The Science of Sustainability

Stars and Sand Grains

  • share this article
  • Facebook
  • Email

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…

37.8148 -122.178

Related

Explore: , , , , , ,

Category: Astronomy, Partners

  • share this article
  • Facebook
  • Email

About the Author ()

Andrea is KQED's Senior Science Editor . Andrea was born in Los Angeles and discovered radio news through listening to her college radio station. With a curious mind and a love for telling stories, she set off for Tampa where she landed her first job as a reporter for Florida Public Radio. After three years reporting in an unbearably humid climate and a brief stint as a miscast opera reporter, Andrea returned to L.A. to work for public radio, then for television news and finally as a reporter for CBS radio. Andrea has been at KQED for over twelve years, working first as a producer for Forum, and then as the senior producer for The California Report. She is now KQED's Senior Science and Environment Editor and narrates the QUEST television program. Andrea says she feels lucky to cover emerging science and environmental trends in a place where geek is chic.
  • austin

    amazing. this blew my mind

    thanks for doing the math.

  • Pingback: A Long and Winding DNA | QUEST Community Science Blog - KQED

  • Jonas Kulland

    Mindblowing indeed!
    Thanks for the perspective.

  • Jim Fisher

    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.

  • http://chabotspace.org Ben Burress

    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….

  • George Whaley

    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?

  • http://www.chabotspace.org Ben Burress

    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….

  • George Whaley

    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.

  • fatalflaw
  • Rvaldez4108

    This is so cool! One of the best summaries I've seen on the subject of sand grains versus star counts. Mind boggling until you mention the water molecules being 3000x! But your's is one of the few with depth defined. I told my daughter about this "fact" last summer when we were at the beach and she said "but how deep?". Oops…I hadn't read that anywhere.

  • Rvaldez4108

    So I next asked her to imagine that two of the grains we held in our hand (one representing our sun and one the nearest star) were placed at proportional distances from each other. She'd have to walk the grain a half-mile down the beach. I was doing the numbers in my head so they're very rough. If we took a third grain representing the furthest star in our galaxy, she'd have to walk 13.5 miles. Take a fourth representing a star in Andromeda, and she'd have to fly 338 miles away. Take a fifth representing the furthest star and she'd have to be 1.9 million miles away. She lost interest at 338 miles. ;)

  • Rvaldez4108

    Oops…I was trying to recall the numbers but more acurrately, it would be: first two grains, half-mile, third grain representing furthest star in milky galaxy, 125 miles, fourth in Andromeda – 3,125 miles and finally, fifth representing furthest star in the universe, 17.5 million miles away. Or 700 times around the Earth. At the size of a grain of sand – pretty impressive.

  • http://twitter.com/goldsupernova Chris McCarthy

    Take this kiss upon the brow!
    And, in parting from you now,
    Thus much let me avow–
    You are not wrong, who deem
    That my days have been a dream;
    Yet if hope has flown away
    In a night, or in a day,
    In a vision, or in none,
    Is it therefore the less gone?
    All that we see or seem
    Is but a dream within a dream.

    I stand amid the roar
    Of a surf-tormented shore,
    And I hold within my hand
    Grains of the golden sand–
    How few! yet how they creep
    Through my fingers to the deep,
    While I weep–while I weep!
    O God! can I not grasp
    Them with a tighter clasp?
    O God! can I not save
    One from the pitiless wave?
    Is all that we see or seem
    But a dream within a dream?

    E.A. Poe

  • Joanengirls

    So what if you add all sand grains. Like the ones on the ocean floor,
    and the desert sand? Would your conclusion be different?

    • Ben Burress

      A LOT different :). My estimate of sand grains on beaches alone assumes a narrow strip of sand–and even though it takes into account the length of all coastline in the world, the estimate of sand grains would go up enormously if it starts taking into account land areas of deserts–just the Sahara alone is huge–and the bottoms of the oceans. And since my estimate is not only calculated very conservatively, but also only puts only 5 times as many stars in the Universe, it doesn't take much to put the estimate well over that, I think.

  • What if?

    what if grains of sand were stretched in a striaght line, each representing1 light year. How long would it be to represent the diameter of the visible universe?

    • Ben Burress

      Well–without mixing models here (I'm not exactly sure what you mean by "each representing 1 light year"), if you simply lined up my 1 mm sand grains end to end, that would give you a line of sand a bit over 11 light years long. (1.068×10^20 grains at 1 mm each = 10.068×10^20 millimeters, or 10.068×10^14 kilometers = 11.29 light years.)

  • scotian

    most estimates for average sand grain size are in mid-range of .25-.5 mm rather than 1mm…perhaps .375 is good midpt…with finer sand being far less (.063mm, etc.)…this could tighten things up a bit…

    • Ben Burress

      That's, of course, the average size for medium class sand–in which case I'd get almost the opposite result: four times the sand grains over stars. Coarse sand (on the same classification scale) has average grains between 0.5 and 1 mm. Actually, if I do a little cherry picking and choose 0.6 mm, my calculation comes out at 1:1! :)
      But other factors affect the number, of course; maybe coarse sand isn't a conservative choice for favoring objectivity, but I tried to overestimate the width and depth of typical beaches, and also how much of the world's coastlines actually are sandy.
      However, those details aside, whatever number you use here, the number for sand grains and stars comes out in the same neighborhood, empowering one to say there are about as many stars in the observable universe as there are sandgrains on the world's beaches…. (And of course I wasn't taking into account the idea of a multiverse.)

  • Dave Abeyta

    Am I missing something or did u go to all the trouble to ad up the length of all the shorelines on earth without giving them any width or depth besides 1m x 1m ?