Stars and Sand Grains
Are there more actually more stars in the sky, than there are
grains of sand on all the world's beaches?
I think most of us have heard that perennial estimate of the number of stars in the Universe being greater than all of the grains of sand in all of Earth’s beaches.
Sitting on Limantour Beach at Point Reyes awhile back, watching the waves slosh in and out, listening to gulls and feeling very lazy, I found myself looking about me at all that sand, and wondering how it could possibly be true. Reaching out, scooping up a mere handful of grains and letting–what?–a few hundred thousand of the would-be star proxies fall through my fingers, the notion seemed even more absurd.
Raising my eyes from the bit of the cosmos cupped in my hand and taking in the comparatively vast reaches of sand about me–a hundred or so feet between me and the waves, at least a mile or two of beach visible to the north, another stretch to the south, and who knows how many feet of depth beneath the surface? I simply couldn’t believe it. So, I pulled out my journal and started to write down some figures, working out the problem rationally.
So, is it true? Well, here's what I came up with:
Stars: Astronomers have estimated that there are about 200 billion stars in the Milky Way Galaxy. Galaxies come in many sizes, both much larger and considerably smaller than our home galaxy. I don't know what the average number of stars in each galaxy is, but for the sake of this calculation I chose a conservative 10 billion stars per galaxy. Astronomers have also estimated that there are between 50 billion and 100 billion galaxies in the Universe, based on observations made by the Hubble Space Telescope. Again being conservative, I chose the lower figure of 50 billion. So, with those numbers, I calculate a number of stars in the Universe at 10 billion times 50 billion, or 500 billion billion—or in exponential notation, 5 X 1020.
So how does the number of sand grains in the entire world's beaches stack up against that?
To get to that number, I had to do some estimation. First, pulling some numbers out of the air, I decided that an average sandy beach is 30 meters wide (about 100 feet), and 10 meters deep (about 33 feet). Some beaches are wider, some much less so. I don't imagine that the sand on the average beach is as deep as 10 meters—but I've never taken a shovel and found out, either.
Next, I assume that the average sand grain is a millimeter across, giving it a volume of about a cubic millimeter. With that number, I figure the sand grain density to be 10003, or one billion, sand grains per cubic meter of beach.
The final piece of the equation–after density, width, and depth–is length: the total length of beach shorelines in the entire world. Here's where I made some serious assumptions. Starting with the total length of shorelines of all continents and islands in the world, I got a figure of 356,000 kilometers from the CIA World Factbook. That's 356 million meters.
Now here's where my estimate becomes truly conservative. In my final calculation, I assumed that all 356 million meters of world coastline consisted of sandy beaches– which is not the case, of course; there are plenty of coastlines that are rocky, pebbly, gravely, ice-covered, or sheer cliffs, all without much, if any, sand.
So what were my results? Well, doing the math, 1 billion grains per cubic meter times a 30 meter beach width times a 10 meter beach depth times a 356 million meter beach length and assuming 100% of the coastlines consist of my hypothetical average beach, I get:
1 billion x 30 x 10 x 356 million x 100% = 1.068 x 1020 grains of sand
Compared to the estimate of stars in the Universe, that's about 5 times as many stars in the Universe as grains of sand in all the beaches in the world! I guess the old adage was not only right, but somewhat of an understatement…
But it's all a thing of scale. I also calculated that there are about 3000 times as many water molecules in a glass of water than there are stars in the Universe…
8 Comments
amazing. this blew my mind
thanks for doing the math.
[...] is an awful lot of DNA stuffed into every cell.Ben's blog on stars and grains of sand got me to thinking about DNA. How long would the DNA from every living [...]
Mindblowing indeed!
Thanks for the perspective.
I've been meaning to calculate this ever since I first read the "sand in the beaches" statement in Carl Sagan's "Cosmos."
Thanks for saving me the time.
And even after doing the math, part of me still can't believe it. This was reinforced recently as I sat on a beach in Half Moon Bay, surveyed all that sand, and just could not get my belief in gear.
There's another sand and star scale mind game that goes like this: If all the stars in the sky that we can see with our eyes (without a telescope) were stand grains, they would fill a thimble. All of the stars in the Milky Way Galaxy would fill a wheelbarrow. To represent all the stars in the visible universe this way, you would have to haul in the sand with a train, one boxcar-ful per second, 24 hours a day for 3 years….
This longstanding issue has been discussed again recently (on BBC)and notwithstanding many web pages giving calculations I am deeply distrusting of the maths. I have just measured (roughly) some garden sand and reckon it at 100 grains per mm^3. 10^22 (stars) = 100×1000^3×1000^3×100 =100 km^3 of garden sand.
The sandy region of the Sahara desert (alone) is some 2.5 million km^2 which is 2500 km^3 or 25 universes per metre depth.
As to the rest of the world's deserts, beaches…
Or have I missed something?
There are many ways to slice and dice this calculation. In my own, I was confining my example to only the sand of Earth's beaches (not deserts), and taking every opportunity to use conservative estimates for the variables. But the point of my estimation was not so much to try to calculate how many grains of sand there are, but demonstrate the number of stars in the Universe. Even if you regard my conservative beaches with their coarse sand grains, the fact is, that's a heck of a lot of sand! And if my (maybe unrealistically) conservative sand sum is in the ballpark of the Universal star-sum, as long as I've achieved mind-boggledom, I'm satisfied….
I take your point about considering only beaches. It is clearly an important difference as many instances of this question being discussed do fail to make the distinction.
In any case the visible universe is only a fraction of the (unknowable?) total so the universe may well win out.