Triangle Calculator

- May 10, 2025
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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).

What Is the Triangle Calculator?

The Triangle Calculator is a useful tool for solving various triangle problems. Whether you're tackling homework or just curious about Geometry, this calculator can help. It finds unknown sides, angles, area, and perimeter of a triangle based on the information you provide. Simply input what you know, and the calculator will determine all Other properties for you.

How to Use the Triangle Calculator

Using the Triangle Calculator is straightforward. Start by selecting what you already know about the triangle. Here are your options:

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

Select the relevant option, enter your values, and let the calculator do the rest!

Features of the Calculator

This tool comes with several features that enhance its functionality. You can easily select the number of decimal places for your answers and choose your preferred angle measurement (degrees or radians). Additionally, there’s an option to display a triangle visualisation to better understand the results. These features make it easier for users to grasp complex concepts and calculations.

Understanding Triangle Types

The Triangle Calculator can also help you identify different types of triangles. There are several classifications to consider, including:

  • Equilateral Triangle: All sides and angles are equal.
  • Isosceles Triangle: Two sides are equal, and the angles opposite these sides are equal.
  • Scalene Triangle: All sides and angles are different.

Knowing these types can help you understand your calculations better and their practical applications in real life.

Calculating Area and Perimeter

One of the primary uses of the Triangle Calculator is to calculate the area and perimeter. The area can be found using formulas related to the triangle’s base and height or through Heron’s formula. The perimeter is simply the sum of all three sides. Understanding how to derive these values can be especially helpful in various fields, such as architecture and engineering.

Advanced Options for Users

For those who want a deeper understanding, the calculator offers advanced options. Users can choose to display calculation steps, which guide you through the problem-solving process. This feature is beneficial for students learning geometry concepts and for anyone who wants to confirm their answers.

Additional Properties of Triangles

Beyond just sides and angles, triangles have several other important properties. The calculator can also provide information about the semiperimeter, heights from vertices to sides, and the radii of the incircle and circumcircle. This additional data can enrich your understanding of triangle geometry and its applications.

Wrapping Up Triangle Calculations

The Triangle Calculator is an essential tool for anyone dealing with triangle problems. Whether you're a student, teacher, or simply a geometry enthusiast, this calculator makes solving triangles easier and more accessible. With just a few inputs, you can unlock a wealth of information about any triangle!