Venn Diagram Maker

How to Use the Venn Diagram Maker

1. 1. Choose two or three sets. Give each set a name and a color. A name that is left blank shows as its letter, A, B or C.
2. 2. Fill in the regions. Pick how you want to enter them. Items in each region gives you one box per region — Mitosis only, Both, Meiosis only — for notes and phrases. Members of each set lets you list each set in full and sorts anything listed twice into the overlap for you. Counts takes one number per region, for survey and probability problems.
3. 3. Add the universal set if you need it. Tick the box to draw a rectangle around the circles and name it — All students in Year 9, or simply U. Whatever lies outside every circle goes in the rectangle's corner.
4. 4. Check the working, then download. Under the diagram the tool lists the size of every set and works through the inclusion–exclusion sum. Download SVG for documents (it stays sharp at any size) or PNG for slides, and switch on APA style figure if the diagram is going into a paper.

Regions and Set Notation

Two overlapping circles make three regions, and three circles make seven. Each region is one combination of in and not in: the left crescent holds what is in A but not in B, the lens in the middle holds what is in both. In set notation ∩ means and (intersection), ∪ means or (union), and a prime marks the complement — B′ is everything that is not in B. The data table under the diagram gives every region's notation.

The diagram is the classic kind: the circles are always the same size and every region is drawn, even an empty one, because an empty region is information too. A diagram whose circles are sized to the counts is an area-proportional or Euler diagram, which this tool does not draw.

The Arithmetic: Inclusion–Exclusion

To count the members of A ∪ B — everything in at least one set — you cannot simply add the two sets, because the overlap would be counted twice. You add them and subtract the overlap once: n(A ∪ B) = n(A) + n(B) − n(A ∩ B), where n( ) means the number of members of. With three sets the pairwise overlaps are subtracted and the centre, which those subtractions took away three times after the sets added it three times, is added back: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(A ∩ C) − n(B ∩ C) + n(A ∩ B ∩ C).

Members of each set does the sorting for you. List the multiples of 2 up to 12 as one set and the multiples of 3 as the other, and the tool puts 6 and 12 in the overlap, 2, 4, 8 and 10 in the first crescent and 3 and 9 in the second. Give it the universal set 1 to 12 and it places 1, 5, 7 and 11 outside both circles.

Venn Diagrams for Compare-and-Contrast Essays

Before you write a comparison, a Venn diagram sorts your notes: shared features go in the overlap, differences in the crescents. The example compares mitosis and meiosis — both follow DNA replication and both run through prophase, metaphase, anaphase and telophase, but mitosis makes two identical cells for growth and repair while meiosis makes four genetically different cells — in animals, the gametes.

• Balance the crescents. If one side is full and the other nearly empty, you know more about one subject than the other — research before you draft.
• Turn regions into paragraphs. In a block essay, each crescent becomes a section; in a point-by-point essay, pair matching items across the crescents (two daughter cells against four) and give each pair its own paragraph.
• Write the thesis from the overlap. The interesting claim is usually why two things that share so much still differ — the diagram shows both halves of that sentence.

When a Venn Diagram Helps — and When It Doesn't

• It helps with two or three categories that overlap: comparing two texts, periods or theories; sorting survey answers; and set and probability problems, where the regions are the arithmetic.
• Use a table for four or more sets. Four circles cannot show all sixteen combinations; four-set diagrams need ellipses and are hard to read.
• Use a bar graph when the sizes matter. Equal circles show which combinations exist, not how big they are. Print the counts in the regions, or compare the totals in a Bar Graph Maker chart.
• Use a list when nothing overlaps. Two separate circles with an empty middle say only that the groups are distinct.

For an APA 7 paper, tick APA style figure: the title leaves the image and the bold figure number and italic title appear above it, ready to copy. Explain the data in a note under the figure — for example, Note. Survey of 30 students, March 2026.

Frequently Asked Questions

How do I make a Venn diagram with three circles?

Choose Three sets, name the third set, and fill in the seven regions — the three single regions, the three pairwise overlaps and the centre. The circles sit on a triangle so that every combination has its own region. Long lists are fitted inside each region, with smaller type if needed and a “+ more” line if they still do not fit.

What does the overlap in a Venn diagram mean?

The overlap holds whatever belongs to both sets at once — their intersection, written A ∩ B. In a three-set diagram the very centre is in all three, and each lens around it is in exactly two. Anything in a crescent belongs to one set only.

How do you find A union B from a Venn diagram?

Add every region inside the two circles: A only, both, and B only. With set totals, use n(A ∪ B) = n(A) + n(B) − n(A ∩ B), subtracting the overlap because adding the two sets counted it twice. The tool shows this working with your own numbers under the diagram.

What is the rectangle around a Venn diagram?

It is the universal set, U — everything under consideration, such as all students in a class. Members of U that belong to none of the sets sit inside the rectangle but outside every circle. Draw it when the question involves neither or not in any set; leave it out when it adds nothing.

Are the circles drawn to scale?

No. This tool draws the classic Venn diagram, with equal circles and every region shown, so the picture says which combinations exist rather than how large they are. A diagram with circle areas in proportion to the counts is an area-proportional (Euler) diagram, a different figure.

Can I make a Venn diagram with four or more sets?

Not with circles: four circles cannot form all sixteen regions, so four-set diagrams use ellipses and become hard to read. For four or more categories, a table of the combinations, with a row per item and a column per set, is clearer and easier to check.