Herons Formula Calculator

Heron's Formula Calculator

Calculate triangle area directly from the three side lengths using Heron's formula.

Last updated: June 2026 | By Patchworkr Team

Triangle Sides
Area
-
Enter three valid sides
Semi-perimeter
-
Perimeter
-

Enter a real number.

Formula

Heron's formula uses the semiperimeter and the three side-length deficits.

A = √[s(s-a)(s-b)(s-c)]

Triangle inequality is required before the square root is taken.

How to Use

Enter the three side lengths of a valid triangle. The calculator checks positivity and triangle inequality before computing the area.

  1. Enter sides a, b, and c.
  2. Make sure they can form a triangle.
  3. Read the area from the result panel.

Example

For sides 3, 4, and 5, the semiperimeter is 6 and the area is 6.

That matches the classic right-triangle example exactly.

Notes

The implementation rejects impossible triangles before the product under the square root is evaluated.

Blank and malformed inputs are rejected explicitly, so the area cannot silently become zero or NaN.

Related Tools