Triangle Area & Perimeter Calculator
Compute area and perimeter of any triangle from three sides using Heron's formula.
What this calculates
Given any three sides, a triangle's area and perimeter are fully determined. Heron's formula avoids needing angles or heights. This calculator also validates the triangle inequality — three lengths only form a real triangle if each side is less than the sum of the other two.
Formula & how it works
Perimeter = a + b + c. Semi-perimeter s = perimeter / 2. Area = √(s(s−a)(s−b)(s−c)). Valid if a+b>c, a+c>b, b+c>a.
Worked example
Sides 3, 4, 5. Perimeter 12, s = 6. Area = √(6·3·2·1) = 6. Right triangle confirmed.
Frequently asked questions
What if my inputs don't form a triangle?
If any side ≥ sum of the other two, no triangle exists — calculator flags it.
Right triangle?
Use Pythagorean if you have legs and want hypotenuse. Heron's still works on the resulting sides.
From base + height?
Area = ½ × base × height. Heron's is for when you only know the three sides.