What is Heron's formula?

A way to find a triangle's area from its sides alone, without the height.

Why does it show "—"?

The sides don't form a valid triangle (longest side ≥ sum of the other two).

Triangle Area Calculator

Calculate a triangle's area and perimeter from its three side lengths using Heron's formula.

Side a: 3.00 cm

Side b: 4.00 cm

Side c: 5.00 cm

6.00 cm²

Area

Area	6.00 cm²
Perimeter	12.0 cm

ℹ️ Heron's formula: s = (a+b+c)/2, area = √(s(s−a)(s−b)(s−c)). The sides must form a valid triangle.

The triangle area calculator finds a triangle's area and perimeter from its three side lengths using Heron's formula. It is useful when you do not know the height but have measured all the sides.

How the calculator works and what it’s for▾

How Heron's formula works

First it computes the semi-perimeter s, which is the sum of sides a, b and c divided by two. The area is then the square root of s times (s minus a) times (s minus b) times (s minus c).

The perimeter is simply the sum of the three sides. The advantage of Heron's formula is that you never need to know the triangle's height separately.

What you enter and what you get

You enter the three sides in centimetres. The calculator returns the area in square centimetres and the perimeter in centimetres.

For example, with sides of 3, 4 and 5 centimetres the area is 6 square centimetres and the perimeter is 12 centimetres.

Who benefits

The calculator serves students working through geometry as well as practical measuring tasks, such as finding the area of a triangular plot of land or a paving slab.

Good to know

The sides must form a valid triangle: the sum of the two shorter sides has to be greater than the longest side. Otherwise no triangle exists and the area cannot be calculated.

🔄 Reviewed June 2026