How to use this calculator

Interval notation describes sets of real numbers using endpoints. Brackets include an endpoint and parentheses exclude it. A union combines intervals. This tool also merges overlaps while keeping track of whether a touching boundary belongs to the set.

The method

Included endpoint: [ or ]; excluded endpoint: ( or )

Enter the values in the labeled fields, check the units or selected mode, and choose Calculate. The result includes the applicable working and a breakdown or visual when useful. Change an input and calculate again to update the result.

WORKED EXAMPLE

Inequality or interval: -2 <= x < 5

Interval notation: [-2, 5)

-2 <= x < 5

Scope and limitations

Simple numeric inequalities and unions of intervals only; it is not a solver for expressions such as x^2 > 4. Infinity endpoints must be open. Reversed endpoints are rejected.

Common questions

Can infinity use a square bracket?

No. Infinity is not a real-number endpoint that can be included. Use (-inf, ... or ..., inf).

What does U mean?

U means union: any number that belongs to at least one of the intervals is in the combined set.

References & further reading

External references provide background, not an endorsement of this implementation. See our methodology for numerical conventions and limitations.