverse letterboxing,” also called pillar boxing, where the black bars appear not on the top and bottom but on the left and right of the image to make the taller aspect ratio fit into a shorter one. Here again you’re wasting some of your viewing area.

So think about the kinds of programming you watch and consult this handy table that shows the true image size (in square inches) for various combinations of TV diagonal size, TV aspect ratio, and programming aspect ratio. Choose a TV that gives you the best image size you can afford for the types of programming you typically watch.

Program aspect ratio
1.33
(4:3)
very common
1.66
(5:3)
some movies
1.77
(16:9)
“widescreen”
1.85
(13:7)
VistaVision
2.35
(33:14)
CinemaScope
4:3
screens
20″ 192 154 144 138 109
27″ 350 280 262 252 199
32″ 492 393 369 354 279
36″ 622 498 467 448 353
42″ 847 677 635 610 480
46″ 1016 813 762 732 576
50″ 1200 960 900 865 681
16:9
screens
20″ 128 160 171 164 129
27″ 234 292 312 299 236
32″ 328 410 438 420 331
36″ 415 519 554 532 419
42″ 565 707 754 724 570
46″ 678 848 904 869 684
50″ 801 1001 1068 1027 808

## 2 Replies to “World widescreen web”

1. Though many 16:9 TV’s can upconvert a 4:3 signal so it can be displayed pretty well in 16:9 without looking stretched/squished. My TV does a good job of this. Personally, I think if you watch DVD’s at all, you’d have to be nuts not to get a 16:9, and there is a lot of HD programming nowadays as well.

2. I watched my first 4:3 title last night on our new 16:9 TV (Shut Up and Sing, highly recommended) and, using the TV’s automatic aspect-adjustment mode, it looked awful — the height of the image was preserved, and the width was stretched to fill the entire screen, making everyone look 33% fatter than they should have. (Which, in the case of some of the many ignorant rednecks in that film, yikes.)

The TV has another aspect-adjustment mode that widens the image but loses some detail off the top and bottom, like a vertical version of pan-and-scan. That was a little better. But I was happiest to watch the movie pillar-boxed in its correct aspect ratio.