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Venn Diagram (3 Sets) Calculator

Work out venn diagram (3 sets) instantly with clear inputs, formula shown and shareable results.

About Venn Diagram (3 Sets) Calculator

For three sets inclusion-exclusion alternates signs: add the singles, subtract the pairs, add the triple back. Region counts follow from the same principle, for example A only = |A| − |A∩B| − |A∩C| + |A∩B∩C|.

Formula

Three-set inclusion-exclusion

|A∪B∪C| = |A|+|B|+|C| − |A∩B| − |A∩C| − |B∩C| + |A∩B∩C|

Worked example

With the default values below, Venn Diagram (3 Sets) Calculator returns |A ∪ B ∪ C| of 54. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sizes of A, B and C
30, 25, 20
Sizes of A∩B, A∩C and B∩C
10, 8, 6
Size of A∩B∩Cminimum 0
3
Total in the universeminimum 1
60

Results

|A ∪ B ∪ C|
54
In A only
15
In exactly one set
36
Outside all three sets
6

Step by step

  1. 1Values used
  2. 2Three-set inclusion-exclusion
  3. 3|A ∪ B ∪ C|= 54
  4. 4In A only= 15
  5. 5In exactly one set= 36
  6. 6Outside all three sets= 6

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

With the sample figures?

30 + 25 + 20 − 10 − 8 − 6 + 3 = 54, leaving 6 outside all three in a universe of 60.

Why add the triple back?

Subtracting all three pairwise overlaps removes the central region three times after it was added three times, so it must be restored once.

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