Triangle Perimeter Calculator

Calculate the perimeter and semi-perimeter of any triangle given its three sides.

Enter Triangle Sides

Result

Perimeter (P)
--
units
Semi-perimeter (s) --
Valid Triangle? --
Area (Heron's) --

Step-by-Step Solution

P = a + b + c

Understanding Triangle Perimeter

The perimeter of a triangle is the total distance around the triangle, found by summing the lengths of all three sides. It is one of the most fundamental measurements in geometry and is used extensively in construction, surveying, and design.

Key Formulas

Perimeter

Sum of all three sides of the triangle.

P = a + b + c

Semi-Perimeter

Half of the perimeter, commonly used in Heron's formula.

s = P / 2 = (a + b + c) / 2

Heron's Formula

Calculates area using only the three sides via the semi-perimeter.

A = sqrt(s(s-a)(s-b)(s-c))

Triangle Inequality Theorem

For three lengths to form a valid triangle, each side must be less than the sum of the other two sides. This means: a + b > c, a + c > b, and b + c > a. If any of these conditions fails, the three segments cannot form a triangle.

Special Cases

  • Equilateral triangle: All three sides are equal. P = 3a, s = 3a/2.
  • Isosceles triangle: Two sides are equal. P = 2a + b, s = (2a + b)/2.
  • Scalene triangle: All three sides are different.

Practical Applications

Perimeter calculations are essential when measuring fencing around a triangular plot, calculating the length of trim needed for a triangular surface, determining the boundary length for surveying, or computing material requirements in construction and manufacturing.