Triangle Calculator

A triangle calculator is an essential mathematical tool that helps you find various properties of triangles including area, perimeter, angles, and side lengths. Whether you're a student learning geometry, an engineer working on structural calculations, or a professional in construction, our comprehensive triangle calculator provides accurate results for all your triangular computations.

Types of Triangle Calculations

Area Calculations

Our triangle calculator uses multiple methods to find triangle area:

• Base and Height: Area = ½ × base × height
• Heron's Formula: Area = √[s(s-a)(s-b)(s-c)] where s is semi-perimeter
• SAS Method: Area = ½ × a × b × sin(C)
• Coordinate Method: Using vertex coordinates

Perimeter and Semi-perimeter

The triangle calculator computes:

• Perimeter: P = a + b + c (sum of all sides)
• Semi-perimeter: s = P/2 (half the perimeter)

Triangle Classification

By Side Length

• Equilateral Triangle: All three sides are equal
• Isosceles Triangle: Two sides are equal
• Scalene Triangle: All three sides are different

By Angle Measurement

• Right Triangle: One angle equals 90°
• Acute Triangle: All angles are less than 90°
• Obtuse Triangle: One angle is greater than 90°

Advanced Triangle Properties

Circumradius and Inradius

Our triangle calculator also determines:

• Circumradius (R): Radius of the circumscribed circle
• Inradius (r): Radius of the inscribed circle
• Heights: Perpendicular distances from vertices to opposite sides

Triangle Calculation Methods

SSS Method (Side-Side-Side)

When you know all three sides, the triangle calculator uses the Law of Cosines to find angles:

cos(A) = (b² + c² - a²) / (2bc)

SAS Method (Side-Angle-Side)

With two sides and the included angle, use:

c² = a² + b² - 2ab × cos(C)

ASA Method (Angle-Side-Angle)

Using the Law of Sines when you know two angles and one side:

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

Applications of Triangle Calculators

Construction and Architecture

Triangle calculators are essential for:

• Roof design and truss calculations
• Foundation layout and structural support
• Bridge design and engineering
• Land surveying and property boundaries

Navigation and GPS

Triangulation methods using triangle calculations help in:

• GPS positioning systems
• Maritime and aviation navigation
• Satellite communication
• Emergency location services

Education and Research

Students and researchers use triangle calculators for:

• Geometry homework and assignments
• Physics problem solving
• Engineering design projects
• Mathematical research and analysis

Tips for Using Triangle Calculators

• Always check that your triangle is valid (triangle inequality theorem)
• Use consistent units throughout your calculations
• Verify results by checking that angles sum to 180°
• Choose the appropriate calculation method based on known values
• Round final answers appropriately for your application

Special Triangle Types

Right Triangles

For right triangles, the triangle calculator can use the Pythagorean theorem:

a² + b² = c² (where c is the hypotenuse)

45-45-90 Triangles

In these isosceles right triangles, the sides are in the ratio 1:1:√2.

30-60-90 Triangles

These special right triangles have sides in the ratio 1:√3:2.

Our comprehensive triangle calculator handles all these triangle types and more, providing accurate calculations with detailed step-by-step solutions. Whether you need basic area and perimeter calculations or advanced properties like circumradius and inradius, this tool delivers professional-grade accuracy for all your triangular computation needs.