Venn diagram maker for 2, 3 and 4 sets, from blank templates to exact list overlaps

How to make a Venn diagram here

The diagram redraws as you type, and nothing is sent anywhere: the lists are read and the shapes are drawn by code running in your browser tab.

• Pick a template or a number of sets. Two and three sets use circles; four sets use four ellipses, because four circles cannot produce every region.
• Name the sets and choose their colours. The default palette is Okabe-Ito, which stays distinguishable for the common forms of colour blindness; Outline only gives a black-and-white printable.
• To compare and contrast, choose Type in regions and write one item per line in each region’s box. Clicking a region in the diagram jumps to its box.
• To compare lists, choose Paste lists and paste one list per set, or paste two to four spreadsheet columns at once. Every overlap is computed exactly and listed in the region table.
• Under Style, show counts, percentages, the items themselves or the set notation in each region; add a universal set box, writing lines for worksheets, or area-proportional circles.
• Under Shade, type a set expression such as (A ∪ B) ∩ C′ to shade it, and, with lists, see exactly which items it contains.
• Export SVG for editing in Illustrator, Inkscape or PowerPoint, PNG at 2× or 3×, or PDF through the print dialog. The region table downloads as CSV, and the item-by-set membership matrix is ready for an UpSet plot or R.

What is a Venn diagram?

A Venn diagram draws sets as overlapping closed shapes inside a rectangle that stands for the universal set, everything under consideration. Each set is one circle or ellipse, and the shapes are arranged so that every possible combination of membership has its own region: in A only, in A and B but not C, in all of them, in none. John Venn described the method in the Philosophical Magazine in 1880 as a way to picture logical propositions, and it has since become the standard picture of sets in mathematics, statistics, logic and biology.

• The universal set U is the rectangle. A region outside every circle but inside the rectangle holds the items that belong to none of the sets.
• Every region is drawn even when it is empty. An empty region is shown with a 0, or shaded in logic diagrams, rather than left out; that is what separates a Venn diagram from an Euler diagram.
• A “completed” Venn diagram has every region filled in. A blank one is the same drawing with the regions left empty for a student to fill, which is why a worksheet and its answer key can come from the same template here.

How to read the regions of a Venn diagram

Each region is defined by which sets it is inside and which it is outside. A diagram of n sets has 2ⁿ − 1 regions inside the shapes, plus the outside region.

• Two sets: three regions. A only, B only, and the overlap A ∩ B in the middle. In a compare-and-contrast diagram the overlap holds the similarities and the two crescents hold the differences.
• Three sets: seven regions. Three “only” regions on the outside, three regions where exactly two sets overlap, and the centre where all three meet.
• Four sets: fifteen regions. Four “only” regions, six pairs, four triples and one region shared by all four.
• The middle of a Venn diagram is the intersection of every set: what all of them have in common.
• Regions are exclusive. The “A and B only” region leaves out anything that is also in C, so it can be smaller than A ∩ B as a whole. The pairwise table under the diagram gives both numbers.
• Adding the counts of every region inside the shapes gives the size of the union. Each item is counted once, in exactly one region; the region table shows that sum as a check.

Set notation on a Venn diagram: union, intersection and complement

Set operations are easiest to learn by shading. Type any of these into the Shade tab and the matching regions are hatched; the set notation key further down this page shows each one drawn.

• Union, A ∪ B (“A or B”): everything in A, in B, or in both.
• Intersection, A ∩ B (“A and B”): only what is in both. Two sets with nothing in common are disjoint, and their intersection is the empty set, ∅.
• Complement, A′ (also written Aᶜ or Ā, “not A”): everything in the universal set that is outside A.
• Difference, A − B (also A \ B, “A but not B”): what is in A and not in B. It equals A ∩ B′.
• Symmetric difference, A △ B: what is in exactly one of the two sets, the union without the overlap.
• De Morgan’s laws are easy to see shaded: (A ∪ B)′ is the same region as A′ ∩ B′, and (A ∩ B)′ is the same as A′ ∪ B′.
• The tool applies complement first, then intersection, then difference, then union and symmetric difference. When in doubt, use brackets: (A ∪ B) ∩ C and A ∪ (B ∩ C) are different regions.

Counting with a Venn diagram: inclusion–exclusion

Adding the sizes of overlapping sets counts the shared items more than once. The inclusion–exclusion principle corrects for it, and a Venn diagram shows why each term is there.

• Two sets: |A ∪ B| = |A| + |B| − |A ∩ B|. The overlap is counted in both |A| and |B|, so it is subtracted once.
• Three sets: |A ∪ B ∪ C| = |A| + |B| + |C| − |A ∩ B| − |A ∩ C| − |B ∩ C| + |A ∩ B ∩ C|. The centre is added three times, taken away three times, and added back once.
• The same rule gives probabilities: P(A or B) = P(A) + P(B) − P(A and B). Divide each region’s count by the total to turn the diagram into a probability diagram.
• Worked the other way, the rule fills in a Venn diagram from survey totals: start with the centre, then the pairs, then the “only” regions, subtracting as you go.
• The worked example below sorts the numbers 1 to 30 by multiples of 2, 3 and 5 and checks the formula against the regions.

2-, 3- and 4-set Venn diagrams, and what to do beyond four

Two and three sets fit naturally in circles. Four do not: two circles cross at no more than two points, which limits n circles to at most n² − n + 2 regions, counting the outside. For four circles that is 14, two short of the 16 that four sets need, so at least two combinations would have nowhere to go.

• Ellipses can cross at four points, so four ellipses can show all 16 regions. Venn himself drew a four-set diagram this way, and it is the layout used here.
• The four-ellipse diagram is still readable for counts and short labels, but its smallest regions are narrow. Keep the text in them short.
• Five-set Venn diagrams exist, but their 31 regions include slivers too small to label, and readers struggle to find a given intersection.
• For five or more sets, or for many sets of different sizes, use an UpSet plot. It lists the intersections as rows of a matrix with a bar for each one’s size, so it scales to dozens of sets. The membership CSV from this tool is the input it needs.

Area-proportional Venn diagrams: what is exact and what is not

In a standard Venn diagram every region gets similar room whatever its count. An area-proportional (scaled) diagram sizes the shapes so that the areas match the numbers, which shows at a glance that one list is three times another.

• Two sets: exact. The circle areas equal the two set sizes, and the distance between the centres is solved so that the lens of overlap equals the shared count.
• Three sets: the three circle areas are exact, but the seven regions usually cannot all be matched at once. Three circles leave only three distances free to fit four overlap areas, so some combinations of counts cannot be drawn with circles at all. This tool finds the closest placement and reports how far each region’s area is from its count.
• Because of that, the numbers in a scaled three-set diagram are the result; the areas are an approximate guide. Say so in the figure legend.
• Very unequal sets can leave a small region too thin to label, and a region with items can even vanish. The tool lists any such region under the diagram, and the standard layout always draws every region.
• Four or more sets are not drawn to scale here: ellipses with matched areas become unreadable, and an UpSet plot shows sizes more accurately.

Venn diagram or Euler diagram?

The two look alike but answer different questions. A Venn diagram shows every possible combination of sets, empty or not. An Euler diagram, named after Leonhard Euler, who used overlapping circles to teach logic in the 1760s, shows only the relationships that actually occur.

• If no item is in both A and B, an Euler diagram draws A and B apart; a Venn diagram still draws the overlap and marks it empty or shaded.
• If every A is also a B, an Euler diagram puts A inside B. The Venn version keeps the overlap and shades the “A only” region as empty.
• Area-proportional diagrams with a zero region are, strictly, Euler diagrams: an empty overlap is drawn as two separate circles.
• For teaching syllogisms (“all A are B”) an Euler diagram is clearer. For counting, probability and comparing lists, a Venn diagram is the safer choice, because a missing region cannot be mistaken for a forgotten one.

Comparing gene lists and other research data

Venn diagrams are a routine figure in genomics and ecology: differentially expressed genes shared between conditions, proteins detected by two methods, species found at several sites, patients meeting several criteria. A correct one depends on the lists being comparable before they are drawn.

• Use one identifier system throughout. A gene listed by symbol in one list and by Ensembl or Entrez ID in another will never match; neither will a symbol and its older alias.
• Matching ignores letter case and spaces at either end by default, so BRCA1, brca1 and “BRCA1 ” are one item. Turn on Match case where case carries meaning.
• Repeats within a list are counted once, and the tool tells you how many it removed, so a duplicated row cannot inflate an overlap.
• A count of shared items means little without the background. Paste the universal set, such as every gene measured, to see what lies outside all lists; to test whether an overlap is larger than chance, a hypergeometric or Fisher’s exact test needs that background size too.
• The Jaccard index in the pairwise table (shared ÷ union) compares overlaps between pairs of lists of different sizes on one scale from 0 to 1.
• With more than four lists, or when the reader needs to rank intersections by size, an UpSet plot is clearer than any Venn diagram.

Venn diagrams in the classroom

From primary sorting activities to set theory and probability, the same template covers most classroom uses, and the blank and completed versions come from one file.

• Compare and contrast: two circles for two topics, characters, cells, historical periods or materials, with similarities in the middle. The Mitosis vs meiosis template is a ready example.
• Plant and animal cells: the classic biology comparison puts the cell wall, chloroplasts and large central vacuole on the plant side, centrioles on the animal side, and the shared organelles in the middle. The template follows our plant and animal cell diagram page.
• Sorting numbers: multiples, factors, odd and even, or primes, with a universal set box for the numbers that fit none of the rules. The 1 to 30 template shows one.
• Set notation and probability: turn on Region notation to label each region, or shade an expression and ask students to name it.
• Printable templates: Blank 2-circle and Blank 3-circle come with writing lines and write-in name lines; leave everything blank or fill in one region as a model answer.
• Venn diagram foldable: print the blank two-circle template, fold the sheet in half along its long side, and cut the top layer into three flaps, one over each region, so students write the answers underneath.
• Big Venn diagram for a wall or a whiteboard: export the PDF and print it at poster size, or use the 3× PNG; the SVG scales to any size without losing sharpness.

Making a Venn diagram in Word, PowerPoint, Google Slides, R or Python

If the diagram has to be built in another program, these are the usual routes. Each has limits that this maker avoids, such as fixed layouts or no counting.

• Word, PowerPoint and Excel: Insert, SmartArt, Relationship, Basic Venn. The circles are equal and the overlaps have no text boxes of their own, so labels in the overlaps are added as separate text boxes. Pasting this tool’s SVG into Office gives an editable vector drawing instead.
• Google Docs and Slides: there is no Venn template. In Slides, Insert, Shape, Oval, then lower the fill transparency so the overlaps show; in Docs, do the same inside Insert, Drawing, New.
• R: the VennDiagram and ggVennDiagram packages draw standard diagrams from lists, eulerr draws area-proportional Euler and Venn diagrams, and UpSetR draws UpSet plots.
• Python: the matplotlib-venn package draws area-weighted two- and three-set diagrams (venn2, venn3); its documentation notes that three-set areas cannot in general match the counts exactly, for the same geometric reason as here.
• Whichever you use, check the counts by inclusion–exclusion before publishing, and state whether the areas are drawn to scale.

Tips for a clear Venn diagram in a paper, poster or slide

• Print the set size next to each name, and the count in each region. Readers should not have to estimate overlaps from areas.
• Say whether the shapes are drawn to scale. If the three-set layout is area-proportional, note that the overlap areas are approximate.
• Use a colour-blind-safe palette and translucent fills so the overlaps mix visibly, or outlines alone for print. Do not rely on colour alone to name the sets.
• Keep text in the small regions of a four-set diagram short, or show counts in the diagram and the items in a table.
• Export SVG or PDF for journals and posters; a PNG at 3× is roughly 2,400 to 3,300 pixels wide here, comfortably above 300 dpi at a single journal column.
• Report the data behind the figure: the region CSV gives every count and item for supplementary material.