If you are just coming to this page to use the calculator, jump down to here. These next few paragraphs are for people who want a little background on the calculator and wide screen vs. traditional screen aspect ratios.

Anyone who is considering purchasing a new TV is probably at least considering the option of purchasing one of the new "wide screen" televisions. They are becoming more and more popular, and people tend to like the way the look if for no other reason than they look more modern than the mainly square televisions people have had for 60 years. The traditional TV screen has a width to height (aspect) ratio of 4:3 - that means that for every 3 inches in TV screen height, there will be 4 inches of TV screen width. The newer "wide screen" TV screen has a width to height ratio of 16:9, which means that for every 9 inches in TV screen height there will be 16 inches of TV screen width. If we go back to our 5th grade math class where we learned about fractions and denominators, we can figure out that the lowest common denominator for 16/9 and 4/3 is 9 - that is a 4:3 screen is the same as saying a 12:9 screen. Now when we compare a 16:9 screen to a 12:9 screen we can see that a new wide screen TV delivers 4 more inches of width for every nine inches of height as compared to a traditional screen. Clearly, this is what makes the traditional TV look pretty much like a square and a wide screen TV look much more like a rectangle. BTW - less often you'll hear the width-to-height ratios refered to as 1.33:1 and 1.78:1, which is just another way of saying 4:3 and 16:9 respectively.

So, you know all about screen ratios now, but you probably don't know the height or width of your current TV. Why? Because televisions are sold in diagonal inches. This holds true for both traditional TVs and the new wide screen TVs. The "inch size" of the TV always refers to the diagonal measurement of the TV - that is a 31" TV is 31" from one corner to the other corner. To figure out the width and height of your TV you would need to recall your 8th grade math class where you learned about the Pythagorean Theorem. You remember that of course! The Pythagorean Theorem states that A^2 + B^2 = C^2 where A & B are length of the sides of a triangle and C is the length of the hypotenuse. So, on your 31" TV where we are dealing with height and width and a diagonal corner-to-corner dimenson, we would say that W^2 * H^2 = D^2. Since we know that D = 31, we know that D^2 = 961. Knowing that, knowing that there is a 4:3 ratio between width and height, and knowing some basic algebra that we learned in the 9th grade, we can determine the height and width of a 31" diagonal TV. In case you are wondering, a 31" diagonal TV has a width of 24.78" and a height of 18.63".

Eventually if a person ponders the purchase decision enough, they'll come to discover what should have been an obvious fact. If televisions are sold by their diagonal measurement and wide screen and traditional TVs have different aspect ratios, then a 31" traditional TV will have a different height and width than a 31" wide screen TV. So, if you currently have a 31" traditional TV, you might wonder what size wide screen TV will give you the same "amount" of viewing screen. Well, there are two answers to the question. It depends on how you determine the "amount" of viewing screen you currently have. There are generally two ways: the square inches of viewing area and the viewing area height. Your 31" traditional TV has about 461.6 square inches of viewing area. To get a wide screen TV that has 461.6 square inches of viewing area, you'd need a 32.88" diagonal wide screen. As mentioned earlier, your 31" traditional TV has 18.63" of viewing height. To get a wide screen TV that has 18.63" of viewing height, you'd need to purchase a 38.04" diagonal wide screen. That's quite a big difference. But it is an important one. Which method should you choose for comparison? The viewing height comparison is most important. Why? Let me explain.

If you finally do decide to buy a 16:9 aspect ratio TV, you are going to learn something very quickly: not too many programs are broadcast or otherwise delivered in in the 16:9 format. Almost everything is produced in 4:3. As time goes on, and we get closer to the day when HDTV will be mandated by the FCC (currently set for the end of 2006), more and more programming will come in 16:9 format. Until then, however, what does your 16:9 TV do with 4:3 content? Well, it has two choices: manipulate the 4:3 content to fill the entire 16:9 screen or display the 4:3 content in a 4:3 ratio on your 16:9 screen. In the first scenario, the picture gets stretched and smushed to fit your 16:9 screen. At first this is hard to deal with because Jennifer Aniston ends up looking rather fat, your favorite NBA star looks way shorter than he should. You'll eventually get used to it, but most people don't like it. In the second secnario, 4:3 content is displayed in its natural format so Jennifer Aniston looks great and you can again understand why Shaq can dunk without jumping. But since your entire 16:9 screen isn't being used, you have two black bars on either side of the picture. This is called window boxing and is the opposite of a letterbox (where black bars are on the top and bottom of your 4:3 screen in order to display 16:9 content.)

So, why is viewing height comparison so important? Well, let's assume you decide to watch 4:3 content in its normal form allowing your 16:9 TV to window box the content. The height of your picture will be equal to the height of your screen. In the case of a 31" traditional TV, that means 18.63" of screen height. But, if you bought your wide screen TV based on a square inch comparison, you only bought a 32.88" TV (let's call it 33"). Well, at a ratio of 16:9 and a diagonal of 33" diagonal measurement, your screen is only 16.16" high. So you have a TV with 2" greater diagonal size, but because of the screen ratio difference, your wide screen TV actually has 2.5" less height than your 31" traditional TV. So, when watching traditional 4:3 content in its natural form on a 16:9 screen, if you buy a 16:9 based on a square inches comparison to your 4:3 TV, you'll end up with 4:3 content being displayed smaller than it is on your current set. If you buy a 16:9 TV based on a comparison of screen height, and you get a 16:9 with a height at least the same size as the screen height of your current 4:3 TV, then you can watch 4:3 content on your 16:9 TV at least at the same size you are watching your 4:3 content right now. And when you are watching 16:9 content it will be larger than your current 4:3 set. Now, if all you will be watching is 16:9 content or you don't mind a fat Jennifer Aniston, then you could save yourself some money by doing a square inches comparison.

As you can see, this is pretty complex. And it is just one of the many things to consider when purchasing a wide screen TV. I had asked myself all of these questions and more. Since I had already done the math, I figured it might be helpful to put together a calculator that others could use to do an "apples to apples" comparison of their current 4:3 screen size to a new 16:9 screen size.

The calculator will take a diagonal screen size and an aspect ratio, and it will calculate the height, width, and square inches of the specified TV. It will also compare the entered information to an equally sized TV in the other aspect ratio. It provides a size comparison in diagonal inches using both square inches of screen and height of screen. Finally, for illustrative purposes, it tells you the size of native 4:3 content displayed in window box on a 16:9 screen, or conversely, the size of native 16:9 content displayed in letterbox on a 4:3 screen.

Diagonal TV Size in Inches: TV Aspect Ratio: 4:3 16:9
A 50" diagonal 4:3 (1.33:1) screen will have the following dimensions:
Diagonal Inches Width Inches Height Inches Square Inches
50 39.964 30.0481 1200.8423

A 16:9 (1.78:1) screen with the same number of square inches as a 50" diagonal 4:3 screen will have the following dimensions:
Diagonal Inches Width Inches Height Inches Square Inches
53.0296 46.2332 25.9737 1200.8423

A 16:9 screen with the same height as a 50" diagonal 4:3 screen will have the following dimensions:
Diagonal Inches Width Inches Height Inches Square Inches
61.3482 53.4856 30.0481 1607.1407

A 50" diagonal 4:3 screen will display* a 16:9 program source at the following dimensions:
Diagonal Inches Width Inches Height Inches Square Inches
45.8388 39.964 22.4517" 897.2597
* - With letterboxing (black bars on top & bottom) a 16:9 program source displays as if it were a 45.8388" diagonal 16:9 screen.