What is interval notation?

Interval notation is a way of writing sets of numbers between endpoints, showing whether endpoints are included (closed) or excluded (open) using brackets. Example: [a, b] for closed, (a, b) for open intervals.

What are the types of intervals?

Closed [a, b]: includes a and b; Open (a, b): excludes a and b; Left-open (a, b]: excludes a, includes b; Right-open [a, b): includes a, excludes b; and infinite intervals like (a, ∞).

How do I convert inequalities to interval notation?

For example, x > 2 and x < 5 becomes (2, 5). If endpoints are included (x ≥ 2 and x ≤ 5), use [2, 5].

How is interval notation used?

Interval notation is widely used in algebra, calculus, and analysis to describe solution sets, domains/ranges, and answer set questions compactly.

What about infinity in intervals?

Infinity is always written with parenthesis (open), e.g., (−∞, 2), [3, ∞).

How do I plot intervals?

Plot intervals on the number line. Closed points (●) mean included endpoint, open points (○) mean excluded. The calculator will show you the right form!

Notation Tool

Interval Notation Calculator – Convert & Analyze Intervals

Q: How is interval notation used?

Interval notation is widely used in algebra, calculus, and analysis to describe solution sets, domains/ranges, and answer set questions compactly.

Q: What about infinity in intervals?

Infinity is always written with parenthesis (open), e.g., (−∞, 2), [3, ∞).

Q: How do I plot intervals?

Plot intervals on the number line. Closed points (●) mean included endpoint, open points (○) mean excluded. The calculator will show you the right form!

Free interval notation calculator. Instantly convert between inequalities, set notation, and interval notation. Understand whether intervals are open, closed, or half-open, see results in LaTeX, and more. Perfect for algebra, calculus, and your homework!

Last updated: October 30, 2025

Converts inequalities ↔ interval notation

Open, closed, and infinite intervals

Clear explanations with LaTeX result

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Interval Notation Calculator

Convert between interval notation and inequalities. Analyze whether endpoints are included or excluded (open/closed/half-open intervals).

Result

Interval: [0, 1]

Notation: \left[0, 1\right]

Analysis: The interval [0, 1] is closed and includes both endpoints.

Description: Closed interval: both endpoints are included.

Interval Calculator Types & Features

Inequality to Interval Notation

Convert math inequalities (e.g., x > 3) into interval notation

Supports

Strict, non-strict, double inequalities

Also handles infinite endpoints

Interval Analysis

Determine open/closed status, endpoint inclusion/exclusion

Visual Help

Open, closed, half-open

Clear explanations for students

LaTeX & Math Expressions

Get results in interval notation and LaTeX/markdown

Professional Output

LaTeX, markdown, raw

Copy for homework or documents

Example: Closed vs Open Interval

[2, 5] (Closed)

Endpoints included: 2, 5

(2, 5) (Open)

Endpoints NOT included

Try different interval types to see automatic updates!

How Does the Interval Calculator Work?

This calculator lets you enter any interval endpoints and choose open/closed/half-open. It shows results in standard math notation, LaTeX, and provides a clear English explanation. Interval notation is foundational to expressing solution sets, domain/range, and more in math.

Interval Notation Chart

[a, b]: closed\n(a, b): open\n[a, b): right-open\n(a, b]: left-open

Infinity always means parenthesis: (a, ∞), (−∞, b)

Frequently Used

Converting inequalities to intervals
Writing solution sets for equations
Describing domains or ranges for functions

References

Precalculus – Blitzer, 7th ed.Detailed discussion of sets and interval notation.
Algebra and Trigonometry – StewartIntroductory perspective on inequality/set/interval conversion.
Khan Academy – Inequalities & intervalsInteractive learning and interval tutorials.