Triangle Calculator

Calculate all properties of triangles including area, perimeter, angles, and side lengths. Supports all triangle types and multiple calculation methods.

Calculate Triangle Properties

Enter at least 3 values (sides or angles) to calculate the triangle

Understanding Triangles

A triangle is a three-sided polygon with three angles that always sum to 180 degrees. Triangles are fundamental shapes in geometry, engineering, architecture, and navigation. Understanding triangle properties helps solve real-world problems from construction to GPS technology.

Types of Triangles

By Sides:

  • Equilateral: All three sides equal, all angles 60°
  • Isosceles: Two sides equal, two angles equal
  • Scalene: All sides different lengths

By Angles:

  • Right: One 90° angle
  • Acute: All angles less than 90°
  • Obtuse: One angle greater than 90°

Triangle Formulas

Area Formulas:

Base × Height / 2
Heron's Formula: √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2

Law of Sines:

a/sin(A) = b/sin(B) = c/sin(C)

Law of Cosines:

c² = a² + b² - 2ab×cos(C)

Pythagorean Theorem (Right Triangles):

a² + b² = c² (where c is hypotenuse)

Real-World Applications

  • Construction: Roof trusses, bridges, structural supports
  • Navigation: Triangulation for GPS and maritime navigation
  • Surveying: Land measurement and mapping
  • Engineering: Force analysis, mechanical design
  • Astronomy: Calculating distances to stars
  • Art & Design: Perspective drawing, composition

Frequently Asked Questions

Can any three sides form a triangle?

No. The Triangle Inequality Theorem states that the sum of any two sides must be greater than the third side. For example, sides 2, 3, and 10 cannot form a triangle because 2 + 3 < 10.

Why do triangle angles always equal 180°?

This is a fundamental property of Euclidean geometry. On a flat plane, the internal angles of any triangle always sum to exactly 180 degrees. This property is used to solve for unknown angles.

What information do I need to solve a triangle?

You need at least three pieces of information (sides or angles), with at least one being a side length. Common combinations: three sides (SSS), two sides and included angle (SAS), two angles and one side (AAS/ASA).