<-- .. title: Grains of Sand .. date: 2011-07-18 11:33:00 .. tags: sand, order of magnitude, carl sagan .. category: old .. slug: grains-of-sand .. author: Jesse .. has_math: true --> [](http://3.bp.blogspot.com/-87-vnzGa9Po/TiRR2qFWprI/AAAAAAAAAF0/KsfRQhoL5Ds/s1600/SandUDunesUSoft.jpg) Have you ever sat on a beach and wondered how many grains of sand there were? I have, but I may be a special case. Today we're going to take that a step further, and figure out how many grains of sand there are on the entire earth. (Caveat: I'm only going to consider sand above the water level, since I don't have any idea what the composition of the ocean floor is). I'm going to start by figuring out how much beach there is in the world. If you look at a map of the world, there are four main coasts that run, essentially, a half circumference of the world. We'll say the total length of coast the world has is roughly two circumferences. As an order of magnitude, I would say that the average beach width is 100 m, and the average depth is 10 m. This gives a total beach volume of $$ (100 m)(10 m)(4 \pi (6500 km) )= 82 km^3$$ That's not a whole lot of volume. Let's think about deserts. The Sahara desert is by far the largest sandy desert in the world. Just as a guess, we'll assume that the rest of the sandy deserts amount to 20% (arbitrary number picked staring at a map) as much area as the Sahara. According to wikipedia the area of the Sahara is 9.4 million km^2. We'll take, to an order of magnitude, that the sand is 100 m deep. 10 m seems to little, and 1 km too much. That amounts to \~1 million km^3 of sand. We're going to assume that a grain of sand is about 1 mm in radius The volume occupied by a grain of sand is then 1 mm^3. Putting that together with our previous number for the occupied volume gives $$ \frac{1\cdot 10^6 km^3}{1 mm^3}=\frac{1 \cdot 10^{15}}{1\cdot 10^{-9}}=1\cdot 10^{24}$$ That's a lot of grains of sand. Addendum: Carl Sagan is quoted as saying > "The total number of stars in the Universe is larger than all the > grains of sand on all the beaches of the planet Earth" If we just use our beach volume, that gives a total number of grains of sand as \~1*10^20, which is large, but not as large as what we found above. Is that less than the number of stars in in the universe? Well, that's a question for another day (or google), but the answer is, to our best estimate/count, yes.