General Triangle Solver

You need at least 3 values, and at least one of them must be a side length. For example, three sides (SSS), two sides and an included angle (SAS), two angles and a side (ASA or AAS), or two sides and a non-included angle (SSA) are all valid inputs. Three angles alone (AAA) are not sufficient because they don't define the size of the triangle.

SSA — two sides and a non-included angle — is called the ambiguous case because it can produce zero, one, or two valid triangles depending on the values entered. When two solutions exist, this calculator will return the solution where all angles are positive and sum to 180°.

Yes. Select 'Radians (rad)' from the Angle Units dropdown before entering your values. All angle inputs and outputs will then be interpreted and displayed in radians.

The Law of Sines states that a/sin(A) = b/sin(B) = c/sin(C). It is used when you have ASA, AAS, or SSA configurations — situations where at least one angle and its opposite side are known or can be derived.

The Law of Cosines states that c² = a² + b² − 2ab·cos(C). It is used for SSS and SAS cases, where either all three sides are known or two sides and the angle between them are known.

Triangles are classified by side lengths — equilateral (all sides equal), isosceles (two sides equal), or scalene (no sides equal) — and by angles — acute (all angles < 90°), right (one angle = 90°), or obtuse (one angle > 90°). This calculator identifies and displays the type after solving.

The area is calculated using Heron's formula when all three sides are known: Area = √(s(s−a)(s−b)(s−c)), where s is the semi-perimeter (a+b+c)/2. Alternatively, if two sides and their included angle are known, Area = ½·a·b·sin(C) is used.

A valid triangle requires that the sum of any two sides must be greater than the third side (triangle inequality), and all angles must sum to exactly 180°. If your inputs violate these rules — for example, sides 1, 2, and 10 — no triangle can exist and the calculator will not return results.