### Numbers in the News: Sand, Sand Everywhere

This past Sunday NPR’s Weekend Edition interviewed Vince Beiser about his new book The World in a Grain. During the interview, Beiser made a mind-boggling claim. If you take all the sand used commercially every year, all 50 billion tons of it, you would have enough sand to cover the state of California. To which Californians might ask: “Well, how deep are we talking?”

 California, after we cover it in sand. Image Credit: via Unsplash
To answer this question, there’s a few things we need to find out first. How big is California’s surface area? How dense is the commercial-grade sand? And why are we talking about covering California? The answer to the last one is probably because Beiser is based out of Los Angeles. As for the first two, let’s do some homework.

According the US Census Bureau which keeps track of such things, the surface area of California is 423,967 square kilometers (163,695 square miles). Note that this number includes everything from land to water, but the water surface area of California is only 20,501 sq km (7,916 sq mi), which is less than 5% of the total surface area. Since this is not a large discrepancy, let’s keep things simple and use the big number under the assumption that we can cover all the water area with sand and not have it wash away.

Construction sand isn’t the typical sand you find just anywhere. It has to have a specific composition and consistency to make concrete possible. Here we refer to the class notes from a 2015 course titled “Concrete Technology” through the University of Washington. The section on aggregates gives a range of 1520 to 1680 kilograms per cubic meter (95 to 105 pounds per cubic foot). For this variable, the median will work well giving us 1600 kg/m3 (100 lbs/ft3).

Using the surface area and density, we can calculate the height of the sand over the surface area. This takes some equation manipulation to get us to the variable we need.

 Part 1 of equation manipulation. Image Credit: Amanda Babcock

 Part 2 of equation manipulation, because one Post-it note is never enough. Image Credit: Amanda Babcock
So let’s plug in some numbers. To make the units work, we need to convert square kilometers to square meters. This means the surface area of California is about 4.23x1011 m2 (4.56x1012 square feet). The mass of sand needs to be in kilograms, so 50 billion tons is ~4.53x1013 kg of sand. Plugging these numbers in gives us the height of the sand.

 Let me just scribble that out on a Post-it real quick. Image Credit: Amanda Babcock

So, if we were to take all the sand used commercially in one year, it would cover the state of California about 0.0669m deep. That’s only 2.63 inches. While it's impressive that we could cover the entire state, that’s not very deep.

Bearing in mind that California is about 60% the surface area of Texas and less than 25% the surface area of Alaska, the sand would be even shallower in either of those states. But California is also 106 times the size of Rhode Island. Squeezing all that sand over the surface area of Rhode Island would result in a column over 7 meters (23 feet) tall...and some very upset Rhode Islanders.

 A proud Californian in Death Valley National Park, one area that would not notice the extra sand. Image Credit: Jeremy Bishop, via Unsplash

It’s also fun to note that California is about 25% desert, with the Mojave Desert making up the bulk of that. Would anyone notice an extra 2.63 inches of sand in the Mojave?

—Amanda Babcock

1. That's a lot of digits of significance for this estimate. I'd round 2.63 to 3, personally.

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### The Science of Ice Cream: Part One

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