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Easily Confused Charts: VENN vs EULER



Welcome to my first article about easily confused charts! Let's break down the difference between a Venn diagram and an Euler diagram.

It’s safe to say everyone is familiar with a Venn diagram, but have you heard of Venn’s more sophisticated cousin, the Euler diagram? Once you meet an Euler, there’s no going back. Euler is where the magic happens.

Venn vs Euler diagram

A Venn diagram shows all possible relationships between sets, even if the relationships don’t exist. An Euler diagram, on the other hand, shows only the relationships that actually exist between sets. It's like a more complicated, grown-up Venn.

chart comparing Venn to Euler diagram

When I discovered Euler diagrams, my mind was blown. It had never hit me why certain sections of a Venn diagram are left blank and unlabeled—because nothing exists there. There is no overlap between those sets.

chart comparing Venn vs Euler diagram

A Venn diagram is good for a small number of data points (at least two items, no more than four, generally), while an Euler can handle many more categories and complicated inter-connectedness. I find them both to be pleasing to look at and intuitive to understand.

Below is my favorite Venn of all time, the overlap of life purposes known as ikigai, the Japanese idea of living life with purpose and joy. There is a bestselling book about this concept. But the original Venn is flawed. See below.

Ikigai Venn diagram

In other words, a Venn diagram is more limited. It can have empty relationships. An Euler diagram will never have empty relationships. Who wants an empty relationship? Not me. Below I have applied the ikigai concept to better, 4-set Venn:

Ikigai Venn diagram

An Euler diagram sometimes resembles a lopsided Venn because it distorts its shape only to show overlaps that actually exist. Below is an Euler diagram I recreated on the confusing hierarchy of the British Isles, a common example of the Euler at work:

British Isles Euler diagram

The Euler diagram is named after 1700’s Swiss mathematician Leonhard Euler (pronounced “oiler”). He contributed more to mathematics than probably anyone in history. John Venn was an English mathematician born in 1834. He published his namesake diagrams in the 1881 book Symbolic Logic. Leave it to the mathematicians to come up with these awesome logic diagrams!

Leonhard Euler and John Venn

To recap: A Venn shows all possible overlaps.

An Euler can show nested and excluded sets. It’s more flexible and versatile.

All Venns are Eulers, but not all Eulers are Venns.

Euler Venn diagram

Congratulations, if you’ve read this far, you know now a little bit more about Set Theory!

Try making a Venn for yourself. At what intersection of interests do you sit? How elaborate can you get with the overlaps? Are there any empty ones?

personal Venn diagram of Julie Peasley

EPILOGUE: There is another data visualization technique called a Rainbow Box, which shows overlapping sets in a completely different way from an Euler diagram. It uses spanning horizontal bars in a box. But that’s a post for another day…



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