How many times can you fold a regular piece of paper?

Answer 1

Brittney Gallivan set the record by folding paper in half 12 times ..... while still a junior in high school! You'd think that if she walked into the bar and crushed your can of Foster's, the beer would hit the ceiling, but, actually, she even has an equation explaining why 12 is the maximum number of folds possible.

Edit: Given the restriction "regular" piece of paper, mgmirkin's reasoning makes sense, although you don't have to alternate directions for each fold. The original challenge Gallivan solved was to fold paper of any type and size more than 8 times. She actually used gold foil.

And, actually, you always lose more than half the length of the paper on each fold, since, as the thickness increases, the fold itself takes up more paper.

Using the equation: L = pi t/6 (2^n+4)(2^n-1) you get the minimum length of paper (L) needed to fold a paper of a given thickness(t) certain number of times (n).

With a thickness of about .081 mm and a length of 420 mm, you can fold a paper length wise 6 times (I could only do it 5 times, but I'm not very good at it). Now you can change directions and start folding width wise, except your 'new' piece of paper is 2.6 mm thick. With a width of 290 mm, you can get in three more folds (I was actually able to get in the three folds, but, having only been able to fold the paper length wise 5 times instead of 6, my paper was only 1.3 mm). That would give you a maximum of 9 folds for a 'regular' piece of paper.

Answer 2

Aww cripes people, didn't anyone study math in school??

Okay, so , this is a pretty simple math problem, taken in an "ideal"/"theoretical" way. This will be a really simple and really exaggerated example.

Basically most people had it right you can only fold things until they're as thick as they are wide approximately...

(Just trying it I couldn't get more than 6 folds on a paper appx 4 inches by 8 inches, by well as thin as a piece of paper, maybe a 1/16 of a millimeter?)

So, let's just take the dimensions of a square of paper to make the math simpler:

We'll assume the paper is appx 1000 millimeters long by 1000 milimeters wide, by 1/16 of a milimeter high (3 dimensions).
Each time you fold a paper in half, one of the dimensions stays the same, another doubles and another is halved.

With one fold along the vertical line between the two parallel sides of the paper (we'll use looking at it from above as the vantage point) we get the width halved, the length stay the same and the height doubles (Width=500, length=1000, height = 1/8).

Now, we'll try folding it again, this time along the horizontal axis (then vertical, horizontal, vertical horizontal ...). The new dimensions are:

Fold 2: width = 500, length = 500, height = 1/4
Fold 3: width = 250, length = 500, height = 1/2
Fold 4: width = 250, length = 250, height = 1
Fold 5: width = 125, length = 250, height = 2
Fold 6: width = 125, length = 125, height = 4
Fold 7: width = 62.5, length = 125, height = 8
Fold 8: width = 62.5, length = 62.5, height = 16
Fold 9: width = 31.25, length = 62.5, height = 32

So basically you're halving one dimension while doubling another with each fold. Eventually you get to a point where you'd have to double one to greater than the half of the other, and it just doesn't work.

And that's not taking into account the physics of trying to actually fold a paper. It doesn't fold cleanly, the edge warps with each fold making it increasingly more difficult with each fold.

So, if we take a regular piece of paper, we get 8.5in (216mm) x 11in (279mm) x 1/16mm {maybe more; just guesstimating since I can't find an actual measure of the thickness online, if it's thicker, the unfoldable point comes sooner.}

Fold 1: Width = 216, length = 139.5, height = 1/8
Fold 2: Width = 108, length = 139.5, height = 1/4
Fold 3: Width = 108, length = 69.75, height = 1/2
Fold 4: Width = 54, length = 69.75, height = 1
Fold 5: Width = 54, length = 34.875, height = 2
Fold 6: Width = 27, length = 34.875, height = 4
Fold 7: Width = 27, length = 17.4375, height = 8
Fold 8: Width = 13.5, length = 17.4375, height = 16
Fold 9: Width = 13.5, length = 8.71875, height = 32

So we see that around fold 7-8 it becomes nigh impossible to fold anymore (maybe fold 6-7 or 5-6 if we're talking heavy weight paper).

Even with extremely long thin strips of paper you'll eventually hit a limit of how many halvings and doublings you can do.

Heck, let's figure out how a long thin ribbon of paper would fold...

Let's say it's 10,000,000 millimeters long, 1000 milimeters wide, and 1/16 of a millimeter thick:

Fold 1: Width = 1000, length = 5,000,000, height = 1/8
Fold 2: Width = 1000, length = 2,500,000, height = 1/4
Fold 3: Width = 1000, length = 1,250,000, height = 1/2
Fold 4: Width = 1000, length = 625,000, height = 1
Fold 5: Width = 1000, length = 312,500, height = 2
Fold 6: Width = 1000, length = 156,250, height = 4
Fold 7: Width = 1000, length = 78,125, height = 8
Fold 8: Width = 1000, length = 39,062.50, height = 16
Fold 9: Width = 1000, length = 19,531.25, height = 32
Fold 10: Width = 1000, length = 9,765.625, height = 64
Fold 11: Width = 1000, length = 4882.8125, height = 128
Fold 12: Width = 1000, length = 2441.40625, height = 256
Fold 13: Width = 1000, length = 1220.703125, height = 512
Fold 14: Width = 1000, length = 610.3515625, height = 1024

For this width to length to height ration I'd guess somewhere around fold 10-13 it'll become unfoldable. But for the "regular paper" IE US Letter size, the middle results above say somewhere around 6-8 folds will do it, depending on the thickness of the original paper. Maybe if you had something ultimately thin and ultimately strong (thinner than a hair, stronger than stell and more flexible than rubber; not likely) you could get up to 8, but it's doubtful...

Answer 3

you can fold a piece of regular paper in half 12 times. You can fold paper for ever if you start in the corner and dog ear it that's 4 right there turn it over and there is 8 more dog ears there now fold it in half that's 9 so 8 is straight out.

Answer 4

Until the width after folding is less than the thickness of the paper itself.

Answer 5

No piece of paper can be folded in half more than 7 times.

Answer 6

You can fold it until it becomes as wide as it is thick, which is about 7 times for a normal sheet of paper.

Answer 7

Soon it is very thick. Starting with 1m2 paper, an A0, a can fold 8x.

Answer 8

Twelve Times

See the link below.

Answer 9

It does not matter how big the size of the paper is...you can only fold it seven times...try it with a newspaper sheet or a post-it.
It's all the same.

Answer 10

Yep, I agree, you can't fold a piece of paper in half more than 7 times.