How many grains of sand are in a cubic meter?

Mathematician Marcus du Sautoy replies: Sand is rock with a diameter of between 0.625mm and 0.2mm. 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. So how many grains of sand are there in a metre cube box? It has 109mm cubes inside (10N is how mathematicians write a 1 followed by N zeros), and if they are arranged randomly, about 65% of the box will be sand and the rest air. So we can estimate that the number of grains of sand in a metre cube box is 109 x 0.65/0.00947, or roughly 70bn grains. Now, let's go for an average of 5% of the surface of the Earth being covered in sand with a depth of 100m. The surface area of the Earth is 4 x pi x r2 where r is the radius of the Earth, which is 6,378,000 metres. So the volume of sand comes out at: 2.5 x 1015m3. So my rough estimate is that the number of grains of sand on the Earth is a number with 27 digits.

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How many grains of sand are in a cubic centimeter?
What is the volume of 1 grain of sand?
How big is a million grains of sand?
How much is a cubic Metre of sand?

Marcus du Sautoy is author of The Number Mysteries (Fourth Estate).

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This is a question that cannot be answered with any accuracy. However, it is interesting to consider how we can get as close as possible to a satisfactory answer. We would need first to find the volume of sand in the world (by far the biggest stretches of sand being the Sahara and Gobi Deserts), then plot the particle-size distribution at each place, and finally work out the average particle size of the sand.

If the question is taken literally – namely, how many grains of sand there are in the world – we are interested specifically in rock detritus with a particle diameter of 0.06-2 mm. According to standard sedimentological classification, detrital material is called clay if the diameter of the particles, d, is less than 0.002 mm, silt if d is 0.002-0.06 mm, sand if 0.06-2 mm, gravel if 2-64 mm, cobble if 64-256 mm, and boulder if greater than this.

The Sahara Desert.

Let’s assume that all the grains of sand are spherical and of equal size. If so, they will ‘pack together’ with maximal compaction, such that the spheres themselves fill 68% of the total volume. If the diameter of the grains is on average 1 mm, this would give 1.30 × 109 (1,300 million) grains in one cubic metre of sand.

For the sake of argument, say that all the sand in the world forms an even layer, 10 cm thick, over the entire surface of the earth, which covers 510 million km2 (200 million square miles). Then the volume of the sand will be 5.10 × 1013 cubic metres and the number of grains thus

5.10 × 1013 × 1.30 × 109 = 6.63 × 1022

If the layer of sand was only half as thick, the number of grains would be halved, and if the layer was a metre thick there would be ten times as many. As it is, we simply do not know how thick the layer is in reality, nor what the average particle size is. It is perhaps fun to compare our result with Avogadro’s number, which is about 10 times greater.

By way of comparison, consider the famous Indian legend about the invention of chess and the grains of rice. The inventor presents the game to the king and asks for payment in grains of rice – one for the first square, two for the second, four for the third, eight for the fourth, and so on. There are 64 squares. The result comes out at 1.84 × 1019 grains of rice, which is about 4,000 times less than the number of grains of sand in the world on the basis of our calculations above. To bring the number of grains of rice up to our number for the grains of sand, you would need a chessboard with 76 squares instead of 64.

Translated by Nicholas Jones.

Picture: Astroseti.org

Earth’s beaches contain roughly 5 sextillion grands of sand or 8,000,000,000 grains of sand per cubic meter of beach and that the Earth contains roughly 700,000,000,000 cubic meters of beach.

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Okay well to start off let's guesstimate the average diameter of a grain of sand to be about half a millimeter (5E-4 meter). I am going to assume that a grain of sand is in the shape of a sphere so we'd use the formula: V=(4/3)πr3 to find the volume of 1 grain of sand. If we use 2.5xE-4 meter for "r" we get roughly 6.545E-11 cubic meter as the volume for 1 grain of sand. Now a trillion of these would equal 6.545E1 cubic meters. Now the average joe might not be able to visualize 6.545E1 cubic meters so let's convert that into liters: 65450 liters. But let's not forget that spheres are half as efficient as filling up space as a cube so let's double that and we'd get 130900 liters of sand which can be visualized as 65450 2-Liter soda bottles or about 131 bathtubs. That's A LOT of sand. Cheers!

P.S. first comment/post here hope I did well!

EDIT: I'm bad at fermi. Forgot that spheres are half as efficient as cubes of the same diameter (ratio is like 33:64).

How many grains of sand are in a cubic centimeter?

Simple calculation yields a result that 1 cubic centimeter can contain 151 sand grains with a diameter of 2 mm and 4,959,645 sand grains with a diameter of 62.5 micrometers.

What is the volume of 1 grain 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 big is a million grains of sand?

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.

How much is a cubic Metre of sand?

Weight of 1 cubic metre of sand is about 1600kg, in this regard, volume of a 20kg bag of sand in cubic metre as 20/1600 = 0.0125, so volume of a 20kg bag of sand is about 0.0125 cubic metres.