Triangle Area Calculator
Calculate the area of a triangle from its base and height or from its three sides (Heron’s formula).
Area:
Perimeter:
Semi-perimeter (s):
Base and Height Formula
The most common way to find the area of a triangle uses its base and the perpendicular height drawn to that base:
Area = ½ × base × height
The height must be measured perpendicular to the chosen base, not along one of the slanted sides. This method works for any triangle as long as you know a base and its matching height.
Heron's Formula
When you know the lengths of all three sides (a, b, c) but not the height, Heron's formula gives the area directly. First compute the semi-perimeter, then the area:
s = (a + b + c) / 2
Area = √( s × (s − a) × (s − b) × (s − c) )
The three sides must satisfy the triangle inequality: each side must be shorter than the sum of the other two. If they do not, no triangle exists and the area cannot be calculated.
When to Use Each Method
- Base & Height: Use this when you can measure (or already know) a base and the perpendicular height. It is the simplest and fastest approach.
- Three Sides (Heron's formula): Use this when you only know the three side lengths and have no convenient height, such as for a scalene triangle on a map or plot of land.
Related Calculators
Note: This calculator computes the area of a triangle using the base-and-height formula or Heron's formula as described above. Results are rounded for display. While we strive for accuracy, please verify important calculations independently. This tool is for educational and informational purposes and should not be the sole basis for engineering, construction, academic, or professional decisions.