What Is the 3-Sides Triangle Area Calculator?
This calculator finds the area of any triangle when you know the lengths of all three sides — no height or angle required. It uses Heron's formula, a classic result from geometry attributed to Hero of Alexandria, that works for every valid triangle (scalene, isosceles, or equilateral).
How to Use It
Enter the three side lengths a, b, and c in the same unit (cm, m, inches, etc.). Click calculate to see the area in square units, along with the semi-perimeter and perimeter. The three sides must satisfy the triangle inequality: the sum of any two sides must be greater than the third, otherwise no triangle exists and the area is zero.
The Formula Explained
First compute the semi-perimeter, which is half the total perimeter:
$$s = \frac{a + b + c}{2}$$
Then plug it into Heron's formula:
$$A = \sqrt{s\,(s-a)\,(s-b)\,(s-c)}$$
Because it only depends on side lengths, you never need to know the triangle's height.
Worked Example
For a triangle with sides \(a = 3\), \(b = 4\), \(c = 5\): the semi-perimeter is $$s = \frac{3 + 4 + 5}{2} = 6.$$ Then $$A = \sqrt{6 \times (6-3) \times (6-4) \times (6-5)} = \sqrt{6 \times 3 \times 2 \times 1} = \sqrt{36} = 6 \text{ square units}.$$ This matches the well-known 3-4-5 right triangle, whose area is also \(\frac{1}{2} \times 3 \times 4 = 6\).
FAQ
Do the sides have to be in the same unit? Yes — mix units and the result is meaningless. The area comes out in the square of whatever unit you used.
What if my numbers don't form a triangle? If one side is greater than or equal to the sum of the other two, no triangle exists and the calculator returns an area of 0.
Can I use it for a right triangle? Absolutely. Heron's formula works for any triangle, including right, isosceles, and equilateral triangles.
