Why Does the Number 12 Occur so Frequently?

Eggs are packed in 12, there are 12 inches in a foot, there used to be 12 pennies in a shilling, the analog clock goes to 12. Why always 12?

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A representation of dozenal multiplication table created by treisaran inspired Roman and Mayan numerals.

The Story of 12

To make a long story short, indeed there is. It has to do with division. Historically people have counted things in tens, hundreds and thousands, just like today. Even the ancient Egyptians and romans did that. But here is the interesting part. People have tended to divide things completely different.

The Many Ways in Which 12 Makes More Sense Than 10

There are an awful lot of cases from real life where the usefulness of 12 becomes apparent. What is important about a number base are the factors it contains. 10 contains just 2 and 5, while 12 contains 2, 3, 4 and 6. This has significant implications whether you are packing goods, tiling a floor, dividing up the time on a clock or the degrees in a circle, or creating different denominations of money.

Packaging in 12s vs 10s

People who do any kind of packaging have learned early that basing units on 12 makes sense. It is easier to pack that way, which is why things historically have been sold by the dozen. A grocer is simply somebody who sells goods by the gross.

  • 2 x 6 two rows of six
  • 2 x 2 x 3, two layers with two rows and three columns
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Dividing a Day

A day is naturally represented as a circle, as anything we want to be able to divide whether it is a cake or pizza. You naturally want to be able to divide a pizza into 2, 4, 6 or 8 parts.

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Four pizzas divided into 2, 4, 6 and 8 parts.
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Two pizzas divided into 5 and 10 parts.

Dividing a Circle into Degrees

Our circles are divided into 360 degrees, which is 12 times 30. So we can see the number 10 pops up. But lets say we wanted to reconsider this historical division. Dividing it into 10 parts or a dozen would obviously not make sense, as we would too quickly need to handle decimals.

Tiling Floors

The usefulness of the factors of 12 reveal themselves when trying to tile a floor with various geometric shapes, while the problems with the factors of 10 become apparent. You can’t tile a floor with pentagons.

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Final thoughts

There are actually a lot more to say about 12 based number systems, e.g. how we write numbers in such a system and how we do 12 based arithmetic. But here I just wanted to give the rational or explanation for why 12 is such an important number. If we could have designed our number system over again we probably would have opted for 12 rather than 10.

Geek dad, living in Oslo, Norway with passion for UX, Julia programming, science, teaching, reading and writing.

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