Triangle Calculator

Calculate triangle properties including area, perimeter, sides, and angles using various input methods. Perfect for geometry students and professionals.

Triangle Inputs
Choose your input method and enter the known values
Triangle Properties
Calculated triangle measurements and properties

Enter triangle measurements above to see the calculated properties

Triangle Calculation Methods

Available Methods:

  • SSS (Side-Side-Side): Calculate all properties when three sides are known
  • SAS (Side-Angle-Side): Two sides and the included angle
  • ASA/AAS: One side and two angles
  • Base & Height: Calculate area when base and height are known

Triangle Types:

  • Equilateral: All sides and angles are equal
  • Isosceles: Two sides and two angles are equal
  • Scalene: All sides and angles are different
  • Right: One angle is exactly 90 degrees

Understanding Triangle Calculations

Triangles are fundamental geometric shapes with three sides and three angles. Our triangle calculator uses various mathematical principles to determine unknown properties based on the information you provide.

Calculation Methods

Heron's Formula (SSS)

When all three sides are known, we use Heron's formula to calculate the area: Area = √[s(s-a)(s-b)(s-c)], where s is the semi-perimeter (a+b+c)/2.

Law of Cosines (SAS)

For two sides and the included angle: c² = a² + b² - 2ab·cos(C). This helps find the third side, then other properties can be calculated.

Law of Sines (ASA/AAS)

When angles and one side are known: a/sin(A) = b/sin(B) = c/sin(C). This relationship helps find unknown sides and angles.

Triangle Properties

  • Area: The space enclosed by the triangle
  • Perimeter: The sum of all three sides
  • Angles: Always sum to 180 degrees
  • Type: Classification based on sides and angles

Applications

Triangle calculations are essential in:

  • Architecture and construction
  • Engineering and design
  • Navigation and surveying
  • Computer graphics and game development
  • Physics and astronomy