Venn Diagram Calculator

Enter the counts for your sets — A, B, and C — along with their intersections (A∩B, A∩C, B∩C, A∩B∩C) to calculate union, exclusive regions, and all overlapping segments of a Venn diagram. You get a full breakdown of every region: A only, B only, C only, each pairwise overlap, the triple intersection, and the total union A∪B∪C.

Choose whether to work with 2 or 3 sets.

Only used when 3 sets is selected.

Total elements in both A and B (including those also in C).

Only used when 3 sets is selected.

Only used when 3 sets is selected.

Elements belonging to all three sets. Only used when 3 sets is selected.

Elements that belong to none of the sets.

Results

Total Union (A ∪ B ∪ C)

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A Only

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B Only

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C Only

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A ∩ B Only (not C)

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A ∩ C Only (not B)

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B ∩ C Only (not A)

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A ∩ B ∩ C

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Grand Total (incl. outside sets)

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Venn Diagram Region Breakdown

Results Table

Frequently Asked Questions

What is a Venn diagram calculator?

A Venn diagram calculator computes the sizes of every overlapping and exclusive region when you provide the total counts of each set and their intersections. It saves you from doing the inclusion-exclusion arithmetic by hand, instantly showing you how many elements belong only to A, only to B, to both A and B but not C, and so on.

What is the inclusion-exclusion principle?

The inclusion-exclusion principle is the formula used to find the size of a union of sets without double-counting shared elements. For three sets: |A ∪ B ∪ C| = |A| + |B| + |C| − |A∩B| − |A∩C| − |B∩C| + |A∩B∩C|. This calculator applies that formula automatically.

What is the difference between A ∩ B and 'A ∩ B only'?

'A ∩ B' (the intersection) is the total count of elements in both A and B — this includes elements that are also in C. 'A ∩ B only' is the exclusive overlap: elements in A and B but NOT in C. The calculator derives 'A ∩ B only' as A∩B − A∩B∩C.

How do I enter data for a 2-set Venn diagram?

Select '2 Sets (A, B)' using the radio button at the top. Then enter the total count for Set A, Set B, and their intersection A∩B. The fields for Set C and its intersections are not used in this mode. The calculator will return A only, B only, A∩B, and the total union.

What does 'Outside All Sets' mean?

'Outside All Sets' refers to elements in your universal set that do not belong to any of the defined sets (A, B, or C). For example, if you surveyed 200 people but only 180 belong to at least one group, the remaining 20 would be 'outside all sets'. This value is added to the union to get your Grand Total.

What if a region shows a negative number?

A negative value means your inputs are logically inconsistent — for example, if A∩B∩C is larger than A∩B. Check that all intersection values are less than or equal to the sizes of their parent sets. The most common mistake is entering a pairwise intersection that is smaller than the triple intersection.

Can this calculator handle more than 3 sets?

This calculator supports up to 3 sets (A, B, and C), which covers the most common Venn diagram use cases. Venn diagrams with 4 or more sets become very complex to visualize, typically requiring specialized software or ellipse-based diagrams instead of circles.

What is the Grand Total and how is it calculated?

The Grand Total is the size of your entire universal set: all elements across every region, including those outside all sets. It is calculated as Grand Total = |A ∪ B ∪ C| + (elements outside all sets). This gives you the full population or dataset size your Venn diagram represents.

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