Venn Diagram Calculator

What This Venn Diagram Calculator Does

This tool computes set cardinalities from Venn diagram inputs. For two sets, enter $|U|$, $|A|$, $|B|$, and one known relation such as $|A \cap B|$ or $|A \cup B|$. For three sets, enter pairwise and triple intersections directly. Related tools: Probability Calculator and Outlier Calculator.

Two-Set Inclusion-Exclusion

$$|A \cup B| = |A| + |B| - |A \cap B|$$

$$|A \setminus B| = |A| - |A \cap B|$$

$$|A \triangle B| = |A| + |B| - 2|A \cap B|$$

Three-Set Inclusion-Exclusion

$$|A \cup B \cup C| = |A| + |B| + |C| - |A \cap B| - |A \cap C| - |B \cap C| + |A \cap B \cap C|$$

Example

With $|U| = 50$, $|A| = 20$, $|B| = 20$, and $|A \cap B| = 5$, the union is $35$, $|A \setminus B| = 15$, and $|B \setminus A| = 15$.