I want to be able to watch DVDs or shows that are supposed to be in 4:3 at the same image size as my old tv? Is there a standard formula, or does it depend on the size of the TV (mine is 27")?
If I understand the question correctly - you want to buy an HDTV sized so that, if you play a DVD in 4:3 mode on it (with black bars to the left and right), the picture will be the same size as your old SDTV.
Call D the diagonal size of the HDTV. Since HD sets are 16:9, the height of the screen can be found:
D^2 = h^2 + (16/9 * h)^2
Solving for h:
h^2 = D^2 / (1 + (16/9)^2)
h = D / sqrt(1 + (16/9)^2)
h = D / 2.0397
Since a 4:3 picture on the 16:9 set will have the same height, you can do the same thing to solve for h for a 4:3 set, using S as the diagonal size:
S^2 = h^2 + (4/3 * h)^2
h^2 = S^2 / (1 + (4/3)^2)
h = S / sqrt (1 + (4/3)^2)
h = S / 1.66667
So
D / 2.0397 = S / 1.66667
D = 1.224 S
So if your old TV is 27", the new one will have to be D = 1.224* 27 = 33" to preserve the size of a 4:3 image.
Nice work! I have a related question, if I may piggyback:
How far do I sit from an HDTV to appreciate the clarity of the picture? Or, how far away should I not sit, since I won’t be able to see the difference? Related to the size of the screen and the resolution, of course, so we’ll need another formula.
Thanks. That’s exactly what I was looking for.
Here’s a little article with some numbers.
It tells you the min. and max. viewing distance for both 4:3 and 16:9 TVs. Here is a nice website with a calculator.