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I got the following information from the respective websites about each airlines carry on baggage allowance:

Emirates    7KG     55x38x20cm
Turkish     8KG     55x40x23cm  
Copa        10KG    56x26x36cm
Bahamas     13.6KG  22″ x 14″ x 9″

My question is, in the above 4, what is the order of length width height? Based on all 4 above, What is the maximum allowed common carry on baggage size?

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    I think you are allowed to rotate the bag so that it fits (if it does), ie l/w/h not relevant. – Tomas By Feb 28 at 13:34
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    If your bag can't safely be turned on its side, you have bigger problems. – Nate Eldredge Mar 1 at 20:28
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There is no specific concept of "length", "width" or "height" with these measurements. The longest measurement of your item must be no more than the longest allowed number, the 2nd longest measurement no longer than the 2nd longest allowed number, etc.

After all - if your bag is 50cm high, and you turn it on it's side, it is still 50cm high or is it now 50cm long?

As for your question of what is the maximum allowed common carry on baggage size, it would be the smallest length in each dimension across the three carriers. Thus, 55cm in one dimension (Emirates/Turkish), ~36cm in the second dimension (Copa/Bahamas*), and 20cm in the third dimension (Emirates), with a weight of no more than 7kg (Emirates).

How strictly these measurements are enforced varies depending on the airline, the airport, the specific staff involved, and sometimes how full the plane is. It's possible you will be allowed travel with an item larger then the above measurements, but there is no guarantee.

(* 14" = 35.56cm)

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    There also isn’t really a guarantee that you will be allowed to travel with an item smaller than the above measurements, either, at least in the US. Most flights I’ve been on allowed basically everything until the overhead bins were full (even if some of those were larger than the maximums), and then allowed nothing that couldn’t fit below the seat in front of you (even if they were smaller than the maximums), which made the whole concept moot. The size of your bag was irrelevant; your boarding position is all that mattered. – KRyan Mar 1 at 21:17
  • @KRyan - at least in Europe, it seems common to have a sort of glass or wire mesh box with those dimensions, and they make you put your bag inside. If it can't fit, well, you're not carrying it into the cabin. – Davor Mar 2 at 13:51
  • @Davor Oh yeah, those definitely exist in the US too, I just have never seen one used. Considering how long it takes to load the plane already, stopping everyone and having them put their luggage in the thing (and then try to finesse it so it fits, and maybe reorganize stuff, and then argue about how it should count anyway, etc. etc.) doesn’t seem worth it, even from a “I followed all the rules and I’m still screwed because the people ahead of me in line were selfish and the airline didn’t enforce the rules” perspective. – KRyan Mar 2 at 13:55
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    @KRyan - the fact I fly mostly low costs in Europe explains this. They have paper thin margins, a cabin bag is usually free, and if they bump you to paid luggage, they now make money, so it's very much in their interest to check. I assume that this isn't a significant source of income in US domestic flights? – Davor Mar 2 at 13:59
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    @Davor “Gate-checked” bags are (in every case I’ve experienced) free. Of course, it kind of has to be that way under the current scheme (since they aren’t enforcing the rules). It also helps them try to get things gate-checked early—full flights often have announcements ahead of boarding like “we are definitely going to have to gate-check a few bags, it’s free, if you don’t mind checking something please come now so we don’t delay things.” I get the impression that tightening their schedules is more valuable than anything they could get out of charging for gate-checked bags. – KRyan Mar 2 at 14:15
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What you have to do is picture a box. In the case of Emirates the box is 55x38x20 cm. If your luggage fits in the box it can travel with you in the cabin.

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    Be aware that some airlines are very strict and the whole bag must fit in the box, including any wheels, handles, straps, pockets, etc. Also some bags have a tendency to expand when you put too much stuff in them and no longer fit the original size. – jcaron Feb 28 at 15:19
  • @jcaron "very strict" doesn't seem quite fair as a statement, given these sizes should be a portion of the overhead bin you've paid for being relaxed about this means allowing things that don't fit, or take space from others. – Jontia Mar 2 at 11:21
  • In some cases you don't even need to picture the box - some airlines a box of the appropriate size near the check-in desk, that you can try putting your luggage in. – James_pic Mar 2 at 14:58
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Conventionally, the order is determined decreasingly. Since you can basically rotate a piece of bag to any direction, we conventionally assume that the item is placed horizontally and in width

So the largest measurement of the parallelepiped is width. Second is length, and third is height.

Nonetheless, when you are required to prove your bag fits with size by inserting it into the sized box provided by the airplane, the bag is inserted vertically, so the longest measurement becomes height.

This has absolutely no effect as all the three dimensions must fit the limit individually, unlike the post office service where you can mail a box of any size which fits a given volume.

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