Interval Notation Calculator
Convert bounded, one-sided, or outside inequalities into interval notation, set-builder notation, endpoint rules, and a live number-line graph.
Interval Notation Calculator inputs
Choose a solution-set shape, enter its boundary values, and specify whether each finite endpoint is included.
Infinity always uses a parenthesis. The calculator never places a square bracket beside ±∞.
Interval Notation Calculator results
How the interval notation calculator works
This page answers the exact search intent represented by interval notation calculator. The calculator keeps definitions, assumptions, intermediate values, and warnings visible so the result can be checked rather than accepted as an unexplained number.
Brackets, parentheses, and infinity
A square bracket means a finite endpoint belongs to the solution set. A parenthesis means the endpoint is excluded. Positive and negative infinity are directions rather than attainable numbers, so they always receive parentheses. The calculator enforces that notation automatically.
Inequalities and unions
A bounded interval describes values between two endpoints. One-sided inequalities create rays extending toward positive or negative infinity. An outside solution uses a union because it contains two disconnected rays. The result displays interval notation, an equivalent inequality, and set-builder notation together.
Reading a number-line graph
Filled circles represent included endpoints and open circles represent excluded endpoints. The highlighted segment or ray is the solution set. The graphic is scaled from the entered values, so widely separated or negative endpoints remain readable without changing the mathematical answer.
Reliable-use checklist
Confirm that every endpoint, unit, date, rate, period, inclusion rule, and sign matches the original problem. Save the detailed output with the input values so the calculation can be reproduced. Compare a known example before using a custom case, and consult current professional guidance when the output affects taxes, contracts, regulated benefits, or investment decisions.
The interval notation calculator runs locally in the browser. It does not transmit entered values, create an account, or retain a calculation history. Full internal precision is used for the calculation, while display rounding is applied only to readable result cards and graphics.
Interval Notation Calculator questions
When should I use a bracket instead of a parenthesis?
Use a bracket when a finite endpoint is included by ≤ or ≥. Use a parenthesis for < or >.
Can infinity have a square bracket?
No. Infinity is not a real endpoint that can be included.
How is an outside inequality written?
It is a union of two intervals, such as (−∞, a) ∪ (b, ∞).