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Interval Notation Calculator

Interval Notation Calculator

Write down intervals of numbers and select the nature of the variable. The interval notation calculator will find the set builder notation, length, and topology of the data provided.


Enter the Intervals: Ex. (2,8) or [2,8] or [2,8) or (2,8]


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An online interval notation calculator helps you to find the interval values from the given set interval notation. Also, this set builder notation calculator allows you to find the set builder notation for the given notation. Apart from set builder & set interval notation, this calculator helps to find total length and topology of the data solution set.

In this context, we clarify that how to write interval notation, some basic’s and much more for your convenience.

What is Interval Notation?

According to the mathematics definition, it is the technique of writing subsets of the real number line. An interval notation example is one that includes its endpoints: for example, if we have the set \({x |−2≤x≤1}\) then according to a definition it will be written as: \([−2,1]\).

Interval (Set Builder) Notation formula is: \(= n1<=x <=n2\)

  • \(n1\) is representing the First Number
  • \(n2\) is representing the Second Number

Well, an online interval notation solver will solve the notation and provides you with the interval values.

When numbers are written as \([a,x]\) then they are indicating that “\(a\)” and “\(x\)” are included in a set. On the other hand \((a,x)\) indicates that“\(a\)” and “\(x\)” is omitted from the set. “\([b,y)\)” known as half-closed and indicates that b is included but y is excluded. Similarly \((b,y]\) will be recognized as half-open that specifies \(b\) is omitted and \(y\) is included in the set.


Interval notation shows that values fall between two endpoints. For example, if we have \(-2≤x≤3, [-2,3]\), it means that \(x\) is between \(-2\) and \(3\) and could be either endpoint. An interval notation calculator has the ability to simplify such calculation within few seconds.

Also, the free exponent calculator is the best way to solve the exponent operations & find the value of any positive or negative integer raised to nth power.

Types of Interval Notation:

Before you write a number in interval notation, you need to determine its types. Basically, there are two types of it:

Open Interval Notation:

In this type, both endpoints will not be included in the interval. It can be written in the format \((a,b)\) as“\(a\)” and “\(b\)” are the endpoints.

Closed Interval Notation:

in this type the endpoints will be included in the interval. Interval set notation calculator is functioned to write in both types. You can pick one just according to the requirement.

You can also mention the intervals using inequalities, such as greater than, less than, greater than or equal to, less than or equal to.

How to Write Interval Notation?

An interval notation calculator is functioned to write numbers in interval notation. Furthermore, it can be written with rectangular brackets or parentheses, and two numbers that will be enclosed with a comma. These two numbers are known as the endpoints of the interval. The left number denotes the least element or lower bound. However, if you are using a set builder notation calculator you can have interval notation and set builder notation for any numerical statement simultaneously.

For example: If we have \(= 0≤x≤4\)

  • \(X > -1\)
  • \(X ≤ 2\)
  • \(X ≤ 0 or x > 3\)

So it will be: \((0, 4)\)

Well, by using a simple online binary calculator you can readily perform basic mathematics operations on two numbers with base \( \text{ 2, 8, 10 & 1} \).

How to use Interval Notation Calculator to Find Interval Values?

The procedure to use this interval notation calculator is as follows:


  • In the first step, you have to Enter the interval (closed or open interval) in the given input fields
  • Select the value of \(x\), whether you need to get a data solution set in the form of even, odd, or prime
  • In the final step, you have to click the button “Calculate” to get the results


Within few moments this set builder notation calculator will display:

  • Interval values
  • Set builder notation
  • Total length of the solution set
  • Topology of the solution set.

How to Convert to Interval Notation?

There are some steps to follow to convert to Interval Notation \(7-x/6>8\).

  • First of all,move all the non \(x\) terms to the right side and then subtract \(7\) from both sides of the inequality: \(7-x/6>8 = -x/6 > 8-7 = -x/6 > 1\)
  • Multiply by \(-1\) and flip the direction of inequality:\(-x/6. -1<1⋅−1 = −x/6⋅−1= x/6<1⋅−1\)
  • Multiply \(-1\) by \(1 = x/6<-1\).
  • Multiply both sides by \(6 = x<-1.6 = x<-6\).
  • Now convert the inequality to write answer in interval notation= \(7-x/6>8\)

You can find an online interval notation converter that helps you to perform conversions for the given notation.


What is an interval notation for a graph?

Graph interval notation included\( x\) and \(y axis\). In graphical representation, you don’t read numbers off the \(y-axis\). You have to stay on the \(x-axis\) only. It is a popular notation for declaring which sections of a graph are increasing, decreasing, or staying constant.

How do you read set builder notation?

If the given set is: \( Q = {x: x  \text{ is an integer} , x > -6}\). You can read it as: “\(Q\) is the set of elements \(x\) such that \(x\) is an integer bigger than \(-6\).” Moreover, use of a set builder calculator is the finest way to deal with such equations.

How do you write intervals of increase?

It increases from the point \((1,1)\) till it reaches the point \((3,4)\). \(T\) can be described as increasing when \(1 < x < 3\). While writing in interval notation, it is labelled as increasing on the interval \((1,3)\).

What is set builder or rule method?

A set can be defined as a well-structured class or collection of objects. In the builder method or Rule methods set is labelled by a describing property \(P(x)\) of its elements \(x\). In these situations,the set is {\(x: P(x)\) holds} or {\(x | P(x)\) holds}. It can be read as ‘the set of all \(x\) such that \(P(x)\) holds’.

What is the interval notation for?

It is useful while describing domain and range. It shows that a value falls between two endpoints.

Wrapping it up:

The team of calculator-online precisely designed interval notation calculator to support an individual who needs to simplify complex mathematical interval notation calculations. So simply add some numbers and leave the rest on this set builder notation calculator to have the final outcomes without doing any manual calculations.


From the authorized source of Wikipedia: The details of Interval (mathematics)

The source of brilliant provides you with: way of writing interval notation

From the source of study: Writing Sets in Interval and its types