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Heron's Formula Triangle Area — result sheet
Calculate a triangle's area, semiperimeter, perimeter, and inradius from its three side lengths.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: s = (a+b+c)/2; area = √(s(s−a)(s−b)(s−c)); inradius r = area/s.
Heron's formula obtains area from all three sides when no height or included angle is supplied. The semiperimeter and inradius are shown as related geometric quantities, while strict triangle inequalities prevent a square root of an invalid or flat triangle.
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 1000000000
- Side b — length units; minimum 1.0E-6; maximum 1000000000
- Side c — length units; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Side a | 3 |
| Side b | 4 |
| Side c | 5 |
Semiperimeter =6; area =6 square units; perimeter =12; inradius =1 unit.
Assumptions and limits
- The three inputs are positive side lengths in one consistent unit.
- The sides satisfy the strict triangle inequalities.
- The triangle is Euclidean and planar.
- The inradius is the radius of the circle tangent to all three sides and uses the same length unit.
- The result is based on entered sides and does not adjust for measurement uncertainty.
- Near-degenerate triangles can have small areas and high relative sensitivity to rounded side measurements.
- The page does not place the triangle in coordinates or choose an orientation.
- Use the unrounded side measurements when comparing the result with a drawing or survey.
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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