Triangle Calculator – Calculate Angles, Sides, Area | CalculusHub.net

Triangle Calculator

Calculate angles, sides, area, perimeter, heights, medians, inradius, and circumradius

Please provide 3 values including at least one side. When radians are selected as the angle unit, it can take values such as pi/2, pi/4, etc.
A B C
a
b
c
∠A
∠B
∠C

Enter triangle values and click calculate to see results here

Triangle Calculation Results

Triangle Type:
A B C
a
b
c
∠A
∠B
∠C
Side a: 0
Side b: 0
Side c: 0
Angle A: 0°
Angle B: 0°
Angle C: 0°
Area: 0
Perimeter: 0
Semiperimeter: 0
Height (ha): 0
Height (hb): 0
Height (hc): 0
Median (ma): 0
Median (mb): 0
Median (mc): 0
Inradius: 0
Circumradius: 0

Triangle Calculator Features

Comprehensive Calculations

Calculate all triangle properties including sides, angles, area, perimeter, heights, medians, inradius, and circumradius.

Multiple Input Methods

Enter any combination of three values (sides or angles) to calculate the remaining properties of the triangle.

Mobile Optimized

Fully responsive design that works perfectly on desktop, tablet, and mobile devices.

Share & Print Results

Easily share your calculation results or print them for reference and documentation.

Understanding Triangles: A Comprehensive Guide

What is a Triangle?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted as △ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

Types of Triangles

Triangles can be classified according to their sides and angles:

  • By sides: Equilateral (all sides equal), Isosceles (two sides equal), Scalene (all sides different)
  • By angles: Acute (all angles less than 90°), Right (one angle exactly 90°), Obtuse (one angle greater than 90°)

Triangle Properties and Formulas

Key properties of triangles include:

  • Area: Calculated as (base × height)/2 or using Heron’s formula
  • Perimeter: Sum of all three sides
  • Angles: Sum of interior angles always equals 180°
  • Pythagorean Theorem: For right triangles, a² + b² = c²
  • Law of Sines: a/sin(A) = b/sin(B) = c/sin(C) = 2R
  • Law of Cosines: c² = a² + b² – 2ab·cos(C)

Applications of Triangles

Triangles are fundamental in various fields including architecture, engineering, computer graphics, and navigation. Their structural stability makes them essential in construction, while their mathematical properties are crucial in trigonometry and calculus.

Using the Triangle Calculator

Our triangle calculator allows you to input any three values (sides or angles) and calculates all remaining properties. Simply enter the known values, select the appropriate units, and click “Calculate” to get comprehensive results including area, perimeter, heights, medians, and more.