Inequality to Interval Notation Calculator
Convert any linear inequality to interval notation in one step. Choose the inequality type, enter the bound or bounds, and get the interval notation with a number-line diagram and set-builder form.
Inequality type
How does this calculator work?
Convert a linear inequality to interval notation: parentheses ( ) exclude endpoints (strict < or >), brackets [ ] include them (≤ or ≥), and infinity always uses parentheses. Example: 2 ≤ x < 5 becomes [2, 5). Choose your inequality type and enter the bound(s) to convert instantly.
Formula
How this is calculated
Interval notation is a compact way to write the set of real numbers satisfying an inequality. A parenthesis ( or ) indicates a strict inequality — the endpoint is excluded (an open circle on a number line). A bracket [ or ] indicates a non-strict inequality — the endpoint is included (a filled circle). Infinity (∞ or -∞) always uses a parenthesis because infinity is never actually reached.
For a single-bound inequality such as x > a, the interval extends infinitely to the right: (a, ∞). For x ≥ a the only change is that a itself is included: [a, ∞). For two-sided inequalities like a < x ≤ b, each endpoint is treated independently — the left uses a parenthesis (a excluded) and the right uses a bracket (b included): (a, b].
Interval notation is standard in algebra, calculus, and real analysis. It is equivalent to set-builder notation { x ∈ ℝ | inequality }. When combining intervals with "or" use the union symbol ∪; for "and" use the intersection symbol ∩.
Frequently asked questions
A parenthesis ( or ) means the endpoint is excluded — the inequality is strict (< or >). A bracket [ or ] means the endpoint is included — the inequality is non-strict (≤ or ≥). Infinity always uses parentheses because it is a concept, not a reachable number.
x ≠ 5 means all real numbers except 5, written as the union (-∞, 5) ∪ (5, ∞). This calculator handles single-range inequalities; a union of two intervals is formed by combining two separate results.
They describe the same set in different forms. For example, x > 3 is (3, ∞) in interval notation and { x ∈ ℝ | x > 3 } in set-builder notation. Interval notation is more concise; set-builder notation makes the membership condition explicit.
Also known as
TG we-Calculate Editorial Team. (2026). Inequality to Interval Notation Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/inequality-to-interval-notation-calculator
TG we-Calculate Editorial Team. "Inequality to Interval Notation Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/inequality-to-interval-notation-calculator.
TG we-Calculate Editorial Team, "Inequality to Interval Notation Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/inequality-to-interval-notation-calculator
@misc{wecalculate_inequality_to_interval_notation_calculator, title = {Inequality to Interval Notation Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/inequality-to-interval-notation-calculator}}, year = {2026}, note = {TG we-Calculate} }
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