Triangle Calculator

Solve any triangle by entering known sides and angles. Choose your known values (SSS, SAS, ASA, AAS, or HL), and this calculator finds all remaining sides, angles, area, perimeter, and classifies the triangle type using the Law of Sines and Law of Cosines.

Triangle Solver

Triangle Solving Methods

Any triangle can be fully solved if you know at least three of its six measurements (sides a, b, c and angles A, B, C — where angle A is opposite side a). The method used depends on which three values you know.

CaseMethodNotes
SSSLaw of Cosinescos A = (b²+c²−a²)/(2bc)
SASLaw of CosinesFind third side, then angles
ASALaw of SinesFind third angle: C=180−A−B
AASLaw of SinesFind third angle: C=180−A−B

Area Formula

Area (SSS via Heron's): s = (a+b+c)/2 Area = √(s(s−a)(s−b)(s−c)) Area (SAS): Area = (1/2)×a×b×sin(C) Law of Cosines: c² = a² + b² − 2ab×cos(C) Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)

Frequently Asked Questions

What is the Law of Cosines?+
The Law of Cosines states: c² = a² + b² − 2ab·cos(C). It generalizes the Pythagorean theorem and is used when you know two sides and the included angle (SAS) or all three sides (SSS).
What types of triangles are there?+
By angles: acute (all angles < 90°), right (one angle = 90°), obtuse (one angle > 90°). By sides: equilateral (all sides equal), isosceles (two sides equal), scalene (all sides different).
What is Heron's formula?+
Heron's formula calculates the area of a triangle when all three sides are known. The semi-perimeter s = (a+b+c)/2, then Area = √(s(s−a)(s−b)(s−c)).

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