Last updated: July 31, 2026
Inequality to Interval Notation Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
Use parentheses for strict inequalities and a bracket at the finite endpoint for inclusive inequalities; infinity always uses a parenthesis.
Where:
- x=Variable being constrained
- b=Bound value
- ( )=Open endpoint marker
- [ ]=Closed endpoint marker
Worked Examples
Strict greater-than inequality
Convert x > 5.
- 1A strict inequality excludes the endpoint.
- 2Use a parenthesis at 5.
- 3All larger values extend toward positive infinity.
Inclusive upper bound
Convert x ≤ 3.
- 1The bound 3 is included, so use a bracket at 3.
- 2The interval extends toward negative infinity.
- 3Infinity endpoints always remain open.
Negative lower bound
Convert x ≥ -2.
- 1Because the inequality includes -2, place a bracket there.
- 2Values continue upward without limit.
- 3Use a parenthesis with infinity.
Strict less-than inequality
Convert x < 1.5.
- 1Strict means the endpoint is not included.
- 2The set contains all numbers below 1.5.
- 3Write the interval from negative infinity up to 1.5 with a closing parenthesis.
Introduction
Inequality notation and interval notation describe the same set of real numbers using different visual formats. This calculator converts one-sided inequalities into interval notation so you can move easily between algebra, graphs, and calculus-style answer forms.
What Interval Notation Shows
Interval notation gives the lower and upper behavior of a set of numbers using endpoints and symbols that indicate inclusion or exclusion.
Parentheses mean an endpoint is excluded.
Brackets mean an endpoint is included.
Infinity endpoints always use parentheses.
Intervals summarize a solution set compactly.
How Each Operator Converts
The operator determines whether the finite endpoint is open or included and whether the interval stretches left or right on the number line.
x > b becomes (b, ∞).
x ≥ b becomes [b, ∞).
x < b becomes (-∞, b).
x ≤ b becomes (-∞, b].
The calculator also formats the inequality output with ≥ and ≤ symbols for readability.
Open and Closed Endpoint Meaning
Strict inequalities exclude the boundary value, so parentheses are used. Inclusive inequalities contain the boundary value, so the finite endpoint uses a bracket.
x > 5 does not include 5.
x ≥ 5 includes 5.
x < 3 does not include 3.
x ≤ 3 includes 3.
You can think of a bracket as “closed around” a value that belongs to the set.
Why Infinity Never Gets a Bracket
Infinity is not a real endpoint you can include as an actual number, so it is always written with a parenthesis in interval notation.
(5, ∞) is valid.
[5, ∞] is not valid.
(-∞, 3] is valid.
[-∞, 3] is not valid.
How to Use This Calculator
Choose the inequality operator first, then enter the bound value. The output gives the interval notation, a formatted inequality string, and the interval type.
Select >, ≥, <, or ≤.
Enter the numeric bound.
Read the interval notation output.
Cross-check the open or half-open classification.
Common Conversion Mistakes
Many errors come from using the wrong endpoint symbol or placing infinity on the wrong side of the interval.
Using a bracket for x > 5.
Putting ∞ first for a greater-than inequality.
Writing a bracket at infinity.
Confusing x < b with x > b when negative numbers are involved.
Why This Matters in Algebra and Calculus
Teachers and textbooks switch between inequalities, number-line graphs, and intervals often. Being fluent in all three forms saves time and reduces notation mistakes.
Solving linear inequalities.
Describing domains of functions.
Writing solution sets in precalculus.
Interpreting graph intervals on the real line.
If you can say the interval aloud—such as “all numbers greater than 5”—you can usually reconstruct the notation correctly.
FAQs
What is interval notation?
It is a compact way to describe a set of real numbers using endpoints with parentheses or brackets.
When do I use a parenthesis?
Use a parenthesis when the endpoint is not included, such as with > or <.
When do I use a bracket?
Use a bracket at the finite endpoint when the inequality includes the boundary value, such as with ≥ or ≤.
Why is infinity always paired with a parenthesis?
Infinity is not an actual endpoint value, so it cannot be included with a bracket.
What does intervalType mean here?
It tells you whether the finite endpoint is open or half-open based on the selected operator.
Can I enter negative bounds?
Yes. Negative, positive, and decimal bounds are all accepted as long as the value is finite.
Does this handle compound inequalities?
No. This specific calculator is for one-sided inequalities only, such as x > 5 or x ≤ 3.
Why does the output also show the inequality string?
It helps you confirm the exact interpretation of the chosen operator and bound before using the interval notation elsewhere.