Why everyone in the media (and Nintendo) are wrong about the 3DS XL screens

I apologize in advance. Virtually the whole purpose of this article is to prove that I am right. In doing so, I do hope it will be informative and useful to those who read it. But it's not primarily for you. Buckle up, this might get wordy.





Let's begin with a question. What size is your PC screen? How about your television? Mine are 32” and 42”, respectively. And that is how most anyone would answer that question, with a single, simple measurement. Originally, televisions were constructed of round cathode ray tube (CRT) displays, and the only realistic way to measure them was by their diameter. Later these were encased in a rectangular bezel, with the corners at the edge of the round or roundish CRT. Thus, we inherited the diagonal measurement as something of an industry standard for display measurement in consumer devices. It's simple and elegant, and in combination with the aspect ratio provides all the information we could want about a given display's dimensions.

You may have inferred what I am driving at. Nintendo claims that the screens of the new 3DS XL are “90% larger.” I take issue not with the absolute accuracy of that statement, but the method by which they arrived at it, and the inherent deception therein.

The primary display (top screen) of the original 3DS measured 3.53”, or 90mm. You know, I'm just going to stick with Imperial units to make this easier. Now, lacking any sort of 3DS XL teardown or caliper measurement of the screen (as it's just today launched in EU territories), I'm going to rely on the figures provided by Wikipedia. Those state that the 3DS XL has a 4.88” top screen. Finding the rate of difference between these two measurements is easy, divide 4.88 by 3.53. The result, 1.3824... indicates that 4.88 is ~138% of 3.53, meaning a ~38% increase. (For what it's worth, the result is 1.377... if you do the calculation with metric units, due to imprecise unit conversion and lack of significant digits, I suspect.)

So where is the 90%? It's in the area.





I made a comment previously that used diagonal²/2 to compare the area of the two screens. That might be okay for an approximation, but it's only truly accurate in the case of a square where sides are equal.. So, in order to find the precise areas for comparison, I started by finding the aspect ratio. The lower screen is simple, 320x240 is a 4:3 display. The top screen has a resolution of 800x240, but as an autostereoscopic display, each eye perceives half of that 800 pixels independently; it is effectively 400x240. Divided, that is 1.66..., equivalent to a 5:3 ratio.

My math was a bit rusty, so I searched around to find this page with a convenient algebraic formula for determining the height and width. Essentially, our variables here will be as follows: x = unknown width, y = unknown height, m = known x ratio, n = known y ratio, d = known diagonal. Using the formula y = (dn)/√(m²+n²) we find the height, and the formula x = (m/n)*((dn)/√(m²+n²)) gives the width.

Using the above information, I've compiled a table of data.





You can clearly see that the area, a product of the width and height dimensions, is approximately 90% greater in the 3DS XL model. This metric was chosen to showcase the increased screen size for the obvious reason that 90 is a bigger number than 38 – it simply makes the marketing look better. However the area's multiplicative nature does not convey the actual improvement in usability. I refer back to the second paragraph; we intuitively use the diagonal measurement because it is simple and conveys the most meaning of any available physical dimension.

The chart also shows the relative reduction in pixels per inch (pixel density), and increase in dot pitch (measure from one pixel to the next adjacent diagonal pixel, usually expressed in mm), which is the direct result of increasing screen size while using the same resolution. This is why some early impressions of the 3DS XL have reported a slightly less sharp display. The pixel density has suffered at a rate of 27.6%, while the dot pitch has widened linearly with the screen size, at a rate of 37.8%.

And that number, 37.8%, is what I believe to be the most genuine measure of the improvement of the 3DS XL's screen size. LCD televisions and monitors aren't sold by their display's area in square inches or millimeters. No one this side of professional commercial displays uses that information, which is why I take issue with Nintendo using those statistics to derive their 90% number to market a consumer product.

I don't have a horse in this race – I neither own nor immediately plan to buy a 3DS, XL, or any of its competitors. I don't even expect this to change anyone's mind regarding a purchase decision. My only motivation is to cut through the marketing talk to arrive at honest information. And, of course, to show that I'm right.