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Scatter Plot Maker

Venn Diagram Maker

Build 2-circle and 3-circle Venn diagrams in seconds. Compare sets, show overlaps, and export print-ready PNG or SVG.

Tip: Click and drag any label - title, subtitle, set names, or region text - to reposition it inside or outside the diagram.

Export Diagram

Set Theory Calculator with Step-by-Step Solver

Enter your sets, choose an operation, and see the worked solution - perfect for homework, classroom practice, and quick checks.

Number of sets:

Set ASet BOperation

Tip: separate elements with commas or spaces. Duplicates are removed automatically - that's how sets work.

Result

{ 2, 4, 6, 8, 10, 12, 3, 9, 15 }

Cardinality: 9

Step-by-Step Solution

Write the sets: A = { 2, 4, 6, 8, 10, 12 }, B = { 3, 6, 9, 12, 15 }.
Union means every element that appears in A or B (or both).
List all elements of A: { 2, 4, 6, 8, 10, 12 }.
Add elements of B that are not already listed (skip duplicates { 6, 12 }).
Result: A ∪ B = { 2, 4, 6, 8, 10, 12, 3, 9, 15 }.
n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 6 + 5 − 2 = 9.

What Is a Venn Diagram?

A Venn diagram is a visual representation of how groups (or “sets”) overlap and differ. Each circle represents one group, and where the circles cross, the overlapping region shows what those groups have in common. Where they don’t cross, you see what’s unique to each. Invented in the 1880s by English logician John Venn, the diagram has become one of the most recognizable shapes in education, business, and logical reasoning.

A 2-circle Venn diagram has three regions: things only in A, things only in B, and things in both A and B (the intersection). A 3-circle Venn has seven regions: each set alone, each pair of intersections, and the central spot where all three overlap. Once you go past three sets, true Venn diagrams become geometrically messy - that’s why most real-world Venns stay at two or three circles.

This free online Venn diagram maker lets you build a clean, customizable 2- or 3-set Venn in seconds. Set the names, colors, and what goes in each region. Export as PNG, JPEG, or SVG. Runs entirely in your browser - no signup, no uploads, your data stays local.

What People Use Venn Diagrams For

Venn diagrams show up everywhere people need to compare groups or ideas. Some of the most common scenarios:

Education & Logic

Math teachers use Venns to introduce set theory, unions, and intersections. Reading teachers use them for comparing characters, themes, or stories. They show up everywhere from primary school to graduate-level statistics.

Strategy & Business

“What sits at the intersection of customer needs, our capabilities, and market gaps?” A 3-circle Venn is a classic strategy framing tool - shown on whiteboards in product, marketing, and consulting meetings every day.

Research & Analysis

Comparing populations of patients, gene sets, survey respondents, or experimental groups. Venn diagrams are a staple of biology papers, social science research, and any analysis that involves overlapping samples.

Brainstorming & Workshops

Facilitators use Venns to map common ground between teams, explore where projects overlap, and visualize stakeholder concerns. A blank Venn on a wall is one of the most generative templates in design thinking.

Comparison Content

Bloggers and content creators use Venns to compare products (iPhone vs Android), career paths, programming languages, or any two-or-three way decision. They’re a quick visual hook in articles and slide decks.

Self-reflection & Goals

The famous Ikigai diagram (what you love, what you’re good at, what the world needs, what you can be paid for) is a 4-set Venn used for life and career planning. Simpler 3-circle versions show up in coaching workbooks and journals.

How to Make a Venn Diagram (Step by Step)

1
Pick 2 or 3 sets. Two sets show one comparison and one intersection (3 regions). Three sets show three pairwise intersections plus a central overlap (7 regions). Stick to 3 or fewer for clarity.
2
Name your sets.Each circle should have a clear, short label - the “Set A”, “Set B” idea is just a placeholder. Replace them with actual concepts: “Marketing”, “Engineering”, “Design”, etc.
3
Fill in each region. For each region (only-A, only-B, A∩B, etc.), add what belongs there. It can be a count (“142 customers”), a short list, or a single concept that captures the overlap.
4
Style and export. Pick colors that match your brand or slide deck, adjust opacity so overlaps are visible, set the border thickness, and download as PNG, JPEG, or SVG. SVG keeps the diagram razor-sharp at any size.

The Power of Comparison

A Venn diagram is more than just circles; it's a tool for critical thinking. By mapping out overlaps, you force yourself (or your team) to define the boundaries of different ideas. In product management, this might mean finding the overlap between "User Desires," "Technical Feasibility," and "Business Viability." In content marketing, it could be the sweet spot between "High Search Volume" and "Low Competition."

Why It Works

Our brains are wired for spatial reasoning. Seeing a shared trait physically placed between two groups is significantly more memorable than reading it in a bulleted list. This is why Venn diagrams remain the gold standard for high-stakes presentations and complex educational materials.

Venn Diagram Variations

While most people use these diagrams for general comparisons, they are also the backbone of specialized fields. If you are working on more technical projects, check out our dedicated generators:

For Statistics & Probability →

Includes sections for Bayes' Theorem, Conditional Probability, and joint distributions. Ideal for stats students and researchers.

For Math & Set Theory →

Focuses on Unions, Intersections, and Relative Complements using standard mathematical notation and discrete elements.

Worked Numerical Examples

The fastest way to get comfortable with Venn diagrams is to work through a few realistic problems. Here are three classics that show up in school maths, GMAT/SAT prep, and competitive exams.

Example 1 — Two-Set Survey

Problem: In a class of 40 students, 22 play cricket, 18 play football, and 8 play both. How many students play at least one sport? How many play neither?

Setup: Let C = cricket players, F = football players. Given: n(C) = 22, n(F) = 18, n(C ∩ F) = 8, n(U) = 40.

n(C ∪ F) = n(C) + n(F) − n(C ∩ F)
n(C ∪ F) = 22 + 18 − 8 = 32

n(neither) = n(U) − n(C ∪ F)
n(neither) = 40 − 32 = 8

Answer: 32 students play at least one sport; 8 play neither.

Example 2 — Three-Set Inclusion-Exclusion

Problem: A survey of 100 software engineers found that 60 know Python, 50 know JavaScript, 40 know SQL, 25 know Python and JavaScript, 20 know Python and SQL, 15 know JavaScript and SQL, and 10 know all three. How many know at least one of these languages?

Setup: P = Python, J = JavaScript, S = SQL. Apply the three-set inclusion-exclusion formula.

n(P ∪ J ∪ S) = n(P) + n(J) + n(S)
− n(P ∩ J) − n(P ∩ S) − n(J ∩ S)
+ n(P ∩ J ∩ S)
= 60 + 50 + 40 − 25 − 20 − 15 + 10
= 100

Answer: All 100 surveyed engineers know at least one of the three languages.

Example 3 — Finding “Only” Region Counts

Problem: Using the data from Example 2, how many engineers know only Python (and neither JavaScript nor SQL)?

Strategy:Start from the centre and work outward. We know n(P ∩ J ∩ S) = 10. Subtract that from each pairwise intersection to find “exactly two” regions, then subtract those plus the triple from n(P) to isolate Python-only.

P ∩ J only (not S) = 25 − 10 = 15
P ∩ S only (not J) = 20 − 10 = 10
P only = n(P) − (P∩J only) − (P∩S only) − (P∩J∩S)
P only = 60 − 15 − 10 − 10 = 25

Answer: 25 engineers know Python and neither of the other two.

Example 4 — Working Backwards from a Total

Problem: 80 people were surveyed about streaming services. 50 use Netflix, 35 use Prime, and 90% use at least one of the two. How many use both?

n(N ∪ P) = 0.9 × 80 = 72
72 = 50 + 35 − n(N ∩ P)
n(N ∩ P) = 85 − 72 = 13

Answer: 13 people use both Netflix and Prime.

Common Venn Diagram Problem Patterns

Most homework, exam, and competitive-test Venn problems fall into one of these patterns. Recognising the pattern early tells you which formula to reach for.

“At least one” problems

Asking for n(A ∪ B) or n(A ∪ B ∪ C). Use inclusion-exclusion directly. Common in surveys.

“None of them” problems

Compute n(A ∪ B), then subtract from the universal set: n(neither) = n(U) − n(A ∪ B).

“Only A” problems

Use n(A) − n(A ∩ B) for two sets. For three sets, subtract every overlap that includes A from n(A).

“Exactly two” problems

Sum of pairwise intersections, minus 3× the triple intersection: (A∩B) + (A∩C) + (B∩C) − 3·(A∩B∩C).

“Find the unknown overlap”

You’re given n(A ∪ B) and the individual sizes - solve for n(A ∩ B) by rearranging the formula.

Probability with Venn

P(A ∪ B) = P(A) + P(B) − P(A ∩ B). Same logic, just divide every count by n(U).

Tips for Better Venn Diagrams

Keep region labels short. Three or four words max. If you have a long list, summarize it - you can put the full list in a caption or the surrounding text. Long labels squeeze each other and make the diagram hard to read.
Use distinct, harmonious colors. Pick three colors from a single palette so the overlap regions blend into pleasant intermediate tones. Random clashing colors make the diagram look amateurish and obscure the message.
Tune the fill opacity. Around 50% is the sweet spot - solid enough to identify each circle, transparent enough for overlaps to show through clearly. Below 30% the circles disappear; above 70% the overlaps get muddy.
Don’t force a Venn diagram on data that doesn’t overlap. If your three groups are mutually exclusive, a Venn is misleading - use a pie chart, bar chart, or table instead. The whole point of a Venn is the overlap.
For numerical sets, label counts in each region.If you’re showing how many items belong in each region (e.g., users who use feature A, B, both), put the actual count in each region. That makes the Venn quantitative, not just qualitative.
Stop at 3 circles. Real Venn diagrams with 4 or more sets need ellipses or weird shapes to capture every possible intersection - they look messy and almost nobody can read them. If you have more than 3 categories, group them first.

Venn Diagram vs. Euler Diagram vs. Other Visuals

Visual	Best For	Limitation
Venn Diagram	Showing every possible intersection of 2-3 sets	Forces you to draw empty regions even if they’re empty
Euler Diagram	Showing only the relationships that actually exist	Less standardized; harder to read at a glance
Pie Chart	Mutually exclusive parts of a whole	Can’t show overlap or shared items
Comparison Table	Detailed, side-by-side feature comparisons	Less visual punch, slower to scan

Frequently Asked Questions

What does a Venn diagram show?+

A Venn diagram shows the relationships between groups, called sets. Each circle represents one group; where circles overlap, you see what the groups share; where they don’t overlap, you see what’s unique to each. The most common forms are 2-circle and 3-circle Venn diagrams.

How many circles can a Venn diagram have?+

Technically you can draw a Venn diagram with any number of sets, but past 3 circles the geometry gets ugly fast - you need ellipses or curves to capture every possible intersection. In practice, almost all Venn diagrams use 2 or 3 circles. This tool supports both.

What is the difference between a Venn and an Euler diagram?+

A Venn diagram always draws every possible overlap, even if that overlap has no members. An Euler diagram only draws overlaps that actually contain something. Venns are more standardized and easier to read; Eulers are more accurate to the underlying data but less common.

Can I import data from Excel?+

Yes. Click “Import Excel” in the Data Entry section. The expected format is two columns: a region code (A, B, C, AB, AC, BC, ABC) in the first column and the label for that region in the second. Download the template to see the exact format.

Is my data private?+

Completely. The diagram is rendered in your browser using SVG - we don’t upload your data anywhere. Close the tab and the data is gone. Safe for sensitive comparisons, confidential strategy work, and internal documents.

What export formats are supported?+

PNG, JPEG, JPG, and SVG. PNG and JPEG are great for slides and documents. SVG is a vector format - it stays sharp at any size, making it ideal for print, posters, and large displays.

Do I need to sign up?+

No. There’s no signup, no account, no email required. Open the page, build your diagram, and export. It works on any modern browser, on desktop, tablet, or phone.

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A great Venn diagram makes a complex comparison readable in seconds - that’s why John Venn’s 1880 idea is still stuck on whiteboards, slide decks, and textbook pages 140 years later. This free online Venn diagram maker handles the standard 2-circle and 3-circle layouts with full customization: pick your colors, fill in each region, tweak opacity and stroke, and export as a high-resolution PNG or a crisp SVG. No signups, no installs, no data leaves your browser.