Venn Diagram Calculator
Find the regions of a two-set Venn diagram.
A Venn diagram splits two sets into the overlap and the parts unique to each.
How the Math Works
The Venn Diagram Calculator uses the fundamental principle of set theory where the union of two sets A and B is calculated by adding their individual counts and subtracting their intersection. This formula A ∪ B = A + B − (A ∩ B) prevents double-counting elements that appear in both sets. When you input the number of elements in set A, set B, and their overlap, the calculator determines the total unique elements across both sets while accurately accounting for shared elements.
Practical Applications
To use this calculator, simply enter the total number of items in your first group (A), the total in your second group (B), and the number of items that belong to both groups simultaneously. The calculator instantly computes how many unique items exist when considering both groups together, making it invaluable for organizing data, solving survey problems, or analyzing overlapping categories in academic and professional settings.
Day-to-Day Use
This calculator helps you make sense of everyday situations involving overlapping choices or characteristics. Whether you're planning events by determining how many guests prefer both vegetarian and vegan options, analyzing market research to find customers who like multiple products, or organizing a library collection to see how many books fall into both fiction and mystery categories, the Venn Diagram Calculator provides quick, accurate insights into how different groups intersect and overlap in your daily life.
Worked example
A 30, B 25, overlap 10 → union 45, only-A 20, only-B 15.
FAQ
What if the sets don't overlap?
Set the intersection to 0; the union is then just A + B.