Venn diagrams explained: when to use one, examples, and how to make one

A Venn diagram uses overlapping circles to show how groups relate to one another. Each circle represents a set, and the shared regions show which items belong to more than one set.

Say you're analyzing customers who use two product features. You know how many people use each feature individually, but that doesn't tell you how many use both. A Venn diagram makes that overlap visible. Add a third feature, and you can see which customers use all three, exactly two, or only one.

The idea is simple enough to explain with circles on a whiteboard. Working with real data takes a little more care, especially when you need to count intersections correctly or compare groups of different sizes.

We'll start with two-circle Venn diagrams, work through a three-circle example using real data, and look at when another visualization would be easier to read. We'll also work through visual examples created in Deepnote to show how sets overlap and how to interpret the different regions.

What is a Venn diagram?

A Venn diagram shows which items belong to different groups and where those groups overlap. Each group is called a set.

For example, one circle might represent customers who use reporting, while another represents customers who use sharing. The overlap contains customers who use both features. The separate parts contain customers who use only one.

Who was John Venn?

The diagrams take their name from John Venn, an English mathematician and logician who introduced them in 1880. Earlier diagrams, including Euler’s, also represented relationships between groups. Venn’s approach showed every possible membership combination, including combinations with no members.

Venn diagram key components & parts

• Circles or other closed shapes: Represent the sets being compared.
• Overlapping regions: Contain items that belong to more than one set.
• Nonoverlapping regions: Contain items that belong only to the indicated set.
• Labels and counts: Explain each set’s membership rule and how many items occupy each region.
• An optional surrounding rectangle: Represents everyone or everything included in the analysis. Items outside the circles but inside this boundary belong to none of the sets.

Three terms help describe these relationships:

Read the labels rather than estimating counts from circle sizes. Unless the diagram explicitly uses proportional areas, a larger-looking region does not necessarily contain more items.

Venn diagram use cases

Use a Venn diagram when you need to understand membership across two or three overlapping groups.

For counts to be meaningful, use a consistent unit throughout: customers, transactions, products, or another clearly defined item. A customer who appears in two groups still counts as one customer in their overlap.

For many groups or detailed comparisons between counts, a table or an UpSet plot is usually easier to read.

How to read a two-circle Venn diagram

The MovieLens sample used here contains ratings from 610 users. We’ll compare two groups:

• Comedy: Users who gave at least four stars to 10 or more Comedy movies.
• Drama: Users who gave at least four stars to 10 or more Drama movies.

A user can qualify for both groups. A movie can also carry both genre labels.

Read the diagram one region at a time:

Each user appears in exactly one row, and the four counts add up to 610.

The whole Comedy circle contains 344 users: 24 in Comedy only plus 320 in the overlap. This is why a circle’s total differs from its “only” region.

How do you calculate the overlap?

When you have individual records, match their IDs to find the members shared by both groups.

If you know only the two group totals and the number of distinct members across them, use:

Both groups = first group + second group − either group

For MovieLens, that is:

344 + 445 − 469 = 320 users

Adding the two circle totals counts shared users twice. Subtracting the number of distinct users leaves the overlap. All three totals must refer to the same population and membership rules.

What if the circles don't overlap?

If two sets have no shared members, their intersection is empty.

For example, a company might classify accounts into two mutually exclusive billing arrangements. If an account cannot belong to both at the same time, the intersection count is zero.

A Venn diagram can still represent that empty intersection. An Euler diagram, which we'll cover later, may instead draw the circles separately.

How to read a three-circle Venn diagram

A three-circle Venn diagram shows how three sets relate to one another.

It contains seven regions inside the circles, plus an eighth region outside them when the universal set is included.

The extra regions are what make three-circle diagrams useful. They distinguish people who belong to exactly two sets from those who belong to all three.

Returning to MovieLens, let's introduce Action as a third genre. Each set contains users who gave four stars or higher to at least 10 movies carrying that genre label.

Each region represents a different combination. “Only” means the user meets the named genre rules and none of the others.

The numbers add up to 610, the complete set of users.

Start with the center

The center contains 258 users who meet all three genre rules. Each of those users belongs to Comedy, Drama, and Action.

Distinguish “both” from “exactly two”

The Comedy-and-Drama-only region contains 62 users. They meet those two rules but not the Action rule.

If the question is how many users qualify for both Comedy and Drama, include the center too: 62 + 258 = 320. If the question specifies Comedy and Drama but not Action, the answer is 62.

Read “none” using the membership rules

The 112 users outside the circles meet none of the three thresholds. That does not mean they never rated those genres. They may have rated fewer than 10 movies or given lower scores.

To check the diagram, add the seven internal regions and the outside count. Together, they should account for all 610 users once.

Venn diagram vs. Euler diagram

A Venn diagram reserves a region for every possible membership combination, even when a region contains no items. An Euler diagram shows only the relationships that occur.

For example, suppose two mailing lists have no subscribers in common. A Venn diagram can show an overlap labeled zero. An Euler diagram can draw the circles separately. If everyone on one list also belongs to another, an Euler diagram can place the smaller set inside the larger one.

Use a Venn diagram to inspect all possible combinations. An Euler diagram can be simpler when several combinations are empty.

Venn diagram examples and applications

The same principles apply to audience overlap, product analytics, and segmentation work. What changes is how we define membership.

Example 1: Audience overlap across movie genres

The three-circle MovieLens diagram shows why overlapping audiences cannot simply be added together. A user who qualifies for Comedy and Drama belongs to both circles but is still one person.

For a campaign aimed at anyone meeting at least one of the three genre rules, the relevant count is 498 distinct users. Adding the circle totals would count some people repeatedly.

This illustrates how to combine overlapping audiences. The movie-rating records do not establish advertising reach or purchasing intent.

Example 2: Restaurant transaction segments

A second public dataset contains 244 restaurant bills. We can use three conditions to describe each transaction:

• A total bill of at least $20.
• A party size of at least three people.
• A visit recorded on Saturday or Sunday.

These groups can overlap. A large bill might come from a large party, a weekend visit, or both.

The center contains 49 bills that meet all three conditions: at least $20, a party of three or more, and a weekend visit.

The weekend-only region contains 68 bills. These visits happened on Saturday or Sunday, but their bills were below $20 and their parties had fewer than three people.

These two regions show why “weekend transaction” does not automatically mean “large party” or “large bill.” The records describe transactions, so they should not be treated as counts of distinct customers.

Example 3: Countries meeting three conditions

Using Gapminder’s historical data for 2007, we compare 142 countries against three conditions:

• Life expectancy of at least 70 years.
• GDP per person of at least $10,000 in the dataset’s measure.
• Population of at least 10 million.

Each circle represents one condition. The overlaps show countries that meet two or all three.

Start with the center: 25 countries meet all three conditions. The outside count shows that 23 meet none.

One overlap is labeled zero: no country in this extract meets both the GDP and population conditions without also meeting the life-expectancy condition. Keeping that empty region visible shows a combination that was checked but did not occur.

These thresholds are choices for this example, not official country classifications. The counts describe the 2007 dataset, not current conditions.

How to make a Venn diagram

To make a Venn diagram, start by defining the sets and identifying their shared members. Drawing the circles comes after calculating the intersections.

Make a Venn diagram with Deepnote Agent

In Deepnote’s Venn diagram maker, give Agent the dataset and membership rules in one request. It can calculate the overlaps before drawing the diagram.

This request loads the restaurant-bill dataset used above through Plotly:

Load the restaurant-bill dataset using plotly.express.data.tips(). Treat each row as a separate transaction, not a unique customer.

Create three sets:

• Bills of at least $20.
• Parties of at least three people.
• Visits recorded on Saturday or Sunday.

Calculate the seven exclusive regions inside a three-set Venn diagram and the count outside all three. Give each row a unique record ID for the membership calculations. Check for missing values in total_bill, size, and day before classifying records.

Draw a clearly labeled three-circle Venn diagram titled “Overlapping groups of restaurant bills.” Label the circles “Bill ≥ $20,” “Party ≥ 3,” and “Weekend.” Show every region count, including zeros, and display the outside count separately. Use a schematic layout and state that circle areas are not proportional to counts.

Show a table explaining each region in plain English. Verify that the seven internal counts plus the outside count add up to all 244 transactions. Report how many transactions meet all three conditions.

The center should contain 49 transactions. Use the accompanying table to check what each overlap includes and excludes, then confirm that every transaction appears in exactly one region.

The notebook keeps the membership rules and calculations alongside the diagram. If a threshold changes, Agent can recalculate the groups and update the visualization.

Make a Venn diagram in PowerPoint or Google Slides

Deepnote is the more direct option when the diagram needs calculated overlaps from data. For a simple conceptual illustration in PowerPoint or Google Slides, you can also arrange two or three overlapping circles and add labels.

PowerPoint also has relationship-style SmartArt layouts that can provide a starting point.

This is suitable for conceptual comparisons, such as explaining how three product capabilities relate.

For quantitative analysis, however, drawing circles manually doesn't calculate intersections. We recommend preparing and verifying the counts before placing them in the diagram.

Beyond three sets: when Venn diagrams stop being useful

Venn diagrams become harder to read as the number of sets increases.

With two sets, there are four possible membership combinations, including the region outside both sets. With three, there are eight. With four, there are 16.

Each additional set doubles the number of possible membership combinations.

A diagram containing four or five sets may be mathematically possible, but its regions can become narrow, fragmented, and difficult to label. Some intersections may require shapes more complicated than circles.

For larger intersection problems, an UpSet plot is often a better choice.

An UpSet plot combines bars showing intersection sizes with a matrix indicating which sets participate in each intersection. It allows readers to compare counts directly without searching for small overlapping regions.

For example, a product team studying adoption across eight features would have up to 256 possible membership combinations. An UpSet plot can focus on the intersections that occur most frequently.

Use a Venn diagram when the set relationships themselves are easy to understand visually. As the number of sets grows, prioritize a representation that makes the important combinations and their sizes readable.

Explore the overlap in your own data

A Venn diagram is most useful when the question is about membership. Who belongs to both groups? Which records satisfy all three conditions? How many observations fall outside the sets we're examining?

Get those definitions right first. A polished diagram cannot repair an incorrect intersection count.

With Deepnote’s AI chart generator, include the membership data in your request or name a dataset Agent can load. Ask it to calculate the overlaps, check the totals, and label the diagram. The notebook keeps those steps available for review.

If the relationships become too complex for overlapping circles, our guide to the 31 types of graphs and charts can help you choose a clearer visualization.