Starts With A Bang

# How many times must you fold a paper to reach the Moon?

Each time you fold a piece of paper, you double the paper’s thickness. It doesn’t take all that long to even reach the Moon.
Key Takeaways
• On average, a single sheet of paper is only 0.1 mm thick: on par with the thickness of a single human hair.
• But the Moon, bright and visible from Earth even during the day, is around 380,000 kilometers distant, on average.
• Despite these tremendous differences, it doesn’t take thousands or even hundreds of “foldings” to reach the Moon. Here’s why.
Travel the universe with Dr. Ethan Siegel as he answers the biggest questions of all

The Moon is the closest natural object to Earth.

Its orbital distance ranges from 356,000 to 407,000 km.

Simply folding a paper in half enough times would eventually reach the Moon.

But how many? The answer lies in the mathematics of exponential growth.

To start, you first need to know how thick a single sheet of paper is.

Paper is sold in reams of 500 pages, typically ~5 cm (2 inches) thick.

That implies a single sheet is ~0.1 mm (0.004 inches) thick.

Each time you fold a piece of paper, you double its thickness.

Fold it once, twice, and then three times, and it becomes 0.2, 0.4, and then 0.8 mm thick.

To reach the Moon, however, it must become at least 356,000 km thick.

That’s a factor of 3.56 trillion thicker than a single sheet of paper.

Each successive fold cumulatively doubles its previous thickness.

After 10 folds, its thickness increases by a factor of 1024 (just over 1000).

After 20, 30, and 40 folds, the paper becomes over a million, a billion, and then a trillion times thicker than the original.

Only 42 folds equates to a thickness of 439,804.6511104 km: enough to reach the Moon.

Mostly Mute Monday tells an astronomical story in images, visuals, and no more than 200 words. Thanks to Lewis & Clark College’s Prof. Michael Broide for teaching the author this lesson in 2009.