Statistics & Probability

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Two-Set Venn Diagram Calculator.

Calculate two-set union, exclusive regions, and neither count from explicit cardinalities.

On-device calculationNo signup
01

Set your values

Results update as you type.

union: 60

union

60.000000
onlyA: 25

onlyA

25.000000
onlyB: 20

onlyB

20.000000
neither: 40

neither

40.000000

This is a two-set cardinality model. Enter integer counts for the universe, Set A, Set B, and their intersection; the page reports region counts and does not draw or infer a three-or-more-set diagram.

Results update automatically as you type.

Use Cases

Analyze survey or research data

Use this calculator to quickly determine overlaps and exclusive groups in categorical data, such as customers who bought product A, product B, or both.

Example: If 100 surveyed, 40 like tea, 50 like coffee, and 20 like both, find how many like only tea, only coffee, or neither.

Solve probability or set theory problems

For students or educators, this tool helps verify calculations of union, intersection, and complements in basic set theory exercises.

Example: Given |U|=50, |A|=20, |B|=25, |A∩B|=10, find |A∪B| and |neither|.

Frequently Asked Questions

How do I calculate the union of two sets using this calculator?
Enter the sizes of Set A, Set B, and their Intersection. The calculator uses the formula: Union = A + B - Intersection. It also shows the exclusive parts of each set and the count of elements in neither set.
What does 'neither count' mean in a two-set Venn diagram?
The 'neither count' is the number of elements in the universe that are not in Set A or Set B. It is calculated as Universe size minus the union of A and B.
Can I use this calculator if my sets have no intersection?
Yes, if the intersection size is 0, the calculator will treat the sets as disjoint. The union will simply be the sum of Set A and Set B sizes, and the exclusive regions will equal the full sizes of each set.

Tips & Common Mistakes

Tips

  • Ensure the intersection size is not larger than either set size, as that would be logically impossible.
  • The universe size must be at least as large as the union of the two sets; otherwise, the 'neither' count would be negative.
  • Double-check your inputs: the intersection is the count of elements common to both sets, not the sum of exclusive parts.
  • Use the results to visualize the Venn diagram: exclusive A, exclusive B, intersection, and outside region.

Common Mistakes to Avoid

  • Entering the intersection size as the sum of elements in both sets, which overestimates the overlap.
  • Forgetting to include the universe size, leading to an incorrect 'neither' count.
  • Assuming the union is simply A + B without subtracting the intersection, which double-counts the overlap.

Last updated: August 13, 2026