Simplest Interval Form Calculator

Interval notation is a concise way to represent sets of real numbers. This calculator helps you convert numbers and ranges into standard interval notation quickly and accurately.

What is Interval Notation?

Interval notation is a mathematical shorthand used to describe ranges of real numbers. It's commonly used in calculus, algebra, and other branches of mathematics to represent continuous sets of numbers.

There are four main types of intervals:

Closed interval: Includes both endpoints (e.g., [a, b])
Open interval: Excludes both endpoints (e.g., (a, b))
Half-open interval: Includes one endpoint but not the other (e.g., [a, b) or (a, b])
Infinite interval: Represents numbers extending to infinity (e.g., [a, ∞) or (-∞, b])

Interval notation is particularly useful in calculus for describing domains of functions and limits.

How to Use This Calculator

Using our interval form calculator is simple:

Enter your starting number in the first field
Enter your ending number in the second field
Select whether the interval includes the endpoints (closed, open, or half-open)
Click "Calculate" to see the interval notation

The calculator will display the proper interval notation based on your inputs and selection.

Common Interval Types

Here are some common interval types and their notations:

Interval Type	Notation	Description
Closed Interval	[a, b]	Includes all numbers from a to b, including a and b
Open Interval	(a, b)	Includes all numbers from a to b, excluding a and b
Half-Open (Left)	[a, b)	Includes all numbers from a to b, including a but excluding b
Half-Open (Right)	(a, b]	Includes all numbers from a to b, excluding a but including b
Infinite Interval	(-∞, b]	All numbers less than or equal to b

Interval Notation Examples

Here are some practical examples of interval notation:

Example 1: Temperature Range

If a device operates between 60°F and 80°F (inclusive), the interval notation would be [60, 80].

Example 2: Test Scores

If passing scores are between 70 and 90 (excluding 70 but including 90), the notation would be (70, 90].

Example 3: Age Restrictions

If a movie is rated for ages 13 and up, the interval notation would be [13, ∞).

FAQ

What is the difference between [a, b] and (a, b)?

The square brackets [ ] indicate that the endpoints are included in the interval, while parentheses ( ) indicate that the endpoints are excluded. So [a, b] includes a and b, while (a, b) excludes both.

How do I represent an infinite interval?

Use ∞ (infinity) to represent an unbounded interval. For example, all numbers greater than 5 would be written as (5, ∞).

Can I use interval notation for discrete sets?

Interval notation is primarily for continuous sets of real numbers. For discrete sets, you would typically list the elements individually or use set notation.