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Several times in the books, it is mentioned that Harry put his cloak in his pockets (example taken from HBP, Chapter 26 "The Cave", p.391, American Edition) :

Harry pulled of his [Invisibility] cloak, stuffed it in his pocket, and followed.

Yet the Cloak is also big enough to hide Harry, Ron and Hermione at once (even if their feet are visible by the end of the series (DH, Chapter 32 "The Elder Wand", p.456, American Edition) ) :

"Harry, you get the Cloak on", said Hermione. "Never mind us -" But he threw it over all three of them; large though they were, he doubted anyone would see their disembodied feet through the dust

How is it possible for a Cloak to cover three people and yet being stuffed into a pocket (without an Extension Charm of course) ?

I'm looking for an in-universe canon explanation if possible.

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    I don’t see an issue (regardless of size) if it is thin. I own foldable travel bags and a tent that can be stuffed in an amazingly small pocket. – chirlu Oct 11 '17 at 12:44
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    The amount of volume actually occupied by the cloak will largely depend on how thick the material is and how well it's packed/folded/rolled (i.e. how much distance (air) is between each layer). This can be easily be demonstrated by trying to pack your own clothes (hint: rolled usually uses less room than folded). There is even an entire segment of the pack/ship industry which uses crumpled paper as packing material, because it provides acceptable protection, but has the advantage of the paper originating in rolls, which take up much less volume than the paper does once crumpled for packing. – Makyen Oct 11 '17 at 15:47
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    It is a unique magical artifact, so it can be as small as you want it to be. Or as big as you want it to be. – TimSparrow Oct 11 '17 at 16:53
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    @TimSparrow I would disagree, since it could not be big enough to cover all three of them completely, suggesting there is a limit to its size... unless you're suggesting that Harry didn't want their feet covered for some reason. – Aramis7d Oct 12 '17 at 5:05
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Harry uses the cloak mostly in school. As we know, they are always with magician robes in school territory(In the movies they are not, I know). Now robes have bigger pockets than jeans(e.g. A frog or a rat can fit in). I made the mistake of googling robe pockets,but you can experiment it at home. After a shower try to stuff one of your t-shirts to your bathrobe's pocket. We also know that the Cloak is like a liquid, so you can compress it more than a regular t-shirt. At last, even some parts of your t-shirt may be out of your pocket, remember that the cloak is almost invisible when not worn, it will be super hard to detect it.

Something fluid and silvery gray went slithering to the floor where it lay in gleaming folds. Ron gasped.
(..)
Harry picked the shining, silvery cloth off the floor. It was strange to the touch, like water woven into material.

Harry Potter and the Philosopher's Stone, Ch. 12: The Mirror of Erised

It came to my realization that this answer does not answer your title question, as It gives no insight for the size of the cloak, but for your explanation, This answer still explains how it can be carried along in a pocket

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    "We also know that the Cloak is like a liquid, so you can compress it more than a regular t-shirt." - my first thought was that water is barely compressible at all... After thinking though I assume you mean that a liquid will fill a space more efficiently than a t-shirt would? – Chris Oct 11 '17 at 17:50
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Did you ever see one of these foldable metal foil blankets us Europeans are supposed to have in the emergency kit in every car? These easily fit into a trouser¹ pocket and can easily bag a man. They’re stable enough to not rip easily, either.

① I’d expect robe pockets to be somewhat larger.

They were apparently introduced, in the Muggle world, in 1964 — plenty of time to be known to the public in the 1990s. Dᴇᴀᴛʜ as the presumed creator of these artefacts is not bound to time, and if the Peverell brethren created it they were ingenious enough already, so why not make the material thin enough to fold well? Consider that robes made of Acromantula silk are considered among the finest to be worn; silk is also a very thin yet durable material (Mark remarks that “Ordinary silk can be folded up into absurdly small sizes as well”).

I don’t have a fancy canon quote to show, but it’s likely JKR never thought of this (or had those “space blankets” and/or larger robe pockets in mind) in the first place, considering it appeared in the first book.

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    It's not just space blankets. Ordinary silk can be folded up into absurdly small sizes as well. – Mark Oct 11 '17 at 23:48
  • Oh right. The worse being I have one in my car, but I totally forgot about those. – Falyna Oct 12 '17 at 8:37

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