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Venn Diagram Maker

This Venn diagram maker turns two or three lists into a clear, shaded diagram in seconds. Type the items of each set, and the diagram updates live: every overlap is shaded, every region is labelled with its count, and the full item lists appear below. You can download the finished diagram as a PNG for a slide, a report, or a homework assignment.

How it works

A Venn diagram is a picture of sets. A set is simply a group of things: the numbers {1, 2, 3, 4}, the fruits {apple, banana, cherry}, or the students in a class who play football. Each set becomes one circle. Where two circles cross, the lens-shaped overlap holds the items that belong to both sets. Where three circles cross, the small centre region holds the items that belong to all three. Anything inside one circle only belongs to that set alone, and anything outside every circle belongs to none of the sets.

To use the maker, type each set's items into its own box, separated by commas. You can use numbers, words, or short phrases. The maker cleans up each list for you: it trims extra spaces around every item and drops exact duplicates, because in maths a set never contains the same item twice. Matching is exact and case-sensitive, so "Apple" and "apple" count as two different items. If you want them to match, type them the same way in both sets.

The diagram shows three kinds of information at once. First, the picture itself: the circles and their overlaps show the shape of the relationship. Second, the counts: every region carries the number of items inside it, so you can read sizes without listing anything. Third, the lists below the tool: each region's items are written out in full, so you can check exactly which items fall where. Switch between two and three circles with the diagram type selector, and the maker re-computes everything on the spot.

The formula above is the inclusion-exclusion rule, and it is worth knowing because it stops double counting. If set A has 4 items and set B has 4 items, the union is not 8 items when 2 items are shared: the shared items would be counted twice. Subtract the overlap once and you get the true total of 6. The maker does this arithmetic for you, and the same idea extends to three sets, where the centre region is added and subtracted in turn.

Venn diagrams are used far beyond maths class. Teachers use them to compare two books, two animals, or two historical periods. Businesses use them to show which customers buy product A, product B, or both. Programmers use them to think about data that matches several conditions at once. And in logic and probability, they make ideas like "and", "or", and "not" visible: "A and B" is the overlap, "A or B" is everything inside either circle, and "not A" is everything outside circle A.

Worked example

Take two sets of numbers. Let A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. Which numbers are in both, which are only in A, and which are only in B?

Step 1: Compare the two lists item by item. The number 1 is in A but not in B. The number 2 is in A but not in B.
Step 2: The number 3 is in A and in B. The number 4 is in A and in B. These two go in the overlap.
Step 3: The number 5 is in B but not in A. The number 6 is in B but not in A.
Step 4: Collect the regions. A only is {1, 2}, B only is {5, 6}, and both is {3, 4}.
Step 5: Check the union. The union is every number in either set: {1, 2, 3, 4, 5, 6}, which is 6 items. By the formula, |A| + |B| − |A ∩ B| = 4 + 4 − 2 = 6, which agrees.

Try it yourself: leave the diagram type on "2 circles", type 1, 2, 3, 4 into set A and 3, 4, 5, 6 into set B, and press Draw diagram. The tool gives exactly the same answer — overlap {3, 4}, A only {1, 2}, B only {5, 6} — and the picture shows a count of 2 in each of the three regions.

FAQ