**This began as a simple question, but it has intrigued enough people that I decided to feature it as an article.**

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**Carol:**

“I have heard people say that there are more stars in the universe than there are the grains of sand ‘on the beach.’ What size is the beach and are the grains of sand coarse or fine? Or does the saying go “all the grains of sand on all the world’s beaches,” something I simply can’t believe to be true.”

**Disclaimer:
You and I will work through to get an answer, but be warned — There will never be a definitive, conclusive, absolute, precise or final answer to this question. There simply is no accurate calculation or mathematical proof (or method of counting) – nor will one ever conceivably exist.**

**Its even worse than that — we can’t even get approximate numbers with much confidence.**

**We can only roughly estimate the number of stars in our own galaxy. Estimates easily vary by 150 times (more than two orders of magnitude) and estimates of the number of grains of beach sand are even worse.**

**So if we can credibly get the number of stars or sand grains within say four or five orders of magnitude of either estimate – we’ll be doing well. This essentially guarantees that answers to this question will be off by a few magnitudes; or they will have, in more diplomatic terms, “a high variance” or “a large margin of error.”**

**Even using the best available evidence and methods no one can credibly claim their answers to either estimate of stars or sand grains are within 20 percent (and 20 percent of a trillion stars / sand grains is an error of 200 billion. That’s more than ten magnitudes larger than an error of one star or one grain of sand). And that’s my estimate on the best numbers we can ever do.** (For this article we’ll use the definition of a Star as a luminous body and ignore dark stars.)

**What we can do instead is try to use reasonable methods, use the broadest range of assumptions (lowest and highest) and use the most credible methods available to get estimates for both sand grains and for star counts. **

**Then, after we have estimates (with each having its own range of variance) the only way I can reasonably imagine deciding there are more stars than sand, or more sand than stars, is if one estimate comfortably exceeds the other by six or more magnitudes; a million times larger or smaller.**

* And so, because of the gigantic estimation errors inherent in this exercise – you might take a big breath (now let it out) and try to keep a sense of humor in mind while reading this.

**With that disclaimer in mind, lets star(t).**

**I. Using some credible methods and thoughtful analysis some astrophysicists estimated there are 300 sextillion stars in our visible universe as of 2010. Thats 3 with 23 zeros after it.**

**II. We’re going to play with a method for calculating and estimating stars and sand that is probably less credible than taking one of our important numbers “off the shelf,” but since there is no reasonable way to find out if any answer if even close, instead of worrying about accuracy, how about if we have a little more fun on the way.**

**a. Stars: We are going to multiply estimates of stars in our galaxy with an estimate of the number of galaxies — even though the number of stars in a galaxy can vary by more than five magnitudes; from 10 million to a trillion stars.**

**b. Sand: Then we’ll see how many sand grains we need to represent our own Milky Way galaxy. Finally we’ll ball park estimate the size of beaches on the West Coast of North America. (This “back of an envelope” type of analysis is sometimes called a “Fermi Estimate.”)**

**Estimating Stars**

**There are (very) roughly 125 billion galaxies in our Visible Universe, and there are very roughly 50 to 400 billion stars in our Milky Way galaxy (and compared to most spiral galaxies our Milky Way is big, having an extra large number of stars like our neighboring spiral galaxy Andromeda).**

**Even though our Milky Way is rather large for its spiral type of galaxy, spiral galaxies have dramatically fewer stars than elliptical galaxies.**

**Estimating Sand Grains**

1,000 grains of (Carmel Beach) sand is about a foot long(1).

Your sand may vary enormously. (Fortuitously enough I just happen to have a small spice jar filled with Carmel beach sand which I can measure with a vernier caliper.)

**1,000 grains of sand by 1,000 grains of sand on a flat surface = 1 million grains of sand. (a square foot)**

Now put the vertical dimension of 1,000 grains high = 1 billion grains of sand (one cubic foot). So One Billion grains of sand is a cube only ~ 1 foot on a side.

**So if you believe our galaxy has about 50 billion stars that means you only need about 50 cubic feet of Carmel Beach sand (a cube about 3.7 feet on a side) to represent each star in our galaxy.**

**Not very big is it ?**

**Just for fun we can call this – One cubic “Sand-Galaxy.”**

**You can keep this for reference –**

“You could easily fit a galaxy of sand in a car.”

**Even if you multiply that by 2 (to represent 100 billion stars) – you might still fit that in a Van and maybe a large SUV.**

**However if you believe our Milky Way has closer to one trillion stars, you’d need 20 cubic sand-galaxies to represent the stars in our home galaxy. That size galaxy of sand will take a good sized truck. (10 ft x 10 ft x 10 ft = 1,000 cubic feet of sand)**

**Number of Galaxies**

**Next, because we don’t have a good or simple way to “average” the number of stars in a galaxy (good data doesn’t exist) lets (falsely) assume all galaxies have the same number of stars as our Milky Way. **

(One could reasonably argue that there are a lot more or a lot less stars than the answer this method will produce. There might be less stars because lots of spiral galaxies are smaller than ours. There might be more stars because spiral galaxies have less stars than other kinds of galaxies such as elliptical galaxies. A reasonable alternative at this point would be to estimate of the total number of stars described above)

**There are several “estimates” (all less than fully convincing) of the number of galaxies visible from here – (very) roughly 50 to 100 billion to maybe a trillion galaxies.**

**Next, lets see how big a cube of sand made up of one billion Milky-way type “sand-galaxies” is.**

**Surprisingly the smallest version is a cube of sand only a third of a cubic mile in size ~ about 3,700 feet on a side. (a cubic mile ~ 150 billion cubic feet, 3,700 cubed ~ 50 ****billion cubic feet**)

**That 3,700 foot wide cube of sand represents one billion galaxies. So lets call it a “one billion galaxy sand-cube.”**

**Lets use Carmel Beach for comparison.**

** Its pretty close to a mile long (5,280 ft) and in the summer, lets estimate maybe 100 feet wide and 30 feet deep. That comes to ~16 million cubic feet. That’s about 1/3,100 th of what we need.**

**So we’d need about 3,100 Carmel beaches to make a “one billion galaxy sand-cube.”**

**If we counted all the sand in Carmel Bay – we’d might get enough for a whole “one billion galaxy sand-cube.” (Can you identify SWAG when you see it ? SWAG or SSWAG=Scientific Sounding Wild Ass Guess) I can imagine there is easily enough sand under Carmel Bay to make a few hundred Carmel beaches. I’m not quite as confident there are as many as 3,100 Carmel beaches in the bay though.**

**For the next step of star estimation lets get another reference point.**

**To represent the 50 to 100 to 1,000 billion galaxies – you just multiply the “one billion galaxy sand-cube” by 50, 100 or 1,000. Again, really not that much more (not that many Carmel beaches).**

**Even the biggest estimate of a trillion galaxies “only” needs 1,000 cubes of sand about 3,700 feet on a side (billion galaxy sand-cubes); or 1,000 – 3 million Carmel Bays.**

**I guess there are almost that many cubes of sand (of about 3,700 feet on a side) on the beaches of California alone, but your estimate on this point is as good as mine. If we include the vast beaches of Baja California and (half vast?) beaches of Oregon and Washington – we should easily exceed 1,000 Carmel Bays worth of sand purely with the West Coast. but could we exceed 3 million Carmel Bays? I doubt it.**

**If we then take into account the thousands of miles of beaches on the Brazilian Coast, Africa and Australia – that seems to at comfortably exceed, the 1,000 to 3 million Carmel Bays.**

**However we must now ask — does the sand grains estimate exceed the stars estimate by my original threshold of six magnitudes more of one than the other? I don’t think so. Its too close to call.**

**So by this rough estimate, there might be more grains of sand on our planet’s beaches than there are stars in our known visible Universe. If you want to expand on the original question and include all the sand grains on the ocean bottom (ignoring all the sand on deserts) – then I think the sand wins by far more than 6 magnitudes.**

**Short Answer: Using this analysis method, there might possibly be more grains of sand on the world’s beaches than there are stars in our (visible) Universe. However, remember this is a very rough, back of the envelope estimate with a few major assumptions that could change the estimates by magnitudes. One might reasonably reach a different answer with a different method and different assumptions.**

**Aren’t you glad you asked :-)**

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**References and further reading:**

**1. Using 1,000 grains per foot is just a rough approximation. Carmel Beach sand grains typically measured ~11 to ~14 thousands of an inch with a vernier caliper (though a few grains are much larger and much smaller). Fourteen (14) thousands of an inch is roughly 857 grains per foot. Eleven (11) thousands of an inch is about 1090 grains per foot.**

**“Physical properties of soil” is a source for size of soil grains of sand (and clay).**

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**Finally – if you like this, perhaps you’ll enjoy seeing our Earth from orbit from the live camera in the International Space Station .**

I’m glad I wondered and I’m glad I asked. Thanks for the satisfactory response.

Thank you for your question Carol.

Since you teach lots of very young future scientists I hope this is as educational as it is entertaining for them.

once I hit the equation of one cubic yard being equal to about 50 cubic feet, well… what can I say?

Thank you for your comment Tom.

You’re right — it wasn’t exact.

But then the article never did say a cubic yard is 50 cubic feet does it?

Thats because it derives the cube root of 50 and rounds it down to 3 when the cube root of 50 is closer to 4 (at 3.6840315) than 3.

My only excuse is — remember the disclaimer at the front

This was intended as a back of the envelope estimate – not an equation, and not a serious analysis. Its supposed to be fun, approximate, but fun.

I did warn this could be “off by a few magnitudes.”

Nevertheless, I do have a responsibility to do the math better than I did and I should have done a better job rounding off 3.6840315 to 4 rather than 3. (Thanks to your sharp eye, I’ve just updated the article using “3.7″ as the cube of 50 now. And that doesn’t change the only thing that estimate was used for — that the cube of a billion grains of sand could fit in a car.)

Nevertheless, I don’t know what I was thinking, but I appreciate you bringing it to my attention.

I hope you enjoyed the rest of the admittedly back of the envelope estimate – that was not affected by this minor (~19%) rounding error – when compared with how the sand grain’s size can quadruple from one beach to the next.

Which is similar to how the number of stars in a galaxy can vary by several magnitudes.

This is so fun. Thank you David.

Correct me if I’m wrong but the billion galaxy sand cube is 1000x1000x1000 galaxy sand cubes. The estimates for the milky way cube ranged from 3.7 ft to 10 ft so the billion galaxy sand cube would be 3,700-10,000 ft per side and not 1,000 ft. And the largest universe estimate would therefore be a cube with a side almost 20 miles. I don’t know for sure if this would affect the est for how many it would take to fill

John, you’re absolutely right.

Thank you. I greatly appreciate you taking the effort to examine the data carefully and then ever so diplomatically pointing out my error.

Correction: A cube of one billion (sand) galaxies now comes out to about a “third of a cubic mile” as opposed to “one fifth of a cubic mile” that I had used earlier.

What I believe is an even more important concept is at the heart of science:

The truth is more important than any error.

We all make sincere errors. What transforms a sincere error into an unacceptable problem is when we are unwilling or refuse to acknowledge it – by ignoring it or even fighting against the truth.

I hope this serves as an example of how one can try to “take criticism like ice cream.”

What is almost more important is that those who point out errors should be applauded – not disparaged.

After conducting some exhaustive research, I have come to the conclusion that there are quite coincidentally EXACTLY the same number of grains of sand on all the beaches on Earth as there are stars in the observable universe. I had to count them all again just to make sure .

We all owe Ron a heap of thanks for taking the time to count not merely all the sand grains on Earth – but every star in every galaxy. That’s an incredible feat.

However, the two numbers matching exactly is no more a coincidence than the basis of General Relativity (GR) – where General Relativity assumes (Einstein should have Ron’s ambition and persistence) that every object’s gravity and intertial masses are exactly equal. Its called the Equivalence Principle.

Although a “simple” (?) question, it has quite profound implications. Scientifically, it is probably unanswerable, but an educated guess adds perspective to my individual existence. I can’t comprehend the possible reality of it, let alone what my be responsible for it, if anything!! I think my agnosticism is well-founded!