Is anyone else miffed when manufacturers only give you the diagonal measurement of the screen? I am. When you’re working on a touch screen keyboard, the width of the screen matters. The width of the screen is the practical limit of the key width. It would be nice if the key width was close to the width of my fat fingers. So I am interested in not just the pixel count (640×480 or 320×640) but also the size of each dimension.

Tapping my temple with my forefinger, I hit upon a solution provided by one Pythagoras a few years ago. Typically, the folks reviewing devices with screens will rave about the diagonal measurement, also known as a hypotenuse. The other measurements, the width and height are usually only given in pixel count. But some re3ally bad screens have lots of pixels but they are far apart. Some reallly good screens have fewer pixels, but much closer together. Let’s use these two facts to determine actual screen measurements!

Since the goal is to figure out the relationship between the pixels and the inches we have to use Pythagoras’ theorum to calculate that relationship. As you may recall, this says:

Hypotenuse is equal to the square root of the sum of the squares of the other two sides.

For the iPhone, the hypotenuse is 3.5 inches (I’ll use inches rather than millimeters to simplify my life). The screen width  is 320 pixels and the screen height is 480 pixels. So our formula becomes

3.5 = √(320)² + (480)²

Now we know that, the iPhone uses 576.88 pixels per inch. Well, we do if you do the math! That means that the width of the iPhone screen is

1.94 inches = 320 pixels / 164.8 pixels per inch wide

2.91 inches = 640 pixels / 164.8 pixels per inch long

The HTC (Sprint) Touch Diamond has a fabulous screen! It’s 2.8 inches measured diagonally with a 480×640 pixels. Using this information we now know that the Diamond measurements are

1.68 inches = 480 pixels / 285.7 pixels per inch wide

2.24 inches = 640 pixels / 285.7 pixels per inch long

The fabulous Palm Pre, which I’ve considered buying, is advertising a screen of 3.1 inches diagonally measured at the same resolution as the iPhone which is 320×480 pixels. This makes the screen size of the Pre

1.72 inches = 320 pixels / 186 pixels per inch wide

2.58 inches = 640 pixels / 186 pixels per inch long

My fingers are about 1/2 inch at the tips. The typical software keyboard has 10 keys on the QWERTY row. For the iPhone that leaves you with approximately 2/10ths of an inch per key plus the line in between each one. On the Diamond, it is about 1/6th of an inch per key. Which explains why the soft keyboards on the iPhone and iPod Touch seem easier to use… they’re around a whole .04 inches wider!