Euler Diagram
A set diagram that only draws the relationships that actually exist — no empty zones, no visual clutter. The pragmatic cousin of the Venn diagram.
// 01 — The chart
What it looks like
An Euler diagram showing containment (Primates ⊂ Mammals ⊂ Animals) and disjointness (Mammals and Birds don’t overlap).
// 02 — Definition
What is an Euler diagram?
An Euler diagram (pronounced “OY-ler”) uses closed curves to represent sets, but unlike a Venn diagram, it only shows the relationships that actually exist in the data. If two sets don’t overlap, their circles are drawn apart. If one set is entirely contained within another, its circle sits inside the larger one. Empty intersections simply don’t appear.
This makes Euler diagrams more truthful and readable than Venn diagrams for many real-world situations. In a Venn diagram with 3 sets, you always see 8 regions, even if 5 of them are empty. An Euler diagram would only show the 3 regions that contain data, making the actual relationships immediately clear.
Euler diagrams can also express containment (subset/superset) and disjointness more clearly than Venns. A circle entirely inside another immediately communicates “is a subset of” without needing labels in the outer-only zone to prove it.
Origin: Named after Leonhard Euler, the Swiss mathematician who used these diagrams in his 1768 work Lettres à une Princesse d’Allemagne to explain principles of logic, predating Venn by over a century.
// 03 — Anatomy
Parts of an Euler diagram
// 04 — Usage
When to use it — and when not to
- Some intersection regions are empty — Euler avoids drawing phantom zones
- You want to show subset/superset containment relationships clearly
- The diagram involves 4+ sets where a Venn would be impossibly complex
- You need a clean, uncluttered view of which categories share members and which don't
- Presenting to non-technical audiences who may be confused by empty Venn zones
- You need to show all possible intersections explicitly — use a Venn diagram
- There are many overlapping sets with complex combinatorial relationships — use an UpSet plot
- You need proportional area accuracy — area-proportional Euler diagrams are hard to draw correctly
- The relationships are hierarchical with many levels — use a tree or nested treemap
- Precise quantitative comparisons are needed — use bar charts
// 05 — Reading guide
How to read an Euler diagram
Follow these steps to interpret any Euler diagram.
Identify each curve and its label
Each closed curve represents a set. Read the labels to understand what group each curve represents.
Check for containment
A curve entirely inside another means the inner set is a subset of the outer. All members of the inner set also belong to the outer set.
Look for overlaps
Where curves partially overlap, elements in that region belong to both sets. Unlike Venn diagrams, only existing overlaps are shown.
Note separated curves
Curves drawn apart with no intersection mean the sets are disjoint — they share no members at all. This spatial separation is meaningful.
Read any numbers or labels in regions
Quantitative Euler diagrams label each region with counts. Check whether circle sizes are proportional to set sizes or purely schematic.
// 06 — Pitfalls
Common mistakes
Calling a Venn diagram an Euler diagram (and vice versa)
The terms are often used interchangeably, but they're different. Venn = all possible zones shown. Euler = only existing relationships shown. Using the wrong name confuses technically literate readers.
Failing to represent area proportionally when implied
If circles are drawn with different sizes, readers will assume size represents magnitude. Either make them accurately proportional or make them all the same size with explicit count labels.
Drawing impossible layouts
Some set relationships cannot be represented with simple circles (e.g., three sets where each pair overlaps but no triple intersection exists). Using ellipses or irregular shapes may be needed.
Too many overlapping curves
Beyond 4–5 sets, even Euler diagrams become tangled. Switch to UpSet plots or matrix representations for complex set relationships.
// 07 — In the wild
Real-world examples
Taxonomy and classification
Biology textbooks use Euler diagrams to show containment hierarchies in taxonomy — Kingdom ⊃ Phylum ⊃ Class — where subset relationships are the primary message.
Security access policies
IT architects use Euler diagrams to show which user groups have access to which systems, with overlapping groups having shared permissions and disjoint groups having separate access.
Ontology visualization
Knowledge engineers use Euler diagrams to depict concept hierarchies and category memberships in ontologies, where containment and overlap precisely model 'is-a' and 'part-of' relationships.
// 08 — Quick reference
Key facts
// 09 — Variations
Variations of the Euler diagram
Area-proportional Euler diagram
Circle sizes and intersection areas are scaled to represent actual set sizes and overlap counts — challenging to construct but more informative.
Spider Euler diagram
Adds 'spiders' (lines with feet) to represent specific elements within zones, combining the abstraction of Euler with concrete element placement.
Linear Euler diagram
Uses line segments instead of closed curves — useful when the data can be represented as intervals on a number line.
// 10 — FAQs
Frequently asked questions
What is an euler diagram?+
An Euler diagram (pronounced "OY-ler") uses closed curves to represent sets, but unlike a Venn diagram, it only shows the relationships that actually exist in the data. If two sets don't overlap, their circles are drawn apart. If one set is entirely contained within another, its circle sits inside the larger one. Empty intersections simply don't appear.
When should you use an euler diagram?+
Use an euler diagram when some intersection regions are empty — Euler avoids drawing phantom zones. It also works well when you want to show subset/superset containment relationships clearly, and when the diagram involves 4+ sets where a Venn would be impossibly complex.
When should you avoid an euler diagram?+
Avoid an euler diagram when you need to show all possible intersections explicitly — use a Venn diagram. It is also a poor fit when there are many overlapping sets with complex combinatorial relationships — use an UpSet plot, or when you need proportional area accuracy — area-proportional Euler diagrams are hard to draw correctly.
What is another name for an euler diagram?+
Euler Diagram is also known as Euler circles, set diagram. The name varies between fields, but the visualisation technique is the same.
Is an euler diagram suitable for dashboards?+
Yes — an euler diagram can work well in dashboards as long as the panel is large enough for readers to perceive the encoded values, has a clear title, and includes the legend or axis labels needed to interpret it.
What category of chart is an euler diagram?+
Euler Diagram belongs to the Sets family of charts. Charts in that family are designed to answer the same kind of question, so they often work as alternatives when one doesn't quite fit your data.