A Question from Nobel Laureate Bill Phillips

When I was an undergrad, I had this delusional desire to become an actor. As a male thespian with no experience and mediocre talent, I quickly discovered there's one sure way to get decent theatrical roles: audition for male parts at all girl schools. And so, I auditioned for student productions at Wellesley College where I met a variety of wonderful people. One of said people is my buddy Christine. Christine was (and is) super cool, and not only because she used to get me free food at the Wellesley cafeteria. Christine was also cool because she was taking physics.¹ I distinctly remember one conversation I had with Christine about her physics class:

Christine: I'm taking physics at Wellesley.

Me: You should really see if you can take it at MIT instead.

Christine: [trying to be nice] Um...my dad thinks they do a better job teaching physics at Wellesley.

Me: [offended] What the hell does your dad know about physics?

Christine: Well, he did get his doctorate from MIT, and he just won the Nobel Prize in physics.

Me at this point in the conversation.

This week's question comes from Christine's dad (aka Nobel Laureate Bill Phillips.) He asks, "How many grains of sand are there on the world's beaches?"

Judging from a map, the Eastern Seaboard of the United States appears to be about 2000 miles long. By comparing with other coastlines, we can estimate the total length of coastlines in the world to be about 50 times this.² I'll assume one-third of the world's coastlines are sandy beaches.

Assuming the Cape Cod beaches I grew up near are fairly typical, they might extend about 200 feet up from the water. The depth of sand varies quite a bit from place to place. I've been on beaches where you'll hit rock before finishing the moat around your sandcastle, but many beaches have sand that extends much deeper. I'll assume the sand extends 10 feet deep on average since the actual number is likely to lie between 1 foot and 100 feet. From this, we can calculate the total volume of sand on the beach to be about 10¹⁰ cubic meters.

One type of sand.

Like beach depths, sand grains too vary over a size range that's greater than one order of magnitude. I'll assume 0.3 mm for the width of a sand grain since even the largest sand grains are each only a few millimeters in size. This gives a total volume of 0.03 cubic millimeters. From this and the total beach volume above, we can estimate that there are 10²⁰ grains of sand on all the beaches in the world.

Thanks for the great question, Dr. Phillips!

Aaron Santos is a physicist and author of the books How Many Licks? Or How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions. Follow him on Twitter at @aarontsantos.

[1] Taking physics automatically makes you cool.
[2] It will certainly be between 5 and 50 times the Eastern Seaboard.