Triangle Calculator
A triangle is one of the most fundamental shapes in geometry. This calculator lets you find the area of a triangle using two different methods: if you know the base and height, the area is simply half the product of the two (Area = ½ × b × h). If you know all three side lengths, Heron's formula delivers both the area and the perimeter in one step.
Heron's formula works by computing the semi-perimeter s = (a + b + c) / 2 and then applying Area = √(s × (s−a) × (s−b) × (s−c)). Before calculating, the tool verifies the triangle inequality — each side must be shorter than the sum of the other two — so you always get a meaningful result or a clear error message.
How it works
Mode A (base + height): Area = ½ × b × h. Mode B (three sides a, b, c): s = (a+b+c)/2; Area = √(s·(s−a)·(s−b)·(s−c)); Perimeter = a+b+c. Triangle inequality: a+b > c, a+c > b, b+c > a.
Use cases
- Calculating land or floor area that forms a triangular shape
- Architecture and construction: computing roof pitch surface areas
- Navigation and surveying: finding distances using triangulation
- Academic math problems involving triangle geometry
- Woodworking and DIY: cutting triangular pieces with exact dimensions