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3 Circle Venn Diagram

Fill in the seven parts of three overlapping circles with items or numbers and read off the unions, intersections and complements.

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This free 3 circle Venn diagram tool draws three overlapping circles and lets you fill in all seven parts, so you can compare three sets at once. It runs in your web browser, needs no account or sign-up, and opens with a sample diagram of the numbers 1 to 12 so you can see how the parts work before you change anything. Under the diagram, a table works out the size of each set, the intersections, the unions and, when the outside box is on, the complements. You can use it for homework on three-set problems, class sorting activities, or any comparison of three groups. It works as a three circle Venn diagram generator for any three sets, whether you type items or just numbers.
3 circle venn diagram example

How to use the 3 circle Venn diagram tool

  1. Type a title in the Title box.
  2. Type a name for each set and pick a color for it. The labels on the seven boxes use your names.
  3. Open the What do you type in each part? menu and choose Items (one per line) or Numbers (how many).
  4. Fill the seven boxes: In A only, In B only, In C only, In A and B only, In A and C only, In B and C only and In all sets. In Items mode, put each item on its own line. In Numbers mode, type a number in each box.
  5. If you need a universal set, tick Draw a box around the circles, then type the items or the number that belong to none of the three sets in the Outside all three circles box.
  6. In Items mode, use the Show in the diagram menu to choose The items, Only the counts or Nothing.
  7. Read the table under the diagram for the set sizes, intersections, unions and complements, and the check line, where both sides of the inclusion-exclusion formula show the same number.

The Examples menu has Numbers 1 to 12, Class activities and Animals. The Export menu saves PNG (normal, 2x or 4x), SVG or PDF, or copies the image. The Saved menu keeps your work in this browser, saves named copies and copies a share link. Nothing is uploaded.

What is a 3 circle Venn diagram?

A 3 circle Venn diagram shows three sets (groups of things) at the same time, with each set drawn as a circle. Because the three circles overlap, there are seven parts inside them: three parts that belong to one set only, three that belong to exactly two sets, and one central part that belongs to all three. Each item goes in exactly one part, based on which sets it belongs to. Items that belong to none of the sets sit outside the circles.

Three terms appear throughout. The union of A, B and C is everything in at least one of the sets. The intersection is what is in all the named sets, so A and B means items in both A and B. The complement of A is everything in the universal set (the box around the circles) that is not in A.

To solve a word problem with numbers, work from the centre outwards. Start with the number in all three sets, then subtract it from each pair to find the “exactly two” parts, then subtract those from each set to find the “one set only” parts. In Numbers mode the seven boxes take the values in this order: A only, B only, C only, A and B only, A and C only, B and C only, all three. For the values 7, 5, 4, 3, 2, 1, 2, the set sizes are A = 14, B = 11 and C = 9, the pairwise intersections are 5, 4 and 3, and the union is 24.

What is the formula for three sets?

The formula for three sets is called inclusion-exclusion:

|A or B or C| = |A| + |B| + |C| − |A and B| − |A and C| − |B and C| + |A and B and C|

Adding the three set sizes counts the overlaps more than once. Subtracting the three pairwise overlaps corrects the items that were counted twice. An item in all three sets has now been added three times and subtracted three times, so it is missing from the total, which is why the triple intersection is added back once. An item in exactly two sets is added twice and subtracted once, so it is counted once, as it should be.

Using the same numbers: 14 + 11 + 9 − 5 − 4 − 3 + 2 = 24, which matches the union found by adding the seven parts directly. The check line under the diagram makes this comparison for your data, so you can confirm your counts before you use them.

Frequently asked questions

How many parts does a three circle Venn diagram have?

A three circle Venn diagram has seven parts inside the circles. Three parts belong to one set only, three belong to exactly two sets, and one central part belongs to all three. An optional outside area covers items that belong to none of the sets.

How do I fill in a 3 circle Venn diagram?

Type a name for each set, choose Items or Numbers mode, and then fill the seven boxes. Each box corresponds to one part of the diagram, and the box labels use your set names. The table under the diagram then calculates the totals for you.

How do I find the union and intersection of three sets?

The union is everything in at least one of the sets, and the intersection is what is in all of the named sets. Read the union and intersection values in the table under the diagram, or add up the relevant parts yourself. For example, A and B includes the “A and B only” part and the centre.

How do I solve a three set Venn diagram word problem with numbers?

Start with the number in all three sets, then work outwards: subtract it from each pair to find the “exactly two” parts, then subtract those from each set to find the “one set only” parts. Type those seven numbers into the boxes in Numbers mode and check the totals in the table.

What is the formula for three sets?

The formula is |A or B or C| = |A| + |B| + |C| − |A and B| − |A and C| − |B and C| + |A and B and C|. It adds the set sizes, removes the pairwise overlaps, and adds back the centre once.

Can I export my diagram as a PNG, SVG or PDF?

Yes. The Export menu saves a PNG image, a PNG 2x or PNG 4x (print quality), an SVG (vector) or a PDF. You can also copy the image to the clipboard, and exports have a white background with no watermark.

Can I use my Venn diagrams commercially?

Yes. Venn diagrams you make here are yours to use for personal, school and commercial work, including reports, slides, books and printables you sell. No credit is required. The only thing you may not do is copy the tool or the site itself to run a competing service; see the terms.