What is a Venn diagram?
A Venn diagram is a drawing of overlapping closed shapes, one per set, arranged so that every possible combination of the sets has its own region.
That idea, one region per combination, is what makes a Venn diagram useful. If you are checking which performers sing and dance but don’t act, there is exactly one place to look. On ahaboo, you can move parts of a diagram to understand a topic, whether it is photosynthesis inside a leaf or the way tax brackets are calculated.
The parts of a Venn diagram
- Sets: each circle (or ellipse) is one group, labelled A, B, C or with a name.
- Elements: the individual items written inside the regions.
- Intersection (∩): where circles overlap; items in all of those sets.
- Union (∪): everything inside any of the circles.
- Universal set (U or ξ): the rectangle around the circles, everything under consideration.
- Complement (A′): everything in the rectangle outside a circle.
All the symbols are explained, with a shading calculator, on the Venn diagram symbols page.
A short history
John Venn (1834–1923), a logician at Gonville and Caius College, Cambridge, introduced the diagrams in 1880 in a paper titled “On the Diagrammatic and Mechanical Representation of Propositions and Reasonings”. He improved on the circle diagrams Leonhard Euler had used in the 1760s by insisting that all combinations be drawn, then shading the ones known to be empty. Venn also showed how to draw four sets with ellipses. The name “Venn diagram” was popularised by the American philosopher Clarence Irving Lewis in 1918.
Venn diagram vs Euler diagram
An Euler diagram draws only the overlaps that exist: if every square is a rectangle, the square circle sits inside the rectangle circle. A Venn diagram would draw the overlap and the “square but not rectangle” region anyway, then shade that region as empty. See the difference in the Euler diagram explainer.
Make one
Open the Venn diagram maker to draw your own with two to five sets, or start from examples.
Questions people ask
What is a Venn diagram in simple words?
A picture that uses overlapping circles to show how groups relate. Things in the overlap belong to both groups; things in one circle only belong to just that group.
Who invented the Venn diagram?
John Venn, an English logician and philosopher at Cambridge, described them in an 1880 paper in the Philosophical Magazine and in his 1881 book Symbolic Logic. Similar diagrams had been used earlier by Leonhard Euler.
What is the middle of a Venn diagram called?
The intersection. In a two-set diagram it is A ∩ B; in a three-set diagram the very centre is A ∩ B ∩ C, the items that belong to all three sets.
What is the difference between a Venn diagram and an Euler diagram?
A Venn diagram always shows every possible overlap, even empty ones. An Euler diagram only draws the overlaps that actually exist, so a subset is drawn as a circle inside another circle.
What are Venn diagrams used for?
Comparing and contrasting in reading and writing, sorting numbers and shapes in maths, probability and statistics, logic, and in business or research to show where options, skills or data sets overlap.