Triangle Perimeter Calculator
A triangle is a three-sided polygon. This calculator computes the perimeter by summing the lengths of all three sides. It also calculates the area using Heron's formula, which allows you to find the area of any triangle when you know all three side lengths, without needing the height. The calculator validates that the three sides can form a valid triangle using the triangle inequality theorem, which requires that the sum of any two sides must be greater than the third side.
Triangle formulas
Perimeter = a + b + c
Semi-perimeter: s = (a + b + c) / 2
Area (Heron's) = sqrt(s * (s-a) * (s-b) * (s-c))
Triangle inequality: a + b > c, b + c > a, a + c > b
Example calculation
For a triangle with sides 5, 6, and 7:
- Perimeter = 5 + 6 + 7 = 18 units
- Semi-perimeter = 18 / 2 = 9
- Area = sqrt(9 * (9-5) * (9-6) * (9-7)) = sqrt(9 * 4 * 3 * 2) = sqrt(216) = 14.70 square units
Triangle perimeter calculator: frequently asked questions
What is the perimeter of a triangle?
The perimeter of a triangle is the sum of all three sides: Perimeter = side1 + side2 + side3. Any valid triangle must satisfy the triangle inequality theorem.
What is Heron's formula?
Heron's formula calculates the area of a triangle from its three sides without needing the height. First calculate the semi-perimeter: s = (a + b + c) / 2. Then Area = sqrt(s * (s-a) * (s-b) * (s-c)).
What is the triangle inequality theorem?
The sum of any two sides of a triangle must be greater than the third side. For a valid triangle: a + b > c, b + c > a, and a + c > b. If this is not true, the three sides cannot form a triangle.
How do I find the area of a right triangle?
For a right triangle with legs a and b, the area is simply: Area = (a * b) / 2. The hypotenuse c can be found using: c = sqrt(a^2 + b^2).
What are different types of triangles?
Triangles are classified by sides (equilateral, isosceles, scalene) or by angles (acute, right, obtuse). Equilateral has all sides equal. Isosceles has two equal sides. Scalene has all different sides.
Official sources
- Wolfram MathWorld: Triangle.
- ISO 80000-2: Mathematical signs and symbols.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.