Can You Really Only Fold A Piece Of Paper 7 Times?

The "you can only fold a piece of paper 7 times" claim is a myth. With an ordinary sheet you’ll typically stall after 6–7 folds, but with a long enough piece of paper you can do many more. The standing record on a single continuous sheet is 12 folds, set by Britney Gallivan on 27 January 2002 using a 4,000-ft (1.2 km) roll of toilet paper; a group of students at St. Mark’s School later managed 13 folds by taping rolls together.

For all those who didn’t know this, there are plenty of people who argue that you can only fold a piece of paper in half a maximum of 7 times.

Go ahead, give it a try. This is one of those experiments which does not come with the disclaimer of: “Don’t try this at home.” A small suggestion would be, however, to not to use a piece of paper torn from a notebook.

So how many did you manage with the folding project?

If you’re a normal human being with normal strength (unlike the Hulk), then I would imagine that you could have managed a maximum of 5 folds. Maybe 6…if you’re quite strong. It is highly unlikely, however, that you would have managed 7 or more folds in the piece of paper.

So why is such a seemingly easy task actually so difficult to accomplish? Why can’t you go beyond 7 folds?

Let’s start with the investigation of the reality of the 7-fold concept.

It’s A Myth!

Yes, absolutely. A piece of paper can, in fact, be folded more than 7 times.  It has been done many times in many places all around the world. It’s just that the people who accomplished the feat used a lot of paper! In other words, it was not a piece of paper that you could simply tear from some notebook. Also, there were numerous people involved in the process.

So, good luck trying to manage more than 7 folds all on your own with a small piece of paper. Under those conditions, it is basically impossible.

A World Record

Britney Gallivan, from California, was one woman with the determination to prove this long-held concept incorrect and totally baseless. On 27 January 2002, this then-high-school student from Pomona, California took a rather long piece of paper (a single piece of toilet paper) that measured 4,000 feet (1,219 m, or about 1.2 km) and folded it ….. (drumroll please…)

She folded it 12 times!

That accomplishment definitely deserves some applause, and there was more to her achievement than bragging rights! She also provided an equation that yielded the width of paper or the length of the paper necessary to fold a piece of paper in a single direction. For single-direction folding, the following equation applies:

where t represents the thickness of the material to be folded, L represents the length of a piece of paper to be folded in only one direction, and n represents the number of folds desired.

Since Britney’s accomplishment, there have been many instances of people breaking the barrier of 7 folds. The one which got a lot of coverage was a group of students from St. Mark’s School.

In December 2011, working in MIT’s Infinite Corridor, they used about 54,000 feet (10 miles, ~16 km) of toilet paper and after roughly seven hours managed 13 folds. (Britney Gallivan has noted that, because that paper was taped together rather than a single continuous sheet, her own 12-fold mark on one piece of paper still stands.)

The number that these industrious students achieved was 13 folds!

Why Is Folding A Paper Many Times So Difficult?

The main difficulty lies in the ever-increasing thickness and thus the strength of the paper itself. It would seem quite plain at a glance, but if you take a piece of paper that is only 0.1 mm thick and fold it in half, the new thickness is 0.2 mm. This thickness goes on increasing exponentially, as does the height of the paper. If you fold the same piece of paper 7 times, it would be as thick as 128 sheets of paper.

Also, with the increase in height, you also have a lesser width at your disposal to use in order to apply some force to keep the paper folding. So yes, not only does the paper become immensely thick, but it also becomes very, very tall.

In fact, it is said that if you folded a paper more than 100 times, you would have a piece of paper that would be thicker than the Universe itself!

How Thick Would It Get If You Could Fold A Paper 100 Times?

Here is the part that breaks your brain. The reason that universe claim sounds absurd is the very reason it is true: each fold doubles the thickness, and doubling adds up frighteningly fast. Start with one ordinary sheet at 0.1 mm. After n folds the stack is 0.1 mm × 2ⁿ thick. That little 2ⁿ is doing all the heavy lifting.

Watch the numbers climb. At 7 folds you have 2⁷ = 128 layers, so a 0.1 mm sheet is about 1.3 cm thick, roughly the spine of a chunky paperback. At 23 folds the stack is around 840 m, taller than the Burj Khalifa. By 30 folds you have punched past 100 km, the edge of space (the Kármán line). And at 42 folds the thickness reaches about 440,000 km, which comfortably clears the roughly 384,400 km (238,900 mi) gap to the Moon. Astrophysicist Ethan Siegel ran the same arithmetic and landed on the identical answer: 42 folds, and you are standing on the lunar surface.

Keep going and you leave the Solar System behind. At around 51 folds the paper would stretch beyond the Sun, and at roughly 103 folds it would be thicker than the observable universe, which is about 93 billion light-years across. So the old playground boast was no exaggeration. Of course, none of this is physically possible; you would run out of paper, strength, and elbow room long before fold 30. But it is a lovely reminder of how violently exponential growth outruns our intuition. The same doubling that stalls you at 7 folds on the kitchen table is what carries an imaginary sheet all the way to the Moon and beyond.