How many times would you have to fold a piece of paper to reach the Moon?

Forty-two.

That's the answer that does the rounds on social media every few months, usually next to a photo of the Moon and a lot of exclamation marks. It also happens to be right, which is more than you can say for most things that go viral.

The one-line version

A sheet of ordinary office paper is about 0.1 mm thick.¹ Fold it in half and it's two sheets thick. Fold it again and it's four. Every fold doubles it, so after n folds you have 2ⁿ layers.

Doubling starts slowly. Ten folds gets you about 10 cm, roughly the height of a mug. Twenty folds is about 105 metres. By 30 folds the stack is 107 km tall, past the 100 km mark usually counted as the edge of space.

The Moon is, on average, 384,400 km away.² Fold 41 times and you're at about 220,000 km, a bit over halfway. Fold 42 times and you're at about 440,000 km. You've arrived, with 55,000 km to spare.¹

Thinner paper barely changes it. Halve the thickness and you need one extra fold. That's exponential growth in a nutshell: the starting number hardly matters, the doubling does all the work.

TED-Ed's lesson on the same question asks whether 45 folds would do it.³ They would. 45 folds of 0.1 mm paper comes to about 3.5 million km, which is nine trips to the Moon. Bring a packed lunch.

What it looks like as a paper size

This is a paper sizes website. We'd be letting you down if we skipped this part.

Fold a sheet of A4 in half and you get A5. Fold it again and you get A6. That's how the A series is designed: every size is the one above it, folded in half. So a sheet of A4 folded 42 times has the footprint of A46.

Nobody has ever needed an A46 template, but the maths still works. It would measure about 0.0001 × 0.00014 mm. That's 100 by 140 nanometres, smaller than a bacterium.¹

So: a tower 440,000 km tall, on a base you'd need an electron microscope to find. Please don't lean on it.

Why nobody has done it

For a long time the received wisdom was that you can't fold paper in half more than seven or eight times, however big the sheet.⁵ That turned out to be wrong, though not by much.

In 2002 Britney Gallivan, a high school student in Pomona, California, took the challenge on for extra credit in maths.⁵ She worked out how much paper each fold uses up, because the outside of every fold has to wrap around everything inside it. Then she folded a single 1,219-metre strip of tissue paper in half 12 times. It's still the Guinness World Record.^4,6

Her formula for the length of paper you need is:

L = (πt ÷ 6) × (2ⁿ + 4) × (2ⁿ − 1)

where t is the thickness of the paper and n is the number of folds.⁴

Put 0.1 mm paper and 42 folds into it and you need a strip about 10¹⁸ km long. That's roughly 107,000 light-years, a little wider than the Milky Way.⁷ To fold your way to the Moon, you'd first need a sheet of paper longer than the galaxy. We checked the maths twice.

The people who got closest

In 2007 the MythBusters team took a sheet the size of a football field and, with the help of a forklift and a steamroller, managed 11 folds.¹

In April 2011 maths teacher James Tanton and 15 students from St. Mark's School in Massachusetts unrolled 13,000 feet of single-ply toilet paper down MIT's Infinite Corridor and folded it 13 times. Tanton called it “backbreaking”.⁸ The finished stack wouldn't stand up on its own, so they didn't count it. That December they went back with about 54,000 feet of toilet paper and did it again.⁹

Thirteen folds. Twenty-nine to go.

So, can you fold paper to the Moon?

On paper, yes. With paper, no.

But the next time someone tells you it only takes 42 folds, you can tell them they're right. Then ask where they're getting the paper.