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Hi Rob -

Actually that is a really good question. I haven't been able to find an "authoritative" answer, but I can show you how I would approach the problem and get some back of the envelop bounds on the answer.

To simplify the question a bit, I am going to restrict the definition of grains of sand to unconsolidated (no sandstone included here), especially that found in the arid regions of the earth excluding polar regions. I am also going to restrict the question to sand residing at or near the surface. If we do that, we find that these regions comprise about 25% of the land area which is ~30% of the surface. If we take those numbers and then multiply them by the surface area of the planet we have the area of the arid regions. If we assume an average depth for sand in all of these regions (maybe 10 meters is reasonable), we can calculate a volume. All we need now is the volume of a sand grain and we can calculate the number of grains needed to fill that volume. Grains of sand range in diameter from ~1mm to 0.0625mm. A simple result would just divide the two volumes, but this would ignore how the grains are packed (how much void space exists) the void space could range from a few to fifty percent.

Doing all of this I find that there are on the order of
10^{22} to 10^{25} grains of sand at the surface. This is
obviously a very gross estimate. If you include sandstone and beaches,
etc., the number will obviously go up. Hope this helps.
Steve

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