Interval Notation Calculator
Build an interval from bounds and inclusivity, and get matching interval notation, inequality notation, and set-builder notation instantly.
Interval notation
[-3, 5)
Inequality notation
-3 ≤ x < 5
Set-builder notation
{ x | -3 ≤ x < 5 }
Recommended Settings
Pro Tips
- •Square brackets [ ] mean the endpoint is included in the interval, while parentheses ( ) mean it's excluded
- •Infinity is never written with a square bracket, since infinity isn't an actual number that can be 'reached' or included
- •An interval open on both ends, like (2, 7), excludes both 2 and 7 but includes everything strictly between them
- •Set-builder notation reads as 'the set of all x such that' followed by the condition x must satisfy
Most Popular
Most algebra problems use a closed lower bound and open upper bound, like [0, 10), for a range that starts at zero and goes up to but not including ten
When to Use This Tool
Convert a described range into proper interval notation for a homework answer.
See the same range expressed as interval, inequality, and set-builder notation together.
Express a function's valid input or output range using standard interval notation.
Verify that your interval notation matches the inequality it's meant to represent.
How It Works
Determine whether each bound is included, excluded, or extends to infinity
Choose the correct bracket type for each bound - square for included, round for excluded or infinite
Build the matching inequality and set-builder representations from the same bound information
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Lightning Fast
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Open Source
Built with verified, open-source libraries. Fully transparent.
Frequently Asked Questions
What's the difference between [ and ( ?
A square bracket [ means the endpoint is included in the set (the inequality uses ≤ or ≥), while a parenthesis ( means the endpoint is excluded (the inequality uses < or >).
Why is infinity always written with a parenthesis?
Infinity isn't a specific number that a variable can actually equal - it represents a range extending without bound - so it's never enclosed with a square bracket.
What does set-builder notation mean?
It's a way of describing a set by stating a condition its members must satisfy, read as 'the set of all x such that [condition]' rather than listing specific bounds directly.
Is my data sent anywhere?
No. All formatting happens locally in your browser.