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Calcimator

Inclusion-Exclusion Calculator

Apply the inclusion-exclusion principle to compute union sizes and exclusive membership for up to three sets.

Inputs

Results

|A∪B∪C| (Union Size)

180

Exclusive to A60
Exclusive to B35
Exclusive to C30
How to Use This Calculator
  1. Enter the sizes of Set A, Set B, and Set C.
  2. Input the pairwise intersection sizes for A and B, B and C, and A and C.
  3. Enter the triple intersection size for A, B, and C.
  4. Review the Union calculated via the inclusion-exclusion principle.
  5. Use this to count elements satisfying at least one of several overlapping conditions.

How the result changes with |A| (Set A size)

|A| (Set A size)|A∪B∪C| (Union Size)
100,000100,080
350,000350,080
650,000650,080
900,000900,080

What each input means

|A| (Set A size)
Number of elements in set A
|B| (Set B size)
Number of elements in set B
|C| (Set C size)
Number of elements in set C
|A∩B|
Elements in both A and B
|B∩C|
Elements in both B and C
|A∩C|
Elements in both A and C
|A∩B∩C|
Elements in all three sets

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    |A| (Set A size) = 100, |B| (Set B size) = 80, |C| (Set C size) = 60, |A∩B| = 30 = 7 input(s) provided
  2. Calculate |A∪B∪C|
    |A∪B∪C|
    180 = 180
  3. Calculate Exclusive to A
    Exclusive to A = max(0
    60 = 60
  4. Calculate Exclusive to B
    Exclusive to B = max(0
    35 = 35

Engine last updated . Checked against 3 independently-derived tests — how we verify calculators.

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