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The Beach

Updated: Oct 26, 2020

How many grains of sand are there on a beach? Could you count them? How long would it take?

We can work this out by making some estimates. By lining up some and against a ruler, I counted 25 grains in 1cm. From this, I can conclude that:

  • a square of side 1cm would hold around 252 = 625 grains of sand.

  • a cube of side 1cm would hold around 253 = 15,625 grains of sand.

  • a cubic metre (100cm x 100cm x 100cm) would hold around 15,625,000,000 grains of sand. That’s more than 15 billion grains! And that’s just in one cubic metre!

  • A small beach with an area of 50,000 square metres, whose sand was 1m deep, would have a volume of 50,000 cubic metres. This would therefore contain 781,250,000,000,000 grains of sand. That’s more than 781 trillion grains!

How long would it take to count the sand?

Assuming you can count 1 grain per second, the table shows how many grains would be counted after different time periods.

If you spent your whole life counting sand, you would only count 16% of a cubic metre! You’d need another 6 people to count with you for their whole lives to complete this task. To count the whole beach, you’d need more than 300,000 people counting sand for their whole lives!

So although it’s an interesting idea to ponder, a little Maths shows you that counting sand will take you a long, long time. Estimating is a much better idea!

Counting sand at 1 grain per second


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