# Inequality to Interval Notation Calculator

URL: https://speedycalculator.com/calculators/math/inequality-to-interval-notation/
Last updated: 2026-10-30

> The inequality to interval notation calculator converts one-sided inequalities such as x ≥ 4 and two-sided inequalities such as −2 ≤ x < 5 into interval notation – and back again.

## Inputs

- Conversion type
- Inequality type
- Inequality
- Interval
- a
- Left end
- Right end
- b

## Results

- Result
- Set-builder form
- The other notation

## Formula

```
x < a → (−∞, a)   x ≤ a → (−∞, a]   a ≤ x < b → [a, b)
```

## Explanation

Interval notation is a compact way to write sets of real numbers: square brackets include an endpoint, round brackets exclude it, and infinity always gets a round bracket. It is the standard way to state domains, ranges and solution sets.

### How to use the Inequality to Interval Notation Calculator

- **Conversion type**
- **Inequality type**
- **Inequality**
- **Interval**
- **a**
- **Left end**
- **Right end**
- **b**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Choose whether the inequality is one-sided or two-sided, pick the signs and enter the endpoints. The calculator writes the interval, the inequality and the set-builder form.

## Worked example

Inputs — Conversion type: Inequality → interval; Inequality type: Two-sided (a … x … b); a: -2; Left end: a ≤ x (closed); Right end: x < b (open); b: 5.

Results — **Result = [−2, 5)**; Set-builder form = [−2, 5) = {x | −2 ≤ x < 5}; The other notation = −2 ≤ x < 5.

## Key terms

- **Open interval**: (a, b), excluding both endpoints.
- **Closed interval**: [a, b], including both endpoints.

## FAQ

**How do I write x > 3 in interval notation?**
(3, ∞).

**How do I write −1 ≤ x ≤ 4?**
[−1, 4].

**Why is infinity never in a square bracket?**
Infinity is not a number, so it cannot be included in the set.

**How do I write "all real numbers"?**
(−∞, ∞).


## Sources

- [OpenStax – College Algebra 2e](https://openstax.org/details/books/college-algebra-2e)
- [OpenStax – Intermediate Algebra 2e](https://openstax.org/details/books/intermediate-algebra-2e)