Free Online Triangle Calculator
Calculate triangle sides, angles, area, and perimeter using our advanced triangle calculator. Supports SSS, SAS, ASA, AAS, and SSA methods with step-by-step solutions and interactive visualization.
How to Use the Triangle Calculator
- 1
Choose Calculation Method
Select your preferred method: SSS (3 sides), SAS (side-angle-side), ASA (angle-side-angle), AAS (angle-angle-side), or SSA (side-side-angle).
- 2
Enter Known Values
Input the known sides (in any unit) and angles (in degrees) based on your selected method. Required fields are highlighted with sparkles.
- 3
View Results Instantly
See all triangle properties calculated automatically including missing sides, angles, area, and perimeter with real-time validation.
- 4
Explore Visualization & Steps
Toggle the interactive triangle visualization and view detailed calculation steps to understand the mathematical process.
Key Features
Multiple Calculation Methods
Solve triangles using SSS (3 sides), SAS (side-angle-side), ASA (angle-side-angle), AAS (angle-angle-side), or SSA (side-side-angle) methods
Complete Triangle Properties
Calculate all triangle properties including sides, angles, area, and perimeter with high precision mathematical formulas
Interactive Visualization
View your triangle with accurate geometric representation, labeled vertices, sides, and angles for better understanding
Step-by-Step Solutions
Learn how triangles are solved with detailed explanations of Law of Cosines, Law of Sines, and triangle inequality principles
What is a Triangle Calculator?
A triangle calculator is a mathematical tool that solves triangles by finding unknown sides and angles when given sufficient information. It uses fundamental geometric principles like the Law of Cosines, Law of Sines, and triangle inequality theorem. The calculator supports five main methods: SSS (three sides), SAS (two sides and included angle), ASA (two angles and included side), AAS (two angles and non-included side), and SSA (two sides and non-included angle). Each method requires different input combinations to uniquely determine a triangle's properties including area and perimeter.
Why Use Our Triangle Calculator?
- 1
Multiple Solution Methods
Support for all five triangle solving methods (SSS, SAS, ASA, AAS, SSA) with automatic method switching and example values for quick testing.
- 2
Real-Time Calculations
Instant results as you type with automatic validation, error checking, and triangle inequality verification to ensure valid solutions.
- 3
Interactive Visualization
Beautiful geometric visualization with accurate triangle representation, labeled vertices, sides, and angles for enhanced learning.
- 4
Educational Features
Detailed step-by-step explanations for each calculation method, showing formulas, principles, and mathematical reasoning behind solutions.
Frequently Asked Questions
What's the difference between SSS, SAS, ASA, AAS, and SSA methods?
SSS uses three sides, SAS uses two sides and the included angle, ASA uses two angles and the included side, AAS uses two angles and a non-included side, and SSA uses two sides and a non-included angle. Each method requires different input combinations to solve the triangle.
Why might SSA method have multiple solutions?
The SSA (Side-Side-Angle) case can be ambiguous because two sides and a non-included angle might form zero, one, or two valid triangles. Our calculator checks for valid solutions and warns about this ambiguity.
How does the calculator verify triangle validity?
The calculator checks the triangle inequality theorem (sum of any two sides must be greater than the third side) and validates that angles sum to 180°. Invalid triangles are rejected with helpful error messages.
What mathematical formulas does the calculator use?
The calculator uses the Law of Cosines (c² = a² + b² - 2ab·cos(C)), Law of Sines (a/sin(A) = b/sin(B) = c/sin(C)), and Heron's formula for area calculations, ensuring mathematically accurate results.
Can I use any units for sides and angles?
Yes, you can use any consistent units for sides (inches, cm, meters, etc.). Angles must be entered in degrees. The calculator maintains unit consistency throughout all calculations and results.