3-Set Venn Diagram Template

About This 3-Set Template

This template uses three overlapping circles to compare sets A, B, and C. The seven internal regions show items in one set only, in exactly two sets, or in all three. Use it for a three-group comparison or a set-counting exercise.

Read the Variables and Regions

Let a = |A|, b = |B|, and c = |C| be the total numbers of items in each set. Let w = |A ∩ B|, x = |B ∩ C|, and y = |A ∩ C|; each of these pairwise counts includes the shared center. Let z = |A ∩ B ∩ C|.

• A only: a − w − y + z.
• B only: b − w − x + z.
• C only: c − y − x + z.
• A and B only: w − z. B and C only: x − z. A and C only: y − z.
• All three: z.

For the B-only calculation shown in the image, use x for the B–C overlap: b − (w + x − z). The expanded expression printed in that region repeats w; the correct expansion is b − (w − z + z + x − z).

Count the Union Without Double-Counting

The inclusion-exclusion formula counts each item in at least one set once: |A ∪ B ∪ C| = a + b + c − w − x − y + z. The universal set may also include items outside all three circles.

For example, if a = 30, b = 25, c = 20, w = 10, x = 8, y = 6, and z = 3, the union is 30 + 25 + 20 − 10 − 8 − 6 + 3 = 54. The A-only, B-only, and C-only counts are 17, 10, and 9; pair-only counts are 7, 5, and 3; the center is 3.

Customize the Template

1. Select Use this template to open the editable example, then rename A, B, and C for your comparison.
2. For a count-based diagram, enter set totals and inclusive pairwise counts, fill the center first, then calculate pair-only and single-set regions. Every region count must be nonnegative.
3. For a concept comparison, replace formulas with shared and unique characteristics. Keep the three-way overlap distinct from the pair-only regions.
4. Review the membership of each item, save the editable copy, and use an available export format for your lesson, report, or presentation.