Advertisement (728×90 Leaderboard)

Triangle Calculator

Angle between sides a and b
Angle opposite to side a

Triangle Properties

Sides

a =

b =

c =

Angles (degrees)

A = °

B = °

C = °

Measurements

Area = square units

Perimeter = units

Semi-perimeter = units

Inradius = units

Circumradius = units

Triangle Type

& -angled

Triangle Visualization

Note: Figure not drawn to scale

How to Use the Triangle Calculator

Our triangle calculator allows you to compute various properties of triangles using different input methods. Here's how to use it:

Calculation Methods

1. Three Sides (SSS)

Enter the lengths of all three sides (a, b, and c). This method uses the SSS (Side-Side-Side) theorem to calculate all triangle properties.

2. Two Sides and Included Angle (SAS)

Enter two sides (a and b) and the angle between them (C). This method uses the SAS (Side-Angle-Side) theorem.

3. Two Angles and Included Side (ASA)

Enter two angles (B and C) and the side between them (a). This method uses the ASA (Angle-Side-Angle) theorem.

4. Two Angles and One Side (AAS)

Enter two angles (A and B) and one side (a). The side doesn't need to be between the angles. This method uses the AAS (Angle-Angle-Side) theorem.

Understanding the Results

After calculating, the calculator displays:

  • All sides and angles of the triangle
  • Area - The space inside the triangle
  • Perimeter - The sum of all three sides
  • Semi-perimeter - Half of the perimeter
  • Inradius - The radius of the inscribed circle
  • Circumradius - The radius of the circumscribed circle
  • Triangle type - Equilateral, Isosceles, or Scalene
  • Angle type - Acute, Right, or Obtuse

Triangle Inequality Theorem

Remember that for a valid triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. If your inputs don't satisfy this condition, the calculator will show an error message.

Related Calculators

Scientific Calculator

A comprehensive scientific calculator with advanced math functions.

Embed This Calculator

Want to include this Triangle Calculator on your website? Copy and paste the code below:

Copied to clipboard!

By embedding, you agree to include the attribution link to Calculators. This embed includes a backlink to our site.

Triangle Formulas and Properties

Triangles are fundamental shapes in geometry with many interesting properties and applications.

Basic Formulas

Area Formulas

  • Using base and height: Area = ½ × base × height
  • Using sides (Heron's formula): Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2
  • Using two sides and included angle: Area = ½ × a × b × sin(C)

Perimeter and Semi-perimeter

  • Perimeter: P = a + b + c
  • Semi-perimeter: s = (a + b + c)/2

Trigonometric Laws

  • Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
  • Law of Cosines: a² = b² + c² - 2bc×cos(A)

Special Triangles

Equilateral Triangle

  • All three sides are equal: a = b = c
  • All three angles are equal (60°)
  • Area = (√3/4) × a²

Isosceles Triangle

  • Two sides are equal
  • The angles opposite to the equal sides are equal

Right Triangle

  • One angle is 90° (right angle)
  • Follows the Pythagorean theorem: a² + b² = c² (where c is the hypotenuse)

Applications

Triangles are used in numerous fields:

  • Construction and Engineering: Triangles provide structural stability in buildings, bridges, and other structures
  • Navigation: Triangulation is used to determine positions and distances
  • Computer Graphics: 3D models are often built using triangular meshes
  • Surveying: Land surveys use triangulation for accurate measurements
  • Physics: Force diagrams often use triangles to represent vector components

Advertisement (728×90 Leaderboard)