I've come up with a handy-dandy calculator which lets you input your diagonal screen size in inches and desired viewing angle in degrees. It spits out the appropriate viewing distance from your 16:9 HDTV screen, in feet and in screen heights, to achieve that viewing angle (i.e., the angle subtended on the retina by the full width of the TV screen). My single-purpose calculator was derived from the more elaborate one by C.M. Collins on this web page. Some folks may find mine easier to use.
The reason I came up with it is that I want to update what I originally suggested in On Viewing Distance. I said there that, however nice it might be to sit approximately 3 screen heights away from a 1080i image or 4.5-to-5 screen heights away from a 720p image, a 6x-to-7x seating distance was more doable in terms of "the exigencies of space, cost, and furniture arrangement." And I intimated that the compromise was perfectly OK.
Then last night I made a liar of myself. I was watching the DVR recording I'd made of HBO HD's The Matrix Revolutions. On impulse, in mid-movie I dragged a chair to the 30° spot that put my retinas roughly 8.3 feet (3.3 screen heights) away from my 61" screen. Plopping myself down in that "sweet spot" made all the difference. It turned a pallid viewing experience into an electrifying one.
The Matrix Revolutions is the final installment in the Wachowski brothers' Matrix trilogy. The original movie met with great applause, the second with much less enthusiasm, and the third with even less. The Matrix "world" is nonetheless one that, obviously, thrills a certain minority of moviegoers. I must say I'm not one of them. Yet when I watched the reputedly weakest of the three Matrix films in hi-def with a 30° viewing angle in my living room, I was swept away.
Whatever else you say about it, Matrix 3 has some pretty cool CGI battle scenes. They're primarily what won me over to the 3.3x/30° camp. I was immersed in the action to an extent I've never experienced at home before.
The psychology was weird. It was late and I was tired, so I was half tempted to shut down for the night and pick up on the morrow ... but I simply couldn't. I was in the grip of the time flow of the movie, and until it ended I knew I wasn't going anwhere. Part of me said, "C'mon. At least, hit pause. Break the spell." The rest of me said, "Not on your life."
I realized then that I had stumbled on the crucial difference between "watching TV" and "experiencing home theater." After all the pieces are in place — a 16:9 HDTV monitor, a 5.1 Dolby Digital sound system, an HD signal source — it's still not "home theater" until you achieve something close to the SMPTE-recommended viewing angle of 30°.
Note that the 3.3x/30° viewing distance/angle is, strictly speaking, right only for 1080i, not for 720p (which is what I actually have). As I said in On Viewing Distance, you need to get that close to 1080i to avoid compromising the ultra-fine-grain "retinal resolution" which the format offers. For 720p, though, 4.5x-to-5x gets you all the "retinal resolution" that format has to offer. Sit any closer and you invite "video noise, artifacts, and poor-quality low-resolution sources" to ruin your day. Moreover, you're eyeballs are supposedly apt to notice, and complain, that they're not getting full 1080i resolution.
Well, none of those things happened. The 1080i of the HBO HD transmission was converted to 720p by my cable box and exported to my Samsung DLP via DVI. On its screen I saw no noise, no artifacts, and no telltale signs of compromised video resolution. So I sat there wondering whether a true 1080i display would have given me any more convincing an experience than I was already having. My best guess was that it wouldn't.