How big is 1 million grains of sand

Here's an old, old, question, but this time with a surprise twist. The question is — and I bet you asked it when you were 8 years old and sitting on a beach: Which are there more of — grains of sand on the Earth or stars in the sky?

Obviously, grains and stars can't be counted, not literally. But you can guestimate.

Science writer David Blatner, in his new book Spectrums, says a group of researchers at the University of Hawaii, being well-versed in all things beachy, tried to calculate the number of grains of sand.

How big is 1 million grains of sand

Emilian Robert Vicol via Flickr

They said, if you assume a grain of sand has an average size and you calculate how many grains are in a teaspoon and then multiply by all the beaches and deserts in the world, the Earth has roughly (and we're speaking very roughly here) 7.5 x 1018 grains of sand, or seven quintillion, five hundred quadrillion grains.

That's a lot of grains.

How big is 1 million grains of sand

Gilles Chapdelaine/NASA & ESA

OK, so how about stars? Well, to my amazement, it turns out that when you look up, even on a clear and starry night, you won't see very many stars. Blatner says the number is a low, low "several thousand," which gives the sand grain folks a landslide victory. But we're not limiting ourselves to what an ordinary stargazer can see.

Our stargazer gets a Hubble telescope and a calculator, so now we can count distant galaxies, faint stars, red dwarfs, everything we've ever recorded in the sky, and boom! Now the population of stars jumps enormously, to 70 thousand million, million, million stars in the observable universe (a 2003 estimate), so that we've got multiple stars for every grain of sand — which means, sorry, grains, you are nowhere near as numerous as the stars.

So that makes stars the champions of numerosity, no?

Ummm, no. This is when Blatner hits us with his sucker punch. Yes, he says, the number of stars in the heavens is "an unbelievably large number," but then, very matter-of-factly, he adds that you will find the same number of molecules "in just ten drops of water."

How big is 1 million grains of sand

Plinkk via Flickr

Say what?

Let me repeat: If you took 10 drops of water (not extra-big drops, just regular drops, I'm presuming) and counted the number of H2O molecules in those drops, you'd get a number equal to all the stars in the universe.

This is amazing to me. For some reason, when someone says million, billion or trillion, I see an enormous pile of something, a grand scene, great sweeps of desert sand, twirling masses of stars. Big things come from lots of stuff; little things from less stuff. That seems intuitive.

But that's wrong. Little things, if they're really little, can pile up just like big things, and yes, says Blatner, water molecules "really are that small."

So next time I look up at the sky at all those stars, I will be impressed, of course, by the great numbers that are out there. But I will remind myself that at the other end of the scale, in the nooks and crannies of the physical world, in the teeniest of places, there are equally vast numbers of teenier things.

We are surrounded by vastness, high and low, and either way, as Blatner's book says, we "can't handle the biggitude."

David Blatner's forthcoming book is called Spectrums: Our Mind-Boggling Universe, from Infinitesmal to Infinity.

Salt is fascinating stuff. Roman legions were payed in it, cities taxed, evaporating salt-water for it was a crime. Politics, rebellions, required for life, preservation of food. Perhaps someone has done a web page...

 2003-Feb-03  Fixed 2 links.
 2000-Oct-17  Repointed "stats" link to something similar that works.  Thanks to a reader.
 1997.May     Created.

Some details about this page:

The back of my envelope...

I'm using "Morton Salt" (table salt).
First, some quick and dirty work...
The grains measure about 1/2 mm,
which gives 20/cm  8000/cm3  8 x 109/m3  1010/m3
Its box is a cylinder 6 x 10-4 m3 (8cm d, 12cm h),
and masses 0.737 kg,
so thats a density of about 1.2 kg/m3 (1.2 g/cm3).
So 10-10 kg/grain, and 5 x 106 grains in the box.

More carefully measuring the grains,
I get 0.5 +- 0.05 (about 1 grain uncertainty in 5mm).
Upping the sample to 10mm didnt seem to help narrow the uncertainty
(due to grain size variations).
With this big an uncertainty, I'm not going to worry about how
tighly packed the grains are.
  20/cm (+-2)   6000 to 11000 /cm3  0.6 to 1.1  × 1010
  so 1010 (+10%-40% for measurement uncertainty)
  which gives worst-case percent errors of +70% and -10%.
  So, probably an overestimate, possibly by a factor of 2, but not
  much of an underestimate.

  grains/m3 1010 × 0.6 to 1.1  
  kg/grain 10-10 × 1 to 2  
  grains/kg 1010 × 0.5 to 1

Ok, what are some accessible volumes.
teaspoon   4.9x10-6 m3
tablespoon 1.5x10-5 m3
cup 2.4x10-4 m3
gallonUS liquid 3.8x10-3 m3
foot3 0.028 m3
bathtub ~0.2 m3 (~8 ft3)
classroom ~200 m3 (10x8x2.5 m)

teaspoon 3 to 6 × 104, or 
tablespoon 0.9 to 2 × 105
cup 1 to 3 × 106
bathtub 1 to 2 × 109
classroom 1 to 2 × 1012

Ok.  Time for a reality check.
A big pinch looks about 103 grains
(by dividing it in half a couple of times and then counting).
So a 1/4 teaspoon seems 104 or two.
Which sortof fits.
(_This_ time it fits.  The first time it didn't.
 Turned out I had mangled the  object vs # grains  paragraph.
 And in tracing it down, I would have done a lot better to
 let the numbers lead me, rather than having an emotional stake
 in their fitting.  A lesson.)

I could do this more carefully, but for now...

Call it
a 1/4 teaspoon for 104
a tablespoon for 105
a 1/2 cup for 108
a bathub for 109
a classroom for 1012.

A quick hack of a graph...
Grain size (on the diagonals) vs volume & how many grains
How big is 1 million grains of sand

I should address the non-linear error "feel". 50% seems a bigger deal for big numbers than for small ones.

How much space is a billion grains of sand?

If it is a billion grains the weight would be approximately 11 tonnes. The specific gravity of quartz is 2.65. The volume of the grains would be 4.15 cubic meters.

How much space would 1 trillion grains of sand take up?

0.000000000062 x 1 1,000,000,000,000 = 62 Therefore, 1 trillion grains of sand would have a volume of 62 meters cubed.

How big is a single grain of sand?

Sand is a naturally occurring, finely divided rock, comprising particles or granules ranging in size from 0.0625 (or 116) to 2 millimeters. An individual particle in this range size is termed a sand grain. The next smaller size class in geology is silt: particles below 0.0625 mm down to 0.004 mm in size.

How many grains of sand is the biggest beach?

8.83 trillion or 10.87 trillion grains.