Triangle Calculator

This tool helps you calculate various properties of a triangle. You can input values for sides A, B, and C, as well as angles a, b, and c. The calculator can handle both degrees and radians for angles. When entering angles in radians, you can use values like pi/2, pi/4, etc.

Triangle Calculator


To get started, enter at least three values, including at least one side, and click “Calculate.” The calculator will determine the missing sides or angles and identify the type of triangle (e.g., Equilateral, Isosceles, Scalene, Right, Obtuse, or Acute).

About Triangles

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. Depending on the lengths of its sides and the measures of its angles, a triangle can be classified as:

  • Equilateral: All three sides are equal, and all three angles are 60°.
  • Isosceles: Two sides are of equal length, and the angles opposite these sides are equal.
  • Scalene: All three sides are of different lengths, and all three angles are different.
  • Right Triangle: One of the angles is exactly 90°.
  • Obtuse Triangle: One of the angles is greater than 90°.
  • Acute Triangle: All three angles are less than 90°.

Origin of Triangles in Mathematics

Triangles have been studied since ancient times, dating back to Euclidean geometry and Pythagorean mathematics. The ancient Greeks, Egyptians, and Babylonians used triangular relationships in construction, astronomy, and navigation. The famous Pythagorean Theorem (a² + b² = c²) is one of the earliest mathematical formulas that relate to triangles.

Types of Triangles

Triangles can be classified based on side lengths or angle measures:

  1. Based on Sides:
    • Equilateral Triangle: All three sides are equal, and all angles measure 60°.
    • Isosceles Triangle: Two sides are of equal length, and two angles are equal.
    • Scalene Triangle: All three sides and angles are different.
  2. Based on Angles:
    • Acute Triangle: All three angles are less than 90°.
    • Right Triangle: One of the angles is exactly 90°.
    • Obtuse Triangle: One of the angles is greater than 90°.

Triangle Properties and Calculations

Some essential properties and formulas used in triangle calculations include:

  • Perimeter = Sum of all three sides
  • Area = ½ × Base × Height
  • Heron’s Formula (for area) = √[s(s-a)(s-b)(s-c)], where s is the semi-perimeter
  • Pythagorean Theorem (for right triangles): a² + b² = c²
  • Law of Sines and Law of Cosines for solving unknown sides or angles

What is the Triangle Calculator?

The Triangle Calculator is an interactive tool designed to compute various properties of a triangle based on user inputs. It helps users determine unknown side lengths, angles, area, perimeter, heights, inradius, and circumradius using fundamental geometric and trigonometric principles.

How Does the Tool Work?

The calculator allows users to input any combination of sides (A, B, C) and angles (A, B, C). It then applies appropriate mathematical formulas, such as:

  • Law of Sines: Used when two angles and one side are known.
  • Law of Cosines: Used when two sides and an included angle are given.
  • Basic Triangle Properties: Ensures that the sum of the angles is always 180°, and the sides satisfy the triangle inequality theorem.

Once the calculations are complete, the tool displays results, including:
✅ Missing sides and angles
✅ Area and perimeter
✅ Triangle heights
✅ Inradius (radius of inscribed circle)
✅ Circumradius (radius of circumscribed circle)

Features of the Triangle Calculator

  • Supports All Triangle Types: Works for right, acute, and obtuse triangles.
  • Accurate Calculations: Uses trigonometric and geometric formulas for precise results.
  • User-Friendly Interface: Simple input fields for sides and angles.
  • Error Detection: Prevents calculations for invalid triangles (e.g., when the sum of two sides is not greater than the third).

Why Use This Tool?

📌 Quick and Reliable – Instant calculations without manual effort.
📌 Educational Purpose – Ideal for students, teachers, and professionals in geometry-related fields.
📌 Versatile Application – Useful in engineering, architecture, construction, and design.

This tool makes triangle calculations easy, fast, and efficient, helping users solve geometric problems effortlessly!

User Guidelines for the Triangle Calculator

🔹 Input Requirements:

  • Users can enter side lengths (A, B, C) and/or angles (A, B, C).
  • At least one side and one angle must be provided for accurate results.

🔹 Understanding the Outputs:

  • Calculated Side Lengths: If one side and an angle are provided, missing sides are determined.
  • Angles Computation: Ensures the total sum is 180°.
  • Triangle Properties: The tool calculates perimeter, area, heights, inradius, and circumradius.

🔹 Usage Tips:
✅ Ensure inputs are valid (sum of two sides should be greater than the third).
✅ If the triangle does not exist, the calculator will display an error message.
✅ Works for both right and non-right triangles.

This tool is an excellent resource for students, engineers, architects, and math enthusiasts looking for quick and accurate triangle calculations!