Heron's formula triangle area calculator
When you know all three sides but not the height, Heron's formula gives the area directly. The tool also checks the triangle can exist.
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How to use it
- Enter side a, side b, side c and length unit.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
s = (a + b + c) ÷ 2 and area = √(s × (s − a) × (s − b) × (s − c)), where a, b and c are the sides.
Example
Inputs: Side a = 13, Side b = 14, Side c = 15, Length unit = Centimeters (cm). Result: Area: 84 cm²; Perimeter: 42 cm; Semi-perimeter: 21 cm.
Limits and caveats
- Very thin triangles (an angle near zero) are sensitive to small measuring errors in the sides.
- The unit choice only labels the results.
Questions about this tool
When should I use Heron's formula?
When you know all three sides but not the height, such as a triangular plot measured only along its edges.
Why does it say the lengths do not form a triangle?
Two of the sides add up to the third or less, like 1, 2 and 3, so the triangle cannot close.
What is the area of a 13, 14, 15 triangle?
The semi-perimeter is 21 and the area is √(21 × 8 × 7 × 6) = 84 square units.