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Calcimator

Venn Diagram Calculator

Calculate exclusive region values for 2-set or 3-set Venn diagrams using inclusion-exclusion principle.

Inputs

Results

A Only

30

B Only

20

Union Total

60

C Only0
A ∩ B (excl. C)10
A ∩ C (excl. B)0
B ∩ C (excl. A)0
A ∩ B ∩ C0
How to Use This Calculator
  1. Enter the total population or universe size.
  2. Input the size of Set A, Set B, and their intersection.
  3. Review the exclusive regions: A only, B only, both A and B, and neither.
  4. Calculate percentages of the universe in each region for proportion analysis.
  5. Use the output to solve inclusion-exclusion problems in probability and combinatorics.

How the result changes with Set A Size

Set A SizeA OnlyB OnlyUnion Total
10,0009,9902010,020
35,00034,9902035,020
65,00064,9902065,020
90,00089,9902090,020

What each input means

Set A Size
Total elements in set A
Set B Size
Total elements in set B
Set C Size (0 for 2-set)
Total elements in set C (set to 0 for a two-set diagram)
A ∩ B Overlap
Number of elements in both A and B
A ∩ C Overlap
Number of elements in both A and C (only for 3-set diagrams)
B ∩ C Overlap
Number of elements in both B and C (only for 3-set diagrams)
A ∩ B ∩ C Overlap
Number of elements in all three sets

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Set A Size = 40, Set B Size = 30, Set C Size (0 for 2-set) = 0, A ∩ B Overlap = 10 = 7 input(s) provided
  2. Calculate A Only
    30 = 30
  3. Calculate B Only
    20 = 20
  4. Calculate Union Total
    60 = 60
  5. Calculate C Only
    0 = 0
  6. Calculate A ∩ B
    10 = 10

Engine last updated . Checked against 5 independently-derived tests — how we verify calculators.

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