Monday, October 6, 2014

Apple Watch – Display Resolution and Display Dimensions



Hello everyone.

Today I want to share some thoughts about the Apple Watch which was announced on September 9th 2014 by Apple. On that day the rumors could finally be set aside and we got the facts straight from Apple. In early 2015 Apple will ship the Apple Watch in two sizes, three distinct collections and in several materials and colors. Unfortunately Apple did not share all the details about the device such as display dimensions and display resolution. These details however can be reconstructed if some valid assumptions are made.

Before I get into further details I want to clarify that in the following I describe my thoughts and I am not claiming to know the actual facts about the Apple Watch. I merely provide reasonable suggestions based on valid assumptions which I will get into shortly. First a quick detour to myself - I have my bachelor's degree in Industrial Engineering and I am working as a product- and price manager. I am also currently doing my Masters in Industrial Engineering. Because of that I have a background of dealing with numbers, calculations and solving problems.

That said….now let´s get to the interesting part of this post.

As mentioned before valid assumptions about some aspects are needed to reconstruct the display dimensions and display resolution. Assumptions about display size (the diagonal size in inch), the aspect ratio of the displays, the pixel density of the displays and whether both display sizes have the same resolution or not are needed. I will address each of these aspects next.

Assumptions for the Apple Watch:
 
1) Display size: 1,5 inch (small watch) and 1,65 inch (big watch)

This information were given by the very popular and reliable Website “theverge.com”. In their coverage right after Apple announced the Watch they wrote an article called “Apple Watch hands-on: a rounded, square wonder” (http://www.theverge.com/2014/9/9/6124253/apple-watch-hands-on-video-photos) and in that article they mentioned these display sizes.


2) Aspect ratio: according to Apple it is 1,25:1
Apple shows a lot of pictures of the Apple Watch on their website in the Gallery section (http://www.apple.com/watch/gallery/) and in one of these pictures the aspect ratio of the display can be determined very easily as shown below.


You can easily calculate the aspect ratio by dividing the pixels of the height and width when you measure it on your own display (dividing y by x).
Up to this point we have enough information to calculate the display dimensions in height and width. For that we need the display size (diagonal in inch) and the aspect ratio. I will show you the mathematical approach on the picture below.

Calculation of display dimensions:
 

With that in mind the display size comparison can be shown like the following.



3) Pixel density: Retina display equals 326 pixel per inch
According to the Apple Presentation on September 9th 2014 the Apple Watch will have a retina display. I think the Apple Watch display is viewed from the same distance as an iPhone display most of the time. Therefore I assume it will have a retina display by standards of an iPhone meaning it will most likely have a pixel density of 326 ppi.
Adding this information to what we have up until now we can almost calculate the display resolution. We only need one more assumption which I will talk about next.


4) Display sizes have the same resolution
I assume that both display sizes have the same resolution for convenient programming by the developers. Otherwise the developers will have to adjust their Apple Watch Apps for two pixel sizes and that’s unlikely in my opinion.

That means compulsorily that both displays might have different pixel densities. I want to explain that in more detail because the display resolution in this case will depend on which display gets a pixel density of 326 ppi.
a) The 1,5 inch display has a pixel density of 326 ppi. This results in a lower pixel density for the 1,65 inch display because of the same resolution.
b) The 1,65 inch display has a pixel density of 326 ppi. This results in a higher pixel density for the 1,5 inch display because of the same resolution.
 
Having said that now we can calculate the display resolution based on these valid assumptions. In the example below I will calculate the display resolution for the 1,5 inch display with a pixel density of 326 ppi (scenario a) from above) . The other display resolutions can be calculated with the same formula just by replacing the specific variables.

Calculation of display Resolution:

 
To simplify the calculation for the other displays the display resolution for the other displays are shown in the Excel-Sheet below.



I hope I could answer a few questions others might also have about the Apple Watch and what resolution and dimensions in might have. As I mentioned before these are reasonable suggestions based on valid assumptions and I am not claiming that they are actual facts.
This is my first blogpost. I am open for discussions and questions. Feel free to comment or give me feedback. Criticism is appreciated as well too.

Thanks for reading.

Yama


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UPDATE (October 6th, 2014)

I want to give you an update about the assumption I made about the pixel density of the Apple Watch. In my article above I bluntly assumed that the Apple Watch might have a pixel density of 326 ppi because of the standards Apple has shown on iPhone displays in the past. Although that might make sense to a certain degree one might think a pixel density of 326 ppi will result in non-practical display resolutions (as seen in the Excel-sheet above).

That’s why I thought about what pixel density will mathematically result in a practical display resolution for the new Apple Watch. To find a practical display resolution I simulated the calculation in Microsoft Excel (for both scenarios) and analyzed the results to give a reasonable suggestion.

Scenario a) - The 1,5 inch display has a fixed pixel density in a certain size. This results in a lower pixel density for the 1,65 inch display because of the same resolution.
Scenario b) - The 1,65 inch display has a fixed pixel density in a certain size. This results in a higher pixel density for the 1,5 inch display because of the same resolution.




In the Excel-sheet above I give two suggestions for each scenario. The first suggestion in each scenario shows a display resolution for a rather high pixel density. The second suggestion in each scenario shows a display resolution for a rather low pixel density.

I personally think these resolutions are more practical for programming and everyday use. Feel free to calculate other display resolutions based on your suggestions for pixel density and post it in the comment section. The mathematical approach I have shown above can be used to calculate the exact resolution for any pixel density and screen size.

If you have any questions fell free to ask me in the comment section too.

Thanks for reading further.

Yama