Saturday, November 17, 2007

Screen Size Calculator

In 1080p, 1080i, and 720p I went into the abstract theory of HDTV resolution. Now for a more practical approach.

If you are in the market for a high-definition TV, you need to figure out what screen size to get. The screen size of a high-definition TV is its screen's diagonal measure in inches. For example, if an HDTV is advertised as having a 42" screen, then there are (nearly) 42 inches separating each pair of diagonally opposite corners of the screen.

Suppose you know that your new HDTV will be 10 feet from your eyeballs as you watch it from your accustomed seating position, and suppose the TVs you are looking at are 720p models featuring a horizontal resolution of 1280 pixels. If, in the table below, you enter 1280 (no commas, please!) as the horizontal pixel count and 10 as the seating distance, and click on "Calculate Now," the optimal screen size will be shown as 51 inches.

Enter horizontal pixel count:pixels
Enter seating distance in feet:feet
Optimal screen size:inches

This means a 51" 1280 x 720p HDTV would be, at a viewing distance of 10 feet, just about ideal. Any 1280 x 720p HDTV with a screen size near 51"— say, 49" to 53" — should do quite well.

By "1280 x 720p" I mean that the screen has 1280 pixels in each pixel row and 720 pixel rows up and down the screen. I specify the first number, 1280, because some HDTVs use a different number of pixels in each pixel row than their nominal format — in this case, 720p — supports. In my example, I am using the actual 1280 pixels per row specified for 720p digital television transmissions.

Since the final letter in 720p is "p," the pixel rows are lit up all at once in "p"-for-progressive fashion, rather than in "i"-for-interlaced mode, in which the even-numbered pixel rows are omitted in the first of two sequential screen refresh operations, then the odd-numbered rows are omitted in the next. (Of course, if the incoming digital TV signal is also interlaced, the TV does not actually omit any of its pixel rows.) The screen refresh mode, whether progressive or interlaced, actually has nothing to do with the horizontal resolution of the picture, stated as the number of pixels in each pixel row. It affects only temporal resolution: how often each pixel gets updated.

At that very same distance of 10 feet your eyes would not be able to pick up all the detail present on the screen of a noticeably smaller — say, 47" — 1280 x 720p HDTV. On the other hand, a noticeably larger, 56" 1280 x 720p model would present too little detail to satisfy your eyes at a viewing distance of 10 feet. The picture would look less crisp. Moving back just slightly to 11 feet away from this HDTV would remedy that situation.

The calculator shows that a "Full HD" 1920 x 1080i/p HDTV at 10 feet away would have to measure fully 77" diagonally to show you all its detail — try it in the table above! At 5 feet from your eyes, though, a set with that maximum-possible screen resolution of 1920 pixels per row could be a mere 38-incher. (The lesson here is that "Full HD" HDTVs have to be either very large or very close to your eyes to yield up all their glorious detail to your retinas.)

Some flat panel HDTVs offer 1366 pixels worth of horizontal resolution, whatever their 720p or 1080p nominal screen format might otherwise suggest. Often, the official resolution stated by the manufacturer is 1366 x 768. At a 12-foot seating distance, the optimal diagonal size of such a panel is 66". Other flat panels are limited to just 1024 pixels of resolution horizontally. At 12 feet, their optimal screen size is only 49".

With standard DVD fare, the upper limit on the horizontal resolution — that of the DVD itself, 720 pixels — will prove the limiting factor, no matter what the actual resolution of the HDTV. At 10 feet away from you, 720 pixels of horizontal resolution in the signal source demand just a 29" TV. But at 15 feet, that same standard DVD needs a 43" screen to show to best advantage.

If you watch nothing but standard-definition TV channels on your HDTV, the limiting factor becomes these channels' maximum available resolution. Stated in pixels across the width of screen, it's about 480 pixels per pixel row. At 10 feet away, a TV with a paltry 19-inch diagonal measurement would do! At 17 feet, you'd be forced to size up to a not-so-humongous 33".

Now, go ahead and play with the screen size calculator above to figure out what size HDTV you need!

This calculator assumes that the picture on an HDTV screen has an aspect ratio of 16 units wide per 9 units of height. It also assumes your eyes get all the picture detail they can handle when each pixel on the screen subtends an angle of 1/60° at your retinas. If it subtends a angle less than 1/60°, some of the fine detail in the picture effectively disappears — until you move closer to the set, thereby returning your retinas to the "sweet spot" where each pixel subtends 1/60°. If each pixel subtends an angle greater than 1/60°, on the other hand, your eye does not receive as much picture detail as it might wish, and the picture looks too "soft."

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