Triangle Calculator

Solve any triangle using our comprehensive calculator. Whether you know three sides (SSS), two sides and an angle (SAS/SSA), or two angles and a side (ASA/AAS), our tool will calculate all missing properties including sides, angles, area, and perimeter with step-by-step explanations.

Triangle Calculator

✨ Beautiful geometry made simple

Input Values

Related Tools

Math Tools

Triangle Calculation Methods

Basic Methods

SSS (Side-Side-Side): When you know all three sides, use the Law of Cosines to find all angles.
SAS (Side-Angle-Side): Two sides and the included angle. Use Law of Cosines for the third side, then Law of Sines for remaining angles.
ASA (Angle-Side-Angle): Two angles and the included side. Find the third angle, then use Law of Sines for the remaining sides.

Advanced Methods

AAS (Angle-Angle-Side): Two angles and a non-included side. Calculate the third angle, then use Law of Sines.
SSA (Side-Side-Angle): Two sides and a non-included angle. This is the "ambiguous case" that may have 0, 1, or 2 solutions.
Area Calculation: Uses appropriate formulas based on known values - Heron's formula, base×height/2, or trigonometric area formulas.

Mathematical Foundations

Law of Cosines

Formula

c² = a² + b² - 2ab·cos(C)

When to Use

Use when you know three sides (SSS) or two sides and the included angle (SAS). This law generalizes the Pythagorean theorem for all triangles.

Law of Sines

Formula

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

When to Use

Use when you know two angles and any side (ASA/AAS) or two sides and a non-included angle (SSA). Perfect for finding unknown sides or angles.

Practical Applications

Construction

Calculate roof angles, determine building layouts, and solve structural engineering problems.

Surveying

Measure land boundaries, calculate distances, and determine property dimensions accurately.

Education

Perfect for students learning trigonometry, geometry, and solving homework problems.