## Are There More Grains of Sand Than Stars?

This question comes from Sheldon Grimshaw. “I’ve heard that there are more stars in our Universe than there are grains of sand on all the beaches on Earth. Is this possible?” Awesome question, and a great excuse to do some math.

As we learned in a previous video, there are 100 to 400 billion stars in the Milky Way and more than 100 billion galaxies in the Universe – maybe as many as 500 billion. If you multiply stars by galaxies, at the low end, you get 10 billion billion stars, or 10 sextillion stars in the Universe – a 1 followed by 22 zeros. At the high end, it’s 200 sextillion.

These are mind bogglingly huge numbers. How do they compare to the number of grains of sand on the collective beaches of an entire planet? This type of sand measures about a half millimeter across.

You could put 20 grains of sand packed in side-by-side to make a centimeter. 8000 grains in one cubic centimeter. If you took 10 sextillion grains of sand, put them into a ball, it would have a radius of 10.6 kilometers. And for the high end of our estimate, 200 sextillion, it would be 72 kilometers across. If we had a sphere bigger than the Earth, it would be an easy answer, but no such luck. This might be close.

So, is there that much sand on all the beaches, everywhere, on this planet? You’d need to estimate the average volume of a sandy beach and the average amount of the world’s coastlines which are beaches.

I’m going to follow the estimates and calculations made by Dr. Jason Marshall, aka, the Math Dude. According to Jason, there about 700 trillion cubic meters of beach of Earth, and that works out to around 5 sextillion grains of sand.

Jason reminds us that his math is a rough estimate, and he could be off by a factor of 2 either way. So it could be 2.5 sextillion or there could be 10 sextillion grains of sand on all the world’s beaches.

So, if the low end estimate for the number of stars matches the high end estimate for the number of grains of sand, it’s the same. But more likely, there are 5 to 10 times more stars than there are grains of sand on all the world’s beaches.

So, there’s your answer, Sheldon. For some “back of the napkin” math we can guess that there are more stars in our Universe than there are grains of sand on all the beaches of Earth.

Oh, one more thing. Instead of grains of sand, what about atoms? How big is 10 sextillion atoms? How huge would something with that massive quantity of anything be? Pretty gigantic. Well, relatively at least. 10 sextillion of anything does sound like a whole lot.

If you were to make a pile of that many atoms… guess how big it would be. It’d be about…. (gesture big then gesture small) 4 times smaller than a dust mite. Which means, a single grain of sand has more atoms than there are stars in the Universe.

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Hmm… this gives new perspective on viewing the microscopic world! If there are as many stars in the entire universe as atoms in 1/4 of a dust mite, then the magnitude of accomplishment in inspecting individual atoms becomes more apparent. It would be like looking at our entire universe and resolving just Earth’s sun, Sol! That’s one heck of a zoom lens!

If there are already more stars in the universe than there are grains of sand on the beaches, think about how many planets there are. There could be 2x to 10x more planets than stars.

Hi, you estimate the number of grains of sand making all the beaches but what the score if you take all sand on Earth including deserts and rivers?

For a 0.5mm diameter sphere of quartz, typical for sand, I get about 5

X10^18 (5 quintillion) atoms, using Avogadro’s number. Quartz is about

2.6 g/cm^3 and 60.08 gm/mole, and then there should be Avogadro’s

number of SiO2 “molecules” in the sand grain, and then multiply by 3 (1

Si, 2 O atoms).

4/3 * pi * 0.025^3 * 2.6 * avogadro’s number / 60.08 * 3 = 5e18 atoms/sand grain

Much smaller than the number of stars in the observable universe.

How big a sand grain contains 1e22 (10 sextillion atoms)?

(1e22 / (avogadro’s number) * 60.08 / 3 / 2.6 /(4/3 * pi))^(1/3)*2 = 0.625 cm diameter, or about a 1/4 inch diameter. I don’t want to see a dust mite 4 times larger than that!!!

Would a 1 and 22 zero’s not be 10.000 billion billion? Or am I missing something…?

Interesting but kind of hard to do the math on that, never been an Algebra guy or a big fan of the whole estimation game, but interesting to wonder