Calculator form
Example data table
| Left Expression | Right Expression | Tolerance | Detected Sign | Difference | Comment |
|---|---|---|---|---|---|
| 7/8 | 0.9 | 0 | < | -0.025 | Left value is smaller. |
| 15 | 15.0004 | 0.001 | = | -0.0004 | Near-equality fits the tolerance window. |
| 3^3 | 24 | 0 | > | 3 | Left value is greater. |
| (10-2)/4 | 2 | 0 | = | 0 | Both expressions evaluate to the same value. |
Formula used
1) Core comparison: Evaluate both expressions first. Then compute Difference = Left − Right.
2) Equality rule with tolerance: If |Left − Right| ≤ Tolerance, the calculator treats both values as equal.
3) Strict relation: If the values are not equal within tolerance, a negative difference gives <, while a positive difference gives >.
4) Absolute difference: |Left − Right| shows the distance between both values.
5) Ratio: Left ÷ Right, when the right value is not zero.
6) Percent difference: |Left − Right| ÷ ((|Left| + |Right|) ÷ 2) × 100. This measures relative separation.
How to use this calculator
- Enter a numeric value or arithmetic expression in the left field.
- Enter the comparison value or expression in the right field.
- Choose Auto detect to reveal the strongest valid sign, or pick a sign to test.
- Set a tolerance when you want near-equal values treated as equal.
- Select the number of decimal places and your preferred output style.
- Click Compare and reveal sign to display the result above the form.
- Review the summary cards, interpretation text, and Plotly number-line graph.
- Use the CSV or PDF buttons to save the result for homework, notes, or reporting.
FAQs
1) What does this inequality sign calculator do?
It compares two numbers or arithmetic expressions, finds the strongest valid relation, tests optional signs, and shows supporting metrics like difference, ratio, and percent difference.
2) Why would I use tolerance?
Tolerance is useful when rounding, measurement error, or approximation matters. Two values can be considered equal when their absolute difference stays inside your chosen margin.
3) Can I enter expressions instead of plain numbers?
Yes. You can enter arithmetic expressions such as 3*(4+2), 18/3, or 2^5. The calculator evaluates each expression before comparing them.
4) What is the strongest valid sign?
It is the most precise relation between the two evaluated values. The result will be <, >, or =, depending on the computed difference and tolerance.
5) What happens when I test ≤ or ≥?
The calculator checks whether your chosen inclusive statement is true. Inclusive signs remain true when values are equal inside the tolerance window.
6) Why can the ratio be undefined?
A ratio requires division by the right value. When that value is zero, division is not defined, so the calculator reports the ratio as undefined.
7) What does the Plotly graph show?
The graph places both values on a horizontal number line. This makes it easy to see which value lies left, right, or at the same point.
8) Can I use this for classwork or checking homework?
Yes. The calculator is useful for practice, verification, and demonstration. The downloadable CSV and PDF options also help with notes, assignments, and revision records.