In the collection Counterintuitive facts
Would 42 paper folds really reach the Moon?
The arithmetic holds: 42 doublings of a 0.1 mm sheet give about 440,000 km, past the Moon. But the fold cannot be done, and a geometric argument says the sheet itself would need to be enormous.
AI-drafted from web search results, then checked by a second, independent AI that read 3 of its 5 cited pages in full and found the thread supported after one error it found was corrected. No person has reviewed it.
The short answer
In arithmetic, yes. Each fold doubles the thickness, and 42 doublings of an ordinary 0.1 millimetre sheet give a stack roughly 440,000 kilometres thick, beyond the Moon's average distance of about 384,400 kilometres. In practice, no. Nobody can fold a sheet that many times, and the sheet would have to be astronomically large to allow it. [1] [2]
Why the numbers work
After n folds the thickness is the sheet's thickness multiplied by 2 to the power n. Ten folds give a stack 1,024 times thicker, about ten centimetres for a 0.1 mm sheet (the cited article says a metre, which does not match its own figures): [scientificamerican.com](https://www.scientificamerican.com/article/how-many-paper-folds-would-get-you-to-the-moon/). Thirty folds reach over 107 kilometres, and 42 folds reach roughly 440,000 kilometres. Computing the base-2 logarithm of the Moon's distance divided by the paper thickness gives about 41.8, so 42 folds is the minimum, as shown on [scipython.com](https://scipython.com/books/book2/chapter-2-the-core-python-language-i/questions/paper-folds/). [1] [3]
The result is not sensitive to the exact thickness. Halving the thickness adds one fold, and doubling it removes one. The Moon's distance also varies, from about 356,500 to 406,700 kilometres, and even the far end is within reach of 42 folds, according to [cleverlearning.co.uk](https://www.cleverlearning.co.uk/foldingPaper.php). At 41 folds the stack is only about 220,000 kilometres, so the last fold supplies as much as all the earlier ones combined. [1] [4] [2]
Why nobody can do it
Folding also halves the sheet's length, and the thickness gets in its own way at the crease. The popular legend that paper cannot be folded more than seven times is roughly right for a standard sheet. In 2001 (one source says 2002), the high school student Britney Gallivan folded a 1,200-metre length 12 times. She worked out a formula for the minimum length needed. Applied to 42 folds of 0.1 mm paper, that formula gives a sheet of about 10 to the power 21 metres, around 107,000 light-years, according to the Mathsy article. [1] [2]
If the folds were somehow possible and the sheet kept shrinking, Scientific American notes that after 42 folds each side would be about 0.1 micron, smaller than a bacterium, which makes the stack useless as a bridge. [1]
A geometric objection
A Math Stack Exchange answer argues the claim fails even for an infinitely foldable sheet. After the last fold, the top and bottom faces are joined at the fold edge, so the path along the paper between them must be at least as long as the straight distance through the stack. A stack reaching the Moon therefore requires a sheet at least about 385,000 kilometres long in one direction. Another answer on the same page notes that the statement is an implication with an impossible premise, so it is logically true but says nothing about what can actually be built. [5]
Sources
- How many paper folds would get you to the moon? | Scientific American (scientificamerican.com) Found by source search. Not checked by a person.
- How many times must you fold a piece of paper to reach the Moon? - Mathsy (mathsy.io) Found by source search. Not checked by a person.
- Paper folding (scipython.com) Found by source search. Not checked by a person.
- Clever Learning - the mathematics of folding paper (cleverlearning.co.uk) Found by source search. Not checked by a person.
- Can a piece of A4 paper be folded so that it's thick enough to reach the moon? (math.stackexchange.com) Found by source search. Not checked by a person.
Questions to follow next
- How did Britney Gallivan work out her folding formula?
- How far would 42 folds go if the paper were thicker, like cardboard?
- What other everyday examples show exponential growth?