How to Use the Triangle Area Calculator
This calculator finds the area of any triangle using two methods: base × height (when the height is known) or Heron's formula (when all three sides are known). The three-side method also provides incircle and circumcircle radii.
Formulas
Base-height: Area = ½ × base × height. Heron's formula: Find semi-perimeter s = (a+b+c)/2, then Area = √(s(s-a)(s-b)(s-c)).
Incircle and Circumcircle
The incircle is the largest circle that fits inside the triangle. Its radius r = Area / s. The circumcircle passes through all three vertices. Its radius R = abc / (4 × Area).
Triangle Inequality
For three lengths to form a valid triangle, any two sides must sum to more than the third side. If this condition fails, the calculator shows an error instead of an incorrect result.
Frequently Asked Questions
Yes. Use the three-side method (Heron's formula). As long as all three side lengths are known, the formula computes the area without needing the height explicitly.
The incircle is useful in geometry proofs, tiling problems, and inscribed-angle theorems. Its radius is directly related to the triangle's area and perimeter.
Yes. Any triangle type — acute, right, obtuse, equilateral, isosceles — works with both methods. Right triangles are a special case where the base-height method is especially straightforward.