# Having problems with the 16:9 calculations

Discussion in 'Displays' started by Monte Montemayo, Aug 14, 2004.

1. ### Monte Montemayo Agent

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Hey there, I am building a 16:9 screen but I’m looking for a formula so I know how to measure the screen. Essentially, I’d like a 100” screen but I’m confused on the measurements. I know I should have paid attention in 9th grade math class. So much for the saying, “I’ll never use this junk”.

2. ### DaveGTP Cinematographer

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Hypotenuse = diagonal of a triangle.

Using a right hand tringle to figure out the diagonal of a square:

Pythagorean theorem:

side1 squared + side2 squared = hypotenuse squared
x^2 + y^2 = z^2

so you want z = 100

so you want the square root of x^2 + y^2 to come out to 100.

and you want 16:9 ratio between x and y --> so pick a number for y, multiply it by 1.7777, and plug into the equation.

Looks like about 50" x 88.88" to me...that comes out to 101.986" diagonal. I think you could elimate the squares from the equation to come up with it exactly, but that would be too much math...

49" x 87.11" = 99.94" diagonal

Someone else to check my math would be appreciated - too much calculus damaged my algebra skills

That doesn't include a frame...depending on how you are doing the frame. I don't have one at all yet.

My screen was done more slapshod for my weak carpentry skills and equipment - I just used nice even hunks of wood. My screen is 51" x 72" --> 1.41:1 ... and I shoot 4:3 onto it - it is too big for the current setup. Maybe in the new house...

3. ### Monte Montemayo Agent

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Thanks! This is very helpful. I have my EXCEL program up trying to figure all this out. I appreciate this advice.

4. ### Monte Montemayo Agent

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I checked your math and you are correct. Well actually its 99.946 but close enough for Gov'mt work.

5. ### Scott Dautel Second Unit

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There's an easier way.....
For any 16:9 screen the diagonal is 18.36 (thank you pythagorus).
This is the only number you need to remember.
The ratio's will always work.

So for a 100" diagonal ...
height is 100*(9/18.36) = 49.02"
width is 100*(16/18.36) = 87.15"

Another example ... say you have 85" of width to work with:
diagonal = 85*(18.36/16) = 97.54"

Scott

6. ### Monte Montemayo Agent

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Ahhh.. there's always a secret. Too bad you didn't sit next to me in Math Class.

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