Analyze overlapping sets with precision and useful context. View unique items and similarity scores instantly. Export clean results for lessons, audits, reporting, and reviews.
| Case | First Set | Second Set | Intersection | Union Size | Jaccard Index |
|---|---|---|---|---|---|
| Numbers | {1, 2, 3, 4, 5, 8} | {3, 4, 5, 6, 7, 8} | {3, 4, 5, 8} | 8 | 0.5000 |
| Letters | {a, b, c, d} | {c, d, e, f} | {c, d} | 6 | 0.3333 |
| Mixed Labels | {red, green, blue} | {blue, gold, red} | {blue, red} | 4 | 0.5000 |
Set intersection: A ∩ B = {x : x ∈ A and x ∈ B}. This returns only the elements common to both sets.
Union: A ∪ B = {x : x ∈ A or x ∈ B}. The union includes every distinct element from both sets.
Difference: A − B = {x : x ∈ A and x ∉ B}. This shows items unique to the first set.
Jaccard index: J(A,B) = |A ∩ B| / |A ∪ B|. It measures similarity between two finite sets.
Dice coefficient: D(A,B) = 2|A ∩ B| / (|A| + |B|). This gives extra weight to shared elements.
Overlap coefficient: O(A,B) = |A ∩ B| / min(|A|, |B|). It shows how fully the smaller set is covered.
Interval intersection: [a,b] ∩ [c,d] = [max(a,c), min(b,d)] when max(a,c) ≤ min(b,d). Otherwise, the intersection is empty.
It finds the common elements between two sets. It also reports union, differences, symmetric difference, Jaccard index, Dice coefficient, overlap coefficient, and interval overlap when numeric endpoints are supplied.
Yes. The set fields accept words, labels, codes, or numbers. Each entry is treated as a distinct token, so exact spelling and capitalization matter during comparison.
Duplicate values are removed automatically before calculations. This keeps each set mathematically valid and ensures the intersection and similarity metrics are based on unique elements only.
The Jaccard index measures similarity between two sets. A value near 1 means very strong overlap, while a value near 0 means very little shared content.
Some problems involve both discrete sets and continuous ranges. The interval feature helps compare overlapping numeric spans, such as time windows, measurement bands, or coordinate segments.
The calculator reports that no interval intersection exists. In that case, the shared interval is empty and the overlap length becomes zero.
Yes. After calculation, use the CSV button for spreadsheet-ready data or the PDF button for printing and saving a quick report of the computed results.
Yes. It supports classroom examples, data comparison tasks, logic exercises, similarity analysis, and quick verification of overlapping members in two finite collections.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.