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## Custom Installer: Calculating HDTV Viewing Distances

People are generally either good with numbers or good with words. Pretty early on I discovered that my destiny lay with words. I don’t hate math, but I don’t really go out of my way to seek it out, either.

However, even for a custom installer, basic math skills can really help out. This is especially true when recommending screen size or calculating viewing distances. Unfortunately, many formulas are complex and difficult to remember: basically, all the reasons you dropped out of high school calculus. (Which I did. In a blaze of, “I will never use calculus. Never!” And, guess what, Mr. Fee? Twenty years later, I’m still not regretting that decision!)

If cosines, tangents, coefficients, and hypotenuses anger up your blood, then read on for some simple tips that might help out on your next TV purchase.

FIND THE WIDTH (AND HEIGHT)

When making the switch from 4 x 3 to 16 x 9, knowing how wide your new set can be is paramount, especially if cabinetry is involved. But since manufacturers only give you the diagonal measurement, what to do? Math.

Figuring the width on a 4 x 3 set is as easy as multiplying the diagonal measurement by 0.8. So, a 50-inch-diagonal 4 x 3 set is 40 inches wide. (Note: This is the screen size only, not including any frame.) If you need to know the height — important in the next section — multiply the diagonal measurement by 0.6, meaning a 50-inch-diagonal 4 x 3 set is 30 inches tall.

The width of a 16 x 9 set can be determined by multiplying the diagonal measurement by 0.87. So, a 50-inch-diagonal 16 x 9 set is 43.5 inches wide. To find the height, multiply the diagonal measurement by 0.49. So, a 50-inch-diagonal 16 x 9 set is 24.5 inches tall. Easy, right?

50 INCHES, 4 x 3 SET

SCREEN HEIGHT 30 INCHES SCREEN WIDTH 40 INCHES TOTAL SCREEN AREA 1,200 INCHES

50 INCHES, 16 x 9 SET

SCREEN HEIGHT 24.5 INCHES SCREEN WIDTH 43.5 INCHES TOTAL SCREEN AREA 1,066 INCHES

THE DOWNSIZING FROM 4 x 3 TO 16 x 9

I can’t tell you how often I hear, “Boy, that set doesn’t look as big as I thought” or “I wish I’d gone larger.” Ever wonder why everyone is having size issues? It’s due to the shrinkage from 4 x 3 to 16 x 9. While we gain some width, we’re losing a ton of height; that’s why the new set doesn’t look as big. In the above switch from a 50-inch 4 x 3 set to a 50-inch 16 x 9 model, we lost 5.5 inches of height and 134 square inches of screen real estate. So, yes, your new TV is smaller.

A good starting point for picking a new screen size is matching the old set’s height. This replaces the “Wow! That looks small!” reaction with “Man! Check out my sweet new TV!” To find a 16 x 9 set’s matching height, divide the 4 x 3 set’s height by 0.49. Keeping with the 50-inch example, dividing 30 by 0.49 equals 61, meaning that it takes a 61-inch-diagonal 16 x 9 set to retain the screen height. That’s why 60 is the new 50.

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