How many paper folds would get you to the moon? | Scientific American
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August 7, 2026<br>5 min read<br>Add Us On GoogleAdd SciAm<br>How a sheet of paper can take you to the moon
Folding a piece of paper makes it thicker. How many folds would it take to reach the moon—and beyond?
By Phil Plait edited by Lee Billings
Art Grafts/Getty Images
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Humans are linear thinkers.<br>That is, when we think of numbers, we tend to do so in a linear sense: 1 + 1 = 2, the difference between integers is a constant equal to 1, and so on. What’s funny about that is that the universe is decidedly nonlinear. Most of the ways humans interact with the world aren’t linear, either!<br>Your eyes don’t see linearly; we see luminance on a modified logarithmic scale. Our hearing sensitivity is logarithmic as well. These perceptions give us a wider range of sensitivity to experience the outside world.<br>On supporting science journalism<br>If you're enjoying this article, consider supporting our award-winning journalism by subscribing. By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.<br>So it’s odd that our brains seem to insist on churning through numbers linearly. We have an intuitive grasp of adding 1 to a number or adding some two numbers together. But if those numbers scale exponentially, our brains often fail us.<br>Here’s a practical example that gets impractical pretty rapidly: When you fold a piece of paper in half, it gets thicker, right? It doubles in thickness, in fact. So how many times do you have to fold a piece of paper in half such that its thickness is equal to the distance to the moon?<br>The moon is, on average, 384,000 kilometers from Earth, if that helps. Okay, now guess!<br>Got your number? Here’s the actual answer: to get a piece of paper 384,000 km thick, you’d have to fold it in half 42 times.<br>Yup. Just 42 (maybe that’s what Douglas Adams was thinking when he came up with this number). How can this be?<br>It’s because of exponential growth. Every time you fold a piece of paper, you’re not just adding two pieces together; you’re doubling them. This piles up much faster than you’d expect.<br>A standard piece of 8.5-by-11-inch (20-by-28-centimeter) paper is approximately 0.1 millimeter thick (as we’ll see in a moment, the exact thickness doesn’t really matter much). Fold it once, and the paper is 0.2 mm thick. Fold it again, and it’s 0.4 mm.<br>The thickness increases as 2 to the power of the number of folds. So after five folds, the paper is 32 times thicker. After 10 folds it’s 1,024 times thicker (in the case of our sheet of paper, that would be about one meter thick).<br>Our brains balk at this. After 10 more folds, you might think it would be 2,048 times thicker than it was originally, but in fact that happens after the next fold (so 11 total)! After 20 folds the paper is actually 1,048,576 times thicker—almost 105 meters, longer than a football field. After 10 more folds, so 30 in total, it’s over 107 kilometers thick. Another 10 (40 total) takes it to almost 110,000 km, so just two more makes it 440,000 km thick, comfortably past the moon. (One fewer only gets us to 220,000 km.)<br>See? You’re only 42 folds away from the moon. You might argue that it’ll take more folds if the paper is thinner—or fewer if it’s thicker. And this is true—but if your paper is half as thick, this only adds one more fold! If it’s twice as thick it takes one fewer fold, so honestly there’s plenty of room for error in our thickness estimate.<br>Now, to be fair, folding a piece of paper this many times is physically difficult, to say the least. The crease in the middle when the paper is folded is the problem here. It’s not too hard to smash that crease flat for the first few folds, but the thickness of the paper itself quickly gets in its own way, making further folding harder and harder.<br>You may have heard the legend that a piece of paper can only be folded seven times before it becomes impossible to do so again. For an 8.5-by-11-inch sheet, that’s not entirely wrong; after seven folds, further progress is very difficult. I’ll note, however, that in 2001 then high schooler Britney Gallivan broke this record by folding a 1,200-meter-long piece of paper 12 times! She even derived a mathematical formula showing that the fold’s curvature is what determines the maximum number of possible...