Triangle Calculator
Free triangle calculator. Find all sides, angles, area and perimeter of any triangle using Law of Cosines and Law of Sines.
Triangle Calculator
Enter any 3 known values (at least one must be a side). Leave unknowns empty.
Comprehensive Guide & Practice
Master the mathematical principles, formulas, and step-by-step methods with worked examples and FAQs.
1. How to Solve Any Triangle
A triangle has 6 elements: 3 sides (a, b, c) and 3 angles (A, B, C). To solve a triangle completely, you need to know at least 3 of these elements — and at least one must be a side length.
2. The Law of Cosines
Used when you know all 3 sides (SSS) or 2 sides and the included angle (SAS): c² = a² + b² − 2ab·cos(C)
This is a generalisation of the Pythagorean Theorem (which only works for right triangles).
3. The Law of Sines
Used when you know 2 angles and a side (AAS, ASA) or 2 sides and a non-included angle (SSA): a/sin(A) = b/sin(B) = c/sin(C)
4. Triangle Area Formulas
- When base and height are known: A = ½ × base × height
- When 2 sides and included angle are known: A = ½ × a × b × sin(C)
- Heron's formula (all 3 sides known): A = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2
See also: Geometry Calculator | Types of Triangles | Pythagorean Theorem