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Triangle Calculator

Free triangle calculator: enter the three side lengths to get the perimeter and exact area with Heron\u2019s formula. Invalid triangles are flagged automatically.

About this tool

Know the three sides of a triangle but not its height? Heron\u2019s formula finds the area from the sides alone - no height measurement needed.

Enter sides A, B and C, and this triangle calculator returns both the perimeter and the exact area, while checking the sides genuinely form a triangle.

How to use

Type the three side lengths in the same unit and press Calculate Triangle. The tool first validates the triangle inequality, then shows perimeter (a + b + c) and area.

Useful for land plots, roof trusses and any triangular frame where measuring the height is awkward.

The math behind it

Perimeter = a + b + c. Area = sqrt(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (a+b+c)/2 - this is Heron\u2019s formula.

A valid triangle needs each side shorter than the other two combined; the calculator flags impossible sets like 2, 3, 10.

Frequently asked questions

What is Heron\u2019s formula?
Heron\u2019s formula finds a triangle\u2019s area from its three sides without knowing the height: area = sqrt(s(s-a)(s-b)(s-c)), where s is half the perimeter. It is named after Hero of Alexandria, who described it nearly 2,000 years ago.
When should I use this instead of the area calculator?
Use this triangle calculator when you know all three sides. If you know the base and height instead, the area calculator\u2019s triangle mode (base x height / 2) is simpler - both give the same answer.
Why does it reject sides like 2, 3 and 10?
Because they cannot form a triangle: the two short sides (2 + 3 = 5) cannot span the long side (10). In any real triangle, each side must be shorter than the other two combined. Check your measurements for a typo.

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