Interactive Venn Diagram

Getting Started

This tool helps you visualize and calculate probability relationships between events using Venn diagrams. The rectangle represents your sample space (total probability = 1.000), and the circles represent different events.

Adjusting Circle Sizes

Using the sliders: Each circle has an area slider in the Controls panel. Drag the slider to set the probability (area) of that event. Values range from 0 to 1, where 1 represents the entire sample space.

Example: If event A has a 25% probability, set Circle 1's area to 0.250.

Moving Circles

Click and drag: Click on any circle and drag it to reposition it within the rectangle. This changes the overlap (intersection) between events.

Tip: Position circles so they overlap to represent events that can occur together (e.g., P(A ∩ B)). Separate circles represent mutually exclusive events.

Switching Between 2 and 3 Circles

Use the "Number of Circles" dropdown to switch between 2-event and 3-event diagrams:

• 2 Circles: Shows A only, B only, A ∩ B, and the area outside both circles
• 3 Circles: Shows individual regions, pairwise intersections (A ∩ B only, A ∩ C only, B ∩ C only), and the triple intersection A ∩ B ∩ C

Adjusting Canvas Size

Rectangle Size controls: Enter custom width and height values (in pixels) and click "Apply Size" to resize the canvas. This is useful for creating diagrams that fit specific presentation needs.

Note: Resizing maintains the relative proportions of your circles and recalculates all areas automatically.

Understanding the Calculations

The "Area Calculations" panel shows probability values for each region:

• A Only, B Only, C Only: Probability of each event occurring without the others
• A ∩ B (only): Probability of both A and B occurring, but not C
• A ∩ B ∩ C: Probability of all three events occurring together (approximated as 0 for simplicity)
• Outside Circles: Probability of none of the events occurring

Important: All values are normalized so the total equals 1.000 (the rectangle area).

Exporting Your Work

Copy Data: Click this button to copy all numerical values and settings to your clipboard as formatted text.

Download Diagram: Click this button to save the current diagram as a PNG image file that you can use in reports or presentations.

Example Use Case

Problem: In a group of students, 30% play basketball (A), 25% play soccer (B), and 10% play both sports. What's the probability a randomly selected student plays neither sport?

Solution:

1. Set Circle 1 (A) area to 0.300
2. Set Circle 2 (B) area to 0.250
3. Drag the circles until A ∩ B shows approximately 0.100
4. Read the "Outside Circles" value - this is your answer (should be 0.550 or 55%)

Tips for Accurate Results

• Labels on the diagram show calculated areas for each region to help verify your setup
• For 3-circle diagrams, the triple intersection (A ∩ B ∩ C) is approximated as 0 for computational simplicity
• If circles exceed the rectangle boundaries, they're automatically constrained to fit within the sample space
• Use smaller area values (0.1-0.3) for better visual separation when working with multiple circles