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#### Michael Grant

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OK, here's a little trick I just realized.

Do you want to know the area of your 16:9 screen, in square feet? Just take the diagonal measurement, in inches, square it, and divide by 337.

Examples:

100" diagonal: area = 100 * 100 / 337 = 29.67 sq. ft.

120" diagonal: area = 120 * 120 / 337 = 42.73 sq. ft.

Believe it or not, this is exact, though only for 16:9 screens. The numbers just work out that way. This may not seem like a big deal to you but frankly I was tired of having to jump through some Pythagorean hoops to calculate the width and height of a screen from its diagonal, convert them to feet, then multiply them together.

If you want to compute your screen brightness in foot-lamberts, just take the calibrated brightness of your projector, in ANSI lumens, multiply by the screen gain, multiply by 337, then divide by the diagonal size (in inches), twice.

Example:

120" diagonal StudioTek 130, 600 calibrated lumens:

brightness = 600 * 1.3 * 337 / 120 / 120 = 18.25 ft-L.

Again, this is exact, but only for 16:9 projectors on 16:9 screens.

See? 337 is a home theater nut's favorite number.

Just remember it. 337. 337. 337. It will never lead you wrong.

Until you get a 2.35:1 screen.

#### David777

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Nice trick Michael.

Another helpful hint: Instead of converting the length and width to feet, just multiply and then divide by 144.

I can tell you've done a lot of math trying to calculate ftL. I feel your pain. I have full pages of formulas written for so many different screen sizes that I've lost count. I've done it so much that I've memorized the square footage of some popular screen sizes.

BTW how did you stumble upon this?

#### Michael Grant

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I stumbled on it because I wanted to compute screen areas from the diagonal size. So what I would do is numerically compute the width, then the height, multiply them together, and divide by 144 to convert from square inches to square feet. When I finally did this algebraically I found that the 144 goes away. You see:

W (in.) = D * 16 / sqrt( 9 * 9 + 16 * 16 ) = D * 16 / sqrt( 337 )

H (in.) = W (in.) * 9 / 16 = D * 9 / sqrt( 337 )

A (sq. in.) = W (in.) * H (in.) = D * D * 9 * 16 / 337 = D * D * 144 / 337

Then I would convert them to square feet:

A (sq. ft.) = A (sq. in) / 144 = D * D / 337

Bingo.

#### KBK

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Works great. All one has to do is remember '337'.

Now, what's the formula for 4x3?

#### KBK

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Oh. it's the same, but the divisor is 300. Stupid me.

#### darinp2

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Quote:
 Originally posted by KBK Oh. it's the same, but the divisor is 300.
And 400 for a 2.35:1 screen.

Just to summarize:

4:3 -> 300

16:9 -> 337

2.35:1 -> 400

I actually haven't figured out the reason that these are the numbers, though.

--Darin

#### craig john

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To get length and width, go to the screen calculator at projector central. The calculator allows you to input any one of the dimensions, length, width or diagonal, and it will calculate the others. Of course, you'll need to do the multiplication to get area, but that's the easy part.

http://www.projectorcentral.com/home.cfm

Go to Find Projectors, select your projector, go to Projection Calculator. It's pretty slick.

Craig

#### Michael Grant

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Craig, Craig... you're pointing us to a programmable calculator when we're all trying to figure out how to do this with a slide rule. Quit spoiling our fun. Seriously though, I'm finding it far too easy to use the 337 trick than to compute the width and height, when I don't need them for other purposes---even if I have a tricked-out web site to compute them for me.

Darin: Here's how to compute the "magic" number for any screen with an aspect ratio of x:y ...

magic number = ( x/y + y/x ) * 144

The reason the numbers work out so nicely for 4:3 and 16:9 is some nice cancellations occur. That doesn't happen for 2.35:1, which is actually 399.68 or so, so it's just coincidence that 400 works so well.

Now, you may ask, why is that the formula? Well, you'll just have to do the algebra yourself. I know you're capable

#### darinp2

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Quote:
 Originally posted by Michael Grant Now, you may ask, why is that the formula? Well, you'll just have to do the algebra yourself. I know you're capable
Thanks, I'll trust you. I was looking for an easy formula without going through all the algebra and was initially thrown off by the fact that 337 for a 16:9 screen is also 9^2 + 16^2 = 81 + 256 = 337. Looks like just a coincidence, though.

--Darin

#### Michael Grant

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Actually, Darin, it's not a coincidence, that's where the number comes from. The coincidence is that 6 x 19 = 144

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