Interval Notation Calculator

Category: Algebra and General
- January 12, 2026
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Convert between different forms of mathematical intervals, including interval notation, set-builder notation, and inequalities.

This calculator helps visualise intervals on a number line and convert between different representations.

Input Interval

Display Options

About Mathematical Intervals

Mathematical intervals represent a set of numbers between two endpoints. They are commonly used in calculus, analysis, and many other areas of mathematics.

Common Notation Systems
  • Interval Notation: Uses brackets and parentheses to indicate inclusion or exclusion of endpoints
  • Inequality Notation: Represents intervals using inequality symbols like <, >, ≤, ≥
  • Set-Builder Notation: Describes the set with conditions, e.g., {x | x > 3}
Applications
  • Function Domains and Ranges: Specifying where functions are defined or what values they can output
  • Solution Sets: Representing solutions to inequalities and equations
  • Confidence Intervals: In statistics, for showing ranges of probable values
  • Constraint Specification: In optimisation problems, for setting boundaries on variables

What is the Interval Notation Calculator?

The Interval Notation Calculator is a handy tool designed for anyone needing to convert between different forms of mathematical intervals. It allows users to switch between interval notation, set-builder notation, and inequalities effortlessly. You can also visualise these intervals on a number line, making it easier to understand the relationships between various mathematical expressions.

Understanding Interval Notation

Interval notation provides a way to represent a range of numbers using brackets and parentheses. Here are some key points about this notation:

  • [ ] - Closed interval (includes the endpoints)
  • ( ) - Open interval (excludes the endpoints)
  • [ ) - Left-closed, right-open interval
  • ( ] - Left-open, right-closed interval

This notation helps clarify which values are included in a given range.

Different Interval Types

Selecting the right type of interval is crucial for accurate representation. The calculator offers various interval types, including:

  • Closed intervals: [a,b]
  • Open intervals: (a,b)
  • Left-closed and right-open: [a,b)
  • Infinite intervals: (-∞, b]

Understanding these types ensures you can accurately communicate mathematical relationships.

Converting Other Notation Formats

One of the standout features of the Interval Notation Calculator is its ability to convert other Mathematics notation formats. You can transform:

  • Inequality expressions, like 2 ≤ x < 5
  • Set-builder notations, such as {x | x > 3}

This versatility makes it valuable for students and professionals alike.

Visualising Intervals on a Number Line

The calculator doesn’t just stop at conversions; it also helps you visualise the intervals on a number line. This visual representation allows you to see how the intervals relate to each other and understand their placement within the number system. Using visual tools can enhance comprehension, especially for visual learners.

Show Conversion Details

When you use the Interval Notation Calculator, you have the option to see detailed conversion steps. This feature is great for those who want to understand the process behind the calculations. You can follow along and learn how to convert between different types of mathematical expressions on your own.

Applications of the Calculator

The Interval Notation Calculator is beneficial in various mathematical fields. Some common applications include:

  • Defining function domains and ranges
  • Representing solution sets for inequalities
  • Creating confidence intervals in Statistics
  • Setting variable constraints in optimisation problems

Its diverse usability makes it a practical tool for students and professionals alike.

Start Using the Interval Notation Calculator Today

Whether you're grappling with homework or working on advanced mathematical projects, the Interval Notation Calculator is here to help. Its user-friendly design and powerful features make it an essential companion for anyone dealing with mathematical intervals. Try it out today and simplify your calculations!