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Venn Diagram (2 Sets) Calculator

Work out venn diagram (2 sets) instantly with clear inputs, formula shown and shareable results.

About Venn Diagram (2 Sets) Calculator

A two-set Venn diagram has four regions: A only, both, B only and neither. Set sizes are recovered by adding the relevant regions, and the union is everything except the outside region.

Formula

From regions

|A| = onlyA + both, |A ∪ B| = onlyA + both + onlyB, universe = union + neither

Worked example

With the default values below, Venn Diagram (2 Sets) Calculator returns |A ∪ B| of 70. Change any input above and every figure here is recalculated in your browser.

Inputs used

In A onlyminimum 0
25
In both A and Bminimum 0
15
In B onlyminimum 0
30
In neitherminimum 0
10

Results

|A ∪ B|
70
|A|
40
|B|
45
Total in the universe
80

Step by step

  1. 1Values used
  2. 2From regions
  3. 3|A ∪ B|= 70
  4. 4|A|= 40
  5. 5|B|= 45
  6. 6Total in the universe= 80

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 25, 15, 30 and 10?

|A| = 40, |B| = 45, the union is 70 and the universe holds 80.

How do I check my figures?

The four regions must add to the total surveyed, and |A| + |B| − |A ∩ B| must equal the union.

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Venn Diagram (2 Sets) Calculator – Calculate |A ∪ B| & |A|