What is a Venn Diagram?

Mary McMahon

A Venn diagram is a graphical illustration of the relationship between various sets of data. Most famously, it includes two sets, represented by two overlapping circles, although these diagrams can also be made with three circles, or a series of complex shapes to represent more than three sets of data. Venn diagrams are widely used in a branch of mathematics known as set theory, and they often appear in classroom exercises which are designed to get students to think about the relationships between things.

Woman standing behind a stack of books
Woman standing behind a stack of books

The Venn diagram was developed by John Venn, an English mathematician who lived between 1834-1923. His famous diagram was invented in 1881, and it is actually commemorated in the form of a stained glass window at his former college. By graphically showing how sets of data related to each other, Venn greatly clarified the field of set theory. Later mathematicians tweaked with the form of the diagram, but the basic system remains the same, and in wide use around the world.

A classic Venn diagram includes two sets, such as a list of all of the doctors in a town and all of the residents of a particular neighborhood. Each set is represented by a circle, and where the circles overlap, a region which includes members of both sets is created. In this case, the region would include all of the residents of a particular neighborhood who are also doctors. A third set can be added to the diagram, such as a list of all of the people in the town who have dogs.

When three circles are included in a Venn diagram, several areas of overlap are formed. In the case of the example above, we could see which doctors have dogs, which doctors live in a particular neighborhood, and which residents of that particular neighborhood have dogs. In the very middle of the diagram, where all three circles overlap, we would have a list of dog-owning doctors in the neighborhood.

The Venn diagram is very helpful for categorizing things and laying out information in a way which makes it easier to grasp. Many people like to use it for problem solving, as many world problems can be untangled with its assistance. When more sets of data are involved in a Venn diagram, a number of convoluted shapes must be created to make the desired areas of overlap, which can result in some truly astonishing illustrations of data.

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Discussion Comments


@David09 - Yeah, I used Venn diagrams as well as other flow charting symbols when I took an introductory course in programming and database design.

I agree, however, that nowadays most programmers never draw these pictures down anymore. I suppose they could use a flow charting tool to do a quick sketch if the relationships between data sets become complex and convoluted, but for the most part they draw the pictures in their heads and go from there.


Venn diagrams are great in software development, especially if you want to visualize queries that you are creating for the database. I used to use these diagrams a lot when I first started learning database design, but gradually I internalized the process so I no longer have to draw the diagrams down.

Basically you have two sets of data and the data that is common to both sets is what is returned from your SQL query.

This can be accomplished by using a standard “join” query where you ask questions like, “Show me all customer orders with prices greater than $5.00 per unit.”

The customers represent one circle; the orders (with their customer IDs) represent another circle. The result, or overlapping circle, is the query result. Both sets of data have a customer ID as a common field, and this is joined together between the data sets; hence the term join query.


@KoiwiGal - Funny venn diagrams are also the best way of teaching them to kids. You can start out with a few that are just normal diagrams, so they get the general gist of it.

Then, try some simple, funny ones that would appeal to kids. I've seen Hannah Montana themed venn diagrams, for example.

Try to pick ones that also make a joke about how much overlap there is between the two sets.

Finally, let your kids try to come up with some venn diagrams.

You can encourage them to be funny, but let them know it's not necessary as long as they get the math right.


Venn diagrams are really popular for humor webites at the moment. If it's done well, it can be hilarious, but if not it's just boring.

One of my favorites has two completely separate circles with no overlap, entitled "Times I am truly happy" and "Times I am wearing pants". I've seen a couple of variations on that one as well.

Sometimes they can make them really complex as well, which can be good, or can be confusing.

In fact, I'm not sure how often I ever actually see Venn Diagrams that aren't supposed to be poking fun at something.

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