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We've been discussing this in the Comms Room on Serverfault, and thought it might make a good question on SuperUser...especially if there's a clear answer. The hope is that it is a Good Subjective question.

Why do laptop screen sizes come in the fractional sizes they do instead of 11/12/13/14/15"? The most frequent I see advertised are 11.6", 12.5", 13.3", 14", 15.6". What's the reasoning behind it? keyboard size? ergonomics? resolution requirements? Most are LCD screens just like TV's, and yet TV's are advertised as whole numbers (19", 26", 46", etc.).

Looking at actual LxWxD dimensions on laptops doesn't really help since screen bezels vary in size.

For instance:

example 11.6" laptop dimensions = 11.55" x 8.50" x 1.27" -- this is due to a rather large bezel.

Whereas my x1 carbon touch, 14" diagonal screen but dimensions = WQHD Touch: 13.03" x 8.94" x 0.55" (Front)-0.79" (Rear) -- again bezel...if it could be edge to edge that would be different, and "normal math" would insist the actual "monitor size" was about 15.5", which it is if you include the bezel.

SO:

Are there actual equations/ratios/mathematical factors in determining screen sizes on a laptop that make certain sizes more common than others? Note I stated screen size (like the common 11.6", 13.3", 15.6", etc.) and not actual dimensions of the monitor lid itself.

TO HELP CLARIFY THE QUESTION:

I'm asking why those particular fractional sizes are so common? Look at HP, Lenovo, and Dell. They all tend to go with those screen sizes. Is it because it is what the consumers are used to seeing/using? Is it dictated by resolution requirements that dictate the screen size (meaning 11.6" works out resolution wise, but 11.7" doesn't)? Or is it something else? If you want to hone in on one: Something somehow determined that 11.6" was a good common screen size...I'm curious what that was.

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    A lot of laptop manufactures do not produce their own screens. They probably adopt which ever screen they can get from their vendor at the best price/quality point. 
    – kobaltz
     Apr 21, 2014 at 15:10
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    @kobaltz - ? LCD manufacturers don't make a bunch and put them on the shelf waiting for HP/Lenovo/Dell to come calling. The laptop OEM dictates size and specs to the LCD manufacturers. 
    – TheCleaner
     Apr 21, 2014 at 15:15
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    @kobaltz That would be in contrast to selecting screens from LCD panel manufacturers based on the worst price/quality point, right? 
    – HopelessN00b
     Apr 21, 2014 at 15:16
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    I think it also has to do with pixel density. These days manufacturers build screens with a large choice on density, but I think this was not the case some years ago. For TV, it is the same as desktop PC screen. Some are advertised as 22" but in reality the LCD is 21,6". If you look at the real specs of the monitor, you'll probably see different data than the advertised ones. Why are laptop screen (and smartphone too) not advertised this manner ? I don't know. It may be related to the smaller screen consummers want nowadays on handled/laptop device, and the bigger on desktop/TV. 
    – piernov
     Apr 21, 2014 at 16:06
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    The relation between neighbouring sizes may be related to the manufacturing technology - if you're currently cutting a glass/lcd plate into 14" pieces, and then want to make a larger/smaller screen from the same-sized plates, then there are very few numbers that "make sense", i.e., divide the same plate without wasting material. Just a hypothesis, but it seems reasonable given that process, i.e., many different screen sizes from a single standard of large screen plates. 
    – Peteris
     Apr 21, 2014 at 20:37 

3 Answers

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Display sizes are determined primarily by how many displays will fit on one mother glass slab at the manufacturing plant.

The manufacturing plant starts off with a single slab of glass, onto which the displays will be manufactured. Mother glass sizes are mostly standardized in the industry, and are increasing:

Generation     Size (mm)                  Diagonal (inches)
1st            300 ×  400                    19
2nd            400 ×  500                    25
3rd            550 ×  650                    33
4th            680 ×  880 or 730 × 920       43 or 46
5th           1000 × 1200 or 1100 × 1300     61 or 67
6th           1500 × 1800                    92
7th           1900 × 2200                   114
8th           2200 × 2400                   128
9th           2400 × 2800                   145
10th          2850 × 3050                   164
10.5          2940 × 3370                   176
11th          3200 × 3600                   189

The larger a piece of mother glass is, the harder it is to work with, due to breakage. However, throughput is counted by number of working displays at the end of the line, and certain line processes take the same amount of time for a small piece of glass as for a large one. So to increase throughput, increase the mother slab and put more displays on it.

It doesn't make sense to create a manufacturing line for a single size of display. It makes more sense to create a manufacturing line that handles the same size mother glass slab, and just change the number of displays created from the mother glass slab based on the order requirements.

Since the manufacturing line glass isn't going to change in size, once you know about the size of the display you want, you can determine how many of them can fit onto one mother slab. If there's additional space, it makes sense to increase the size until you're using as much space on the slab as possible, without going over your size requirement.

So the 10th generation glass will make one 150" TV (which is only used at tradeshows simply to showcase the size of the mother glass a given factory can handle), or it will make nine 50" TVs. The second generation glass was able to make a nice 24" desktop display, or four 11.6" displays.

A more in-depth treatment of this can be found at Norm's Flat Panel. AUO has a nice interactive diagram that shows cutting patterns for a few sizes up to generation 8.5 glass. While I included 11th generation size, there are no plants currently operating at this size. Corning announced the world's first 10.5 generation glass substrate factory in December 2015, and it will take some time to build.

Keep a watch for the next tradeshow as other manufacturers demonstrate 150" TVs to show off their new 10th generation plants, and eventually 170" TVs as the first glass rolls off this new plant's line.

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32

The specific sizes that are in common use today are due to a mix of the following factors:

  • 16:9 aspect ratio has completely taken over the market, due to movies and TV being produced in this aspect ratio, so the only way to display square pixels of 16:9 media (equal width-height ratio with no black bars) is to have 16:9 screens. This makes 4:3 and other aspect ratios pretty much obsolete.
  • It is a well-known fact that almost all laptop manufacturers do not develop every single component they use in-house. Since this is the case, they have to work within specifications of components that are available commercially from other companies. Other companies, in turn, will tend to offer components designed only for a handful of sizes, because they want to be able to sell their product to several vendors.
  • The "de facto effect" causes most (though not necessarily all) vendors to adopt the common sizes which have been chosen. It's generally very difficult to trace the "roots" or "origin" of these size profiles, but sometimes you'll find them in specified in standards documents or industry consortium documents.

Consider all the components which are impacted by the display size (because the other components must be sized relative to the display size):

  • The motherboard
  • The GPU (or more specifically, whether a dedicated GPU is even possible)
  • The weight and thickness of the laptop chassis (make a light, thin lid and a bulky, heavy base and your laptop will be very unstable and liable to break off the hinges, as well as being very fragile if dropped or struck)
  • The size and aspect ratio of the keyboard and touchpad
  • The battery, which is very bulky and heavy, must be designed to support operating at least a reasonable number of hours with the display on, which consumes a substantial fraction of the system's total power draw
  • The size of the bezel of the screen, which must be larger and sturdier if the screen is larger, to provide better support to the glass pane

There are so many things that depend on the size of the screen that exact sizing of all the parts is important. Therefore, unless you are making all the parts yourself, which few do (not even Apple; a lot of their components are commercially sourced), you are pretty much going to be swept along into falling in line with the de facto form factors.

As to your question of whether there is a reason why 13.3" instead of, say, 13.2" was chosen? No, not really. In 3D space, assuming you have exact control over the manufacturing process down to an extremely high precision, you can chunk out a laptop at almost any size; as long as you maintain the proper balance and ratio of size and strength of the components, it'll work fine. If you made an ever so slightly smaller screen, you'd have to have an ever so slightly smaller battery, chassis, keyboard, touchpad, etc.

The standard sizes were probably a result of usability studies and experiments, and were not chosen totally arbitrarily by someone picking a number out of a hat, but it's not like laptops would be less efficient or simply not work if the display had a 13.2" diagonal instead of 13.3".

One way to think of the decision-making process that went into today's presets is that, if you were designing a bunch of laptops in different form factors and you tried to make each laptop "well-balanced" (doesn't tip over, sits firmly on desk, good weight ratio between base and display panel, etc.), then you had people try out the various laptop sizes, you might hear various complaints from the testers:

  • My hands don't fit on the palm rest. It's too short.
  • I have to reach too far to hit these keys.
  • The keys are too small for me to reliably hit them.
  • The huge screen bezel looks like a waste of space; I want the display closer to the edge of the panel.
  • The system feels like it's much heavier than it should be for a system this size.
  • The screen wobbles when I type; it's too light or the hinge is too loose.

Several of these complaints could be narrowed down to "if we change the size of the laptop, we'll be able to solve this problem". For instance, if you have a 13.2" size (and consequently a smaller bezel and chassis, as you don't need these to be quite as big with a smaller display), people may feel that the palm rest is too short. Or if you make the keyboard narrower and the palm rest longer, people may say they have to reach too far with their fingers to hit the keys.

Ergonomic studies are much less equations in a blackboard, and much more empirical testing with sample units and a wide variety of shapes and sizes of people. Ergonomic studies, in turn, inform what component and laptop manufacturers consider to be the most desirable sizes. Once they've isolated those sizes, they go into mass production, to take advantage of economies of scale.

When you're dealing with physical objects subject to gravity and momentum and so forth, the important part is the ratios and densities of the various parts relative to one another; the absolute size is less important from a pure system architecture perspective (although the absolute size is informed heavily by ergonomic studies).

The absolute size would be important if, for example, laptops were frequently subject to significant air resistance, as in the case of an airplane. But they aren't (at least I hope so; otherwise your laptop is in for a world of hurt!) So, based on that fact, I conclude that the sizes that are standard across laptop manufacturers are a result of industry inertia, economy of scale, ergonomic study results, and standardization of commodity parts, moreso than any other factors that may be at play.

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    More "internal research" in the Comms Room -- Looking at this table: en.wikipedia.org/wiki/Display_size it would seem that the metric system pretty much dictates screen dimensions, and that the fractional inches measurements are there for us Americans. Therefore, a diagonal screen of 13.2" can't really exist easily without the W or H being some fraction of a cm. Agree? 
    – TheCleaner
     Apr 21, 2014 at 16:05
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    @TheCleaner Since they've rounded all the cm sizes to integer values in that table (ex in the top row: 9cm 16:9 is listed as 8x4cm); I'm not sure it's safe to assume that the actual panel sizes are even numbers of centimeter in the diagonal. 
    – Dan Is Fiddling By Firelight
     Apr 21, 2014 at 18:15 
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    I have found in the professional market a good number of 16:10 screens are available. They are useful as they allow you to view media at 16:9 while having a little room at the top or bottom for a tool bar or some such if you are doing editing to hold your settings and tools. Still, overall a great answer, I even found out a few things. 
    – Vality
     Apr 22, 2014 at 1:43
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    If you consider MacBooks as part of the market, then 16:9 has not completely taken over, as these use 16:10. 
    – Carsten S
     Apr 22, 2014 at 7:51
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    @TheCleaner Screen sizes in Norway is given in inches. I would expect it to be the same in the rest of Europe. Also according to Google 13.3 inches is 33.782 cm. And 34 cm is 13.38 inches. So if metric values where the driver we would expect to see 13.4 inches. 
    – Taemyr
     Apr 22, 2014 at 8:30
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Great Question. The answer is that typically the screen size advertised is the measured diagonal of the screen. This is the ratio of the length to width, and usually depends on the desired resolution. Consider the following calculation for a diagonal:

enter image description here

This shows you can have a logically sized screen, but a weird advertised size. Now, this provides a marketing advantage such that you are reading that the screen is 15.25", however no one side is bigger than 13". Also, this screen size is an 8:5 ratio, and reading up on display resolutions tells us that I can have the following resolutions should pixel count support it:

  • 1440x900
  • 1680x1050

16:9 is another common ratio for obvious reasons. Along this line you have the common 1366x768 among others.

I have never known why they advertise screen size as a diagonal, TVs are the same way.

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    "I have never known why they advertise screen size as a diagonal" Because it's one number, instead of two (width x height)? 
    – Indrek
     Apr 21, 2014 at 15:20
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    @BigHomie - while I don't disagree with your answer's contents, I was hoping for something that answered "Are there actual equations/ratios/mathematical factors in determining screen sizes on a laptop that make certain sizes more common than others?" 
    – TheCleaner
     Apr 21, 2014 at 15:25
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    This is off-topic, but the reason for diagonal sizes comes from when picture tubes were round. They used to give the diameter of the (round) tube, which was encased in a rectangular box. When rectangular picture tubes were invented, the diagonal was used, because people were used to measuring that way. That is, the diameter of the circular tubes was equal to the diagonal of the rectangle in which they were enclosed. 
    – Patrick Seymour
     Apr 21, 2014 at 15:31
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    @Indrek because for different aspect ratios, width or heigt may be the same for diffrent screen areas. 
    – Volker Siegel
     Apr 22, 2014 at 0:12
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    @BigHomie: I suspect because the diagonal is larger than either the width or the height (and thus sounds better). 
    – Thanatos
     Apr 22, 2014 at 22:42

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