What It Is
This calculator finds the area of any triangle when you only know the lengths of its three sides — no height or angle required. It uses Heron formula, a classical result that lets you compute area directly from \(a\), \(b\), and \(c\).
The Formula
First compute the semi-perimeter \(s\), which is half the triangle perimeter:
$$s = \frac{a+b+c}{2}$$Then the area \(A\) is given by Heron formula, where \(a\), \(b\), \(c\) are the side lengths:
$$A = \sqrt{s(s-a)(s-b)(s-c)}$$The three sides must satisfy the triangle inequality (each side shorter than the sum of the other two) or no real triangle exists.
How to Use It
Enter the three side lengths in any consistent unit (cm, m, ft, etc.). The result is reported in square units of that same length unit. The tool also shows the semi-perimeter and total perimeter.
Worked Example
For a 3-4-5 right triangle, the semi-perimeter is:
$$s = \frac{3+4+5}{2} = 6$$Then:
$$A = \sqrt{6(6-3)(6-4)(6-5)} = \sqrt{6 \times 3 \times 2 \times 1} = \sqrt{36} = 6$$So the area is 6 square units, matching \(\tfrac{1}{2}\times 3 \times 4 = 6\).
FAQ
Do I need the height? No — that is the point of Heron formula. Only the three sides are needed.
What if I get an error or zero? Your sides likely violate the triangle inequality (e.g. 1, 2, 5). Check the measurements.
Does it work for any triangle? Yes — scalene, isosceles, equilateral, and right triangles all work.
