16:9 on a 21:9 Screen

Vizio is introducing ultra-widescreen LCD TVs with an aspect ratio of 21:9. I believe their screen sizes will be 50, 58 and 71 inches. Can you provide the formula that reveals how large a 16:9 unaltered picture will be on such a screen? I’ve read elsewhere that a 50-inch ultrawide would produce an unaltered 46-inch 16:9 image, but I have no idea how 46 inches was arrived at.

Carl King

Keep in mind that the screen size of virtually all TVs—no matter what their aspect ratio—is measured diagonally so manufacturers can specify the largest possible number. Unfortunately, this makes the math a bit tricky. Using the Pythagorean Theorem (the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides), and knowing that the width of a 16:9 image is three quarters the width of a Vizio ultrawide set with the same height, I calculate that the diagonal measurement of a 16:9 image is about 0.8 times the diagonal measurement of the ultrawide screen. Thus, on a 50-inch ultrawide, an undistorted 16:9 image will measure only 40 inches diagonally.

This is akin to the transition from 4:3 to 16:9, when people had to buy a much larger HDTV than they thought in order to get a 4:3 image of the same size as their old square TV. So when going from 4:3 to 16:9 or from 16:9 to 21:9, get the largest screen size you can afford that will fit into the available space.

BTW, calling these ultrawide sets 21:9 is slightly misleading. 21:9 is equivalent to 2.33:1, but the Vizios' pixel array is 2560x1080, which translates to 2.37:1.