Triangle Calculator

Use this triangle calculator to find the area, perimeter, angles and other properties of a triangle by entering the three sides.

Triangle Calculator

Enter the three sides of a triangle, then click Calculate to find its properties.

Result

What is a Triangle?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

The three angles of a triangle always sum to 180 degrees. The sum of the lengths of any two sides must be greater than the length of the remaining side.

Triangle Properties

  • Perimeter: The perimeter of a triangle is the sum of the lengths of its three sides: P = a + b + c.
  • Area: The area can be calculated using Heron's formula: A = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter: s = (a + b + c)/2.
  • Angles: The angles of a triangle can be calculated using the Law of Cosines. For example, angle C can be found using: cos(C) = (a² + b² - c²)/(2ab).

Types of Triangles

  • Equilateral Triangle: A triangle with all sides equal and all angles equal (60°).
  • Isosceles Triangle: A triangle with two sides equal and two angles equal.
  • Scalene Triangle: A triangle with no sides equal and no angles equal.
  • Right Triangle: A triangle with one angle equal to 90°.
  • Acute Triangle: A triangle with all angles less than 90°.
  • Obtuse Triangle: A triangle with one angle greater than 90°.

How to Use the Triangle Calculator

  1. Enter the length of side a.
  2. Enter the length of side b.
  3. Enter the length of side c.
  4. Click 'Calculate' to see the results and step-by-step solution.

Applications of Triangle Calculations

  • Architecture and construction for designing roof trusses and structural elements.
  • Land surveying and mapping to calculate areas and distances.
  • Navigation and GPS systems for determining positions and distances.
  • Computer graphics and game development for rendering 3D objects.