Triangle Calculator

- April 25, 2025
| |

This calculator helps you solve triangle problems by finding unknown sides, angles, area, perimeter, and more based on the information you provide.

Choose what you know about your triangle, input the values, and the calculator will determine all other properties.

Select what you know about your triangle

units
? The length of side a opposite to angle A.
units
? The length of side b opposite to angle B.
units
? The length of side c opposite to angle C.

Advanced Options

About Triangles

A triangle is a polygon with three sides and three angles. The sum of all internal angles in any triangle is always 180° (or π radians).

Triangle Types Based on Sides:
  • Equilateral Triangle: All three sides are equal in length, and all angles are equal (60° each).
  • Isosceles Triangle: Two sides are equal in length, and the angles opposite to these sides are equal.
  • Scalene Triangle: All three sides have different lengths, and all angles are different.
Triangle Types Based on Angles:
  • Acute Triangle: All three angles are less than 90°.
  • Right Triangle: One angle is exactly 90° (a right angle).
  • Obtuse Triangle: One angle is greater than 90°.
Triangle Solution Methods:
  • SSS (Side-Side-Side): When all three sides are known.
  • SAS (Side-Angle-Side): When two sides and the included angle are known.
  • ASA (Angle-Side-Angle): When two angles and the included side are known.
  • AAS (Angle-Angle-Side): When two angles and a non-included side are known.
  • SSA (Side-Side-Angle): When two sides and a non-included angle are known (the ambiguous case).
Key Triangle Formulas:

Area:

  • Area = (1/2) × base × height
  • Area = (1/2) × a × b × sin(C) (using two sides and the included angle)
  • Area = √(s(s-a)(s-b)(s-c)) (Heron's formula, where s is the semiperimeter)

Law of Sines:

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

Law of Cosines:

c² = a² + b² - 2ab × cos(C)
cos(C) = (a² + b² - c²)/(2ab)
Additional Properties:
  • Perimeter: The sum of all three sides (a + b + c).
  • Semiperimeter (s): Half the perimeter, s = (a + b + c)/2.
  • Heights: The perpendicular distance from a vertex to the opposite side.
  • Medians: Lines from a vertex to the midpoint of the opposite side.
  • Incircle: The circle that is tangent to all three sides of the triangle.
  • Circumcircle: The circle that passes through all three vertices of the triangle.
  • Inradius (r): The radius of the incircle, r = Area/s.
  • Circumradius (R): The radius of the circumcircle, R = (abc)/(4×Area).

Understanding the Triangle Calculator

The Triangle Calculator is a handy tool designed to help you solve a variety of triangle problems. Whether you're working on sides, angles, area, or perimeter, this calculator covers it all. By simply entering the information you have, it provides you with the unknown values you need. It's perfect for students, teachers, and anyone who loves Geometry!

How to Start with Triangle Calculations

Getting started with the Triangle Calculator is easy. First, you'll need to select the type of information you have. You can choose from options such as:

  • Three sides (SSS)
  • Two sides and included angle (SAS)
  • Two angles and included side (ASA)
  • Two angles and non-included side (AAS)
  • Two sides and non-included angle (SSA)
  • Right triangle
  • Equilateral triangle

Inputting Your Triangle Data

After choosing the calculation type, you will input your triangle's dimensions. Depending on your selection, the calculator will prompt you for various details. For instance, if you choose the SSS method, you'll need to enter the lengths of all three sides. Each input field is user-friendly, making it simple to provide the necessary information.

Results You Can Expect

Once you've entered your data, the Triangle Calculator will work its magic and give you a comprehensive set of results. This includes the area, perimeter, and type of triangle. You will also receive the exact lengths of all sides and measures of all angles. The results are presented clearly, so you can easily understand them.

Exploring Advanced Features

The Triangle Calculator also includes several advanced options. You can customize your results by selecting:

  • The number of decimal places for the results
  • The angle units (either degrees or radians)
  • An option to visualize the triangle
  • Calculation steps, if you want to see how the results were derived

Why Use the Triangle Calculator?

This calculator is an excellent resource for various users. Whether you're studying for a test, teaching a class, or just curious about triangle properties, it provides accurate and reliable results. You’ll appreciate how quickly it can solve complex problems that would otherwise take time and effort to complete manually.

Getting Familiar with Triangle Concepts

Using the Triangle Calculator also helps reinforce your understanding of triangle properties and types. You’ll learn about different triangle types, such as scalene, isosceles, and equilateral, as well as key formulas for calculating area and perimeter. The more you use it, the more you'll appreciate the beauty of geometry!

Try the Triangle Calculator Today!

Ready to tackle some triangle problems? The Triangle Calculator is just the tool you need. It's simple, intuitive, and designed to help you succeed in understanding triangles. Give it a go and see how it can make solving triangle queries not just easy, but also fun!