# What size 16:9 equivalent to 36" 4:3?

Discussion in 'Displays' started by BrianCC, Oct 28, 2003.

1. ### BrianCC Member

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I watch a lot of 4:3 programming, but I want to buy a 16:9 HDTV before the Red Sox home opener in April. (Sox fans are masochists.) I just can't figure out the math: What size 16:9 set should I be looking at in order for 4:3 programming to be at least 36" corner-to-corner, without stretching, zooming, etc.?? (Yes, a 36" image not including the gray sidebars.) Thanks!

2. ### Mitch Stevens Well-Known Member

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You would need exactly a 44" Widescreen TV in order to get exactly 36" 4:3.

3. ### BrianCC Member

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Thanks for the quick reply, Mitch! Care to share the math? I don't question your answer, I'm just curious what the calculations are....

4. ### Mitch Stevens Well-Known Member

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Actually, I used a calculator that calcutes exact TV sizes and what you get with them:

http://www.cavecreations.com/tv2.cgi

Under 16x9 TV I input 44 inches, and it came out with a 36" full-screen mode.

5. ### BrianCC Member

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BadaBING! That's exactly what I was looking for! Thanks, Matt!

6. ### Tim K Well-Known Member

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You asked for the math so here you go!

Remember the old Pythagorean Theorem (sp?) from school and how you probably thought..."When will I ever need this in real life?" Well...here it is!

A^2 + B^2 = C^2 for right triangles. Cut a rectangle in half along the diagonal and you get a right triangle. So the diagonal measure of a TV is the same as the "hypotenuse" (sp?) of the right triangle formed by the width and height of the screen. So Width squared + Height squared = diagonal squared

The diagonal of the screen is 36". We know that the ratio of the width to the height are 4:3. So, Width = 4/3 height. Then substitute 4/3 Height for the width in the equation...

(4/3 H) squared + H squared = 36 squared
16/9 H^2 + H^2 = 1296
16/9 H^2 + 9/9 H^2 = 1296
25/9 H^2 = 1296
H^2 = 466.56
H = 21.6"

To get the same size picture in a 16:9 TV, you basically need to have the same picture height. So you know the picture height on the 16:9 TV must also be 21.6". Since you know the ratio of width to height is 16/9, the width of your 16:9 TV must be 38.4". So now you have the Height and Width...so back to Pythagoras (sp?) and his theorem.

H^2 + W^2 = Diag ^2
21.6^2 + 38.4^2 = Diag^2
466.56 + 1474.56 = Diag^2
1941.12 = Diag^2
44.06" = Diag

So a 44" 16:9 TV would give you the same size 4:3 image as a 4:3 TV. Now that you know how to calculate it, you can use the simple calculator without feeling like taking the easy way out!

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