Use this free union and intersection of intervals calculator for subsets of the real line.
Enter interval A and B in bracket notation (for example [1, 5) or (-∞, 3]),
choose union or intersection, and read the result. Runs in your browser.
Use [ ] for closed ends, ( ) for open ends. Unbounded ends: -inf / inf or −∞ / ∞.
An interval is a connected set of real numbers. Unlike the set operations calculator (finite lists of items), this tool works on continuous ranges of the number line — the intent behind “union and intersection of intervals calculator” searches.
The union contains every point that lies in A or B (or both). If the intervals overlap or touch in a way that fills the gap, the result is a single interval; otherwise you get two disjoint intervals.
Example: [1, 5] ∪ (4, 10] = [1, 10].
The intersection keeps only points that belong to both intervals. If they do not overlap, the result is empty (∅).
Example: [0, 5) ∩ [3, 8] = [3, 5).
When intervals do not meet, the union stays as two pieces.
Example: [0, 1] ∪ [2, 3] = [0, 1] ∪ [2, 3].
Use square brackets for included endpoints and parentheses for excluded ones:
[a, b] closed, (a, b) open, mixtures like [a, b) allowed.
List sets (home page) compare discrete items. Intervals compare all real numbers between endpoints. Pick the tool that matches your homework notation.