Triangle Calculator

Every triangle is uniquely determined (or nearly so) when you know three pieces of information among its three sides and three angles — provided at least one of those pieces is a side length. This calculator supports the five standard combinations: SSS (three sides), SAS (two sides and the included angle), ASA (two angles and the included side), AAS (two angles and a non-included side), and SSA (two sides and a non-included angle).

When three sides are known (SSS), the Law of Cosines finds each angle: cos(A) = (b² + c² − a²) / (2bc). For SAS, the Law of Cosines computes the third side first: c² = a² + b² − 2ab·cos(C). When two angles are known, the third follows from the fact that interior angles sum to 180°. The remaining sides come from the Law of Sines: a/sin(A) = b/sin(B) = c/sin(C).

Area can be computed as (1/2)ab·sin(C) or by Heron's formula when all three sides are known: Area = √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2. Perimeter is simply a + b + c. The height to side a is h_a = 2·Area/a, with analogous formulas for b and c.

The inradius r = Area/s and circumradius R = abc/(4·Area) are included for completeness. The SSA case can be ambiguous — two different triangles may satisfy the given data — and this calculator reports both solutions when they exist.

An SVG diagram updates in real time, showing the triangle scaled to your side lengths with labeled sides and angles. Select your known combination from the tabs, enter the given values, and all remaining measurements appear instantly.