How do you count sand grains?

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Retired, collecting minerals and stamps, growing flowers and vegetables, and when the spirit moves, toying with technology
How do you calculate grains of sand?
How do you count sand particles?
What does 1 grain of sand weigh?
What does 1 million grains of sand look like?

Did you ever wonder how many grains of sand were on a beach? Or perhaps the simpler question of how many grains of sand fit into a 20 ml collecting vial like the one in the cover photo? I imagine you probably have not, but I did.

To get started, we know that 20 ml is equal to 20 cubic centimeters. Now we also will make three assumptions:

assume a medium-grained, well-sorted sand with a grain diameter of 0.33 mm (all grains equal)
assume well rounded spherical grains
assume hexagonal close packing (HCP) of the grains where alternating layers of grains sit on top of each other. Each sphere will touch 12 others, 6 within its layer and 3 in the layers above and below. With this packing of grains, the grains will comprise 60% of the volume in the vial. The rest will be pore space. Put another way, the porosity in the sand will be 40%

Now we are ready to do some math. There are multiple ways to perform this calculation, but let’s work it two different ways. Why, you ask, do we do it two ways? Well, because we can. And because math with a purpose is fun!

First method: Convert the problem into a standard cube and work only with length dimensions. This simple method requires only the first two assumptions.

Each edge of a cube with a volume of 20 cubic centimeters will be 2.714 cm long. (or the cube root of 20). Yes, I do know I violated significant digit rules with this conversion and others).
This allows for 82.2 cubes with a diameter of 0.33 mm to align along each edge (27.14 mm/0.33 mm = 82.2)
2 x 82.2 x82.2 is ~555,000
There are about 555,000 tiny cubes with an edge length of 0.33 mm in a 20 cubic centimeter or 20 ml volume. Each could hold one spherical grain if they were stacked directly above each other.

Of course, they would never stack that way so …

Second method: Construct the problem to account for the spherical grain shape that is more commensurate with actual sand and incorporating the third assumption.

The volume of a sphere is equal to 4/3 r3 where π is 3.1416 and r is the sphere radius (in this case 0.166 mm). The volume of one sand grain is therefore 0.192 cubic millimeters.
There are 20,000 cubic millimeters in 20 cubic centimeters (or ml).
So there is room for ~1,040,000 sand grains in that volume (20,000/0.0192).
BUT wait, we assumed HCP for these grains and 40% porosity. Therefore, we must multiply our calculated grain count by the percentage of the volume that would be occupied by grains. (60% of 1,040,000 = 624,000.

The larger number (624,000 grains in a 20ml volume) is likely a more accurate assessment because it incorporates the concept that the grains will fill the space more effectively that just sitting atop the center of the one below. In reality all the grains are not the same size or shape and these size variations generally allow for closer packing as smaller grains settle into spaces between larger grains. However, I do not think I plan to count sand grains in any of my 20 ml sample vials to verify this.

20 ml vial of medium-grained garnet-rich sand from Hamlin Beach on Lake Ontario. Imagine that, over half a million grains of sand!

Remember, sand grain size ranges from 0.06mm (very fine) to 2.0 mm (very coarse). There would be a large difference in the number of sand grains in your 20 ml sample vial depending on the grain size of the sand. I will let you calculate this difference. Anyone who does can report on their results at the next club meeting.

I will also leave it to you to calculate how many 20ml vials it would take to remove all the sand from your favorite beach!

Who said math was useless?

Retired, collecting minerals and stamps, growing flowers and vegetables, and when the spirit moves, toying with technology

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.

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.

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."

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.

How do you calculate grains of sand?

Assuming a grain of sand is roughly spherical, the average volume of a grain is 4/3 x pi x r³=0.00947mm³, where r is the radius.

How do you count sand particles?

How to Measure Sand Particle Size.

Dry the sand/clay/silt in a microwave oven for 20 minutes. This is the pipette method. ... .

Use a malt blender to mix carefully weighed sand and silt samples with Calgon. This is the hydrometer method. ... .

Attach an acoustic sand monitor to the outside of any type (underwater or land) pipe..

What does 1 grain of sand weigh?

The weight of a Grain of Sand is about 0.0044 grams. With tremendous variety in the size of grain and the component material, grains of sand weigh an average of 0.0044 grams. In 2007, a team of seven in Myrtle Beach created the world's tallest sandcastle, which measured 15.10 m (49.55 ft) in height.

What does 1 million grains of sand look like?

Each grain is 1/1,000th of a foot wide, so it takes 1,000 x 1,000 or about 1 million grains of sand to cover just 1 square foot. That's just a thin layer of single grains…if you want a few inches of sand, you need hundreds of layers, giving us over a billion grains for a grown-up!

count sand grains