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Triangle Inequality Calculator — result sheet
Check whether three positive lengths can form a non-degenerate triangle, show every inequality slack, and calculate Heron area when valid.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: A non-degenerate triangle requires a < b+c, b < a+c, and c < a+b; when valid, Heron area = √(s(s−a)(s−b)(s−c)).
Three positive numbers are not automatically the sides of a triangle. Each side must be shorter than the sum of the other two. This calculator reports the three slacks, the possible open range for a third side, and the area only when strict conditions are satisfied.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Side a — length units; minimum 1.0E-6; maximum 1000000000000
- Side b — length units; minimum 1.0E-6; maximum 1000000000000
- Side c — length units; minimum 1.0E-6; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Side a | 3 |
| Side b | 4 |
| Side c | 5 |
The sides form a valid triangle; the three slacks are 6, 4, and 2, and Heron area is 6 square units.
Assumptions and limits
- The three inputs are positive real lengths in compatible units.
- A flat zero-area configuration is treated as invalid because the inequalities are strict.
- The sides describe an ordinary Euclidean triangle, not a spherical or hyperbolic triangle.
- Heron's formula is used only after the inequalities pass.
- The possible third-side bounds are open: |a−b| < c < a+b.
- The tool does not account for measurement tolerance, uncertainty, construction fit, or surveying error.
- Very large or very small values remain subject to finite-number display and precision limits.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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