Triangle Calculator (General)
Solve any triangle from 3 known values (sides or angles). Uses law of cosines and law of sines. Returns area, perimeter, inradius, and circumradius.
General triangle
Enter any three values from sides a, b, c and angles A, B, C (degrees). Side a is opposite angle A, side b opposite B, side c opposite C. Three angles alone are not enough, and SSA combinations may be ambiguous.
Enter any three values (at least one side) to solve the triangle.
Frequently Asked Questions about the Triangle Calculator (General)
How does this triangle calculator work?
Enter any three values from sides a, b, c and angles A, B, C. The solver picks the right method automatically: law of cosines for three sides (SSS) or two sides plus the included angle (SAS), and law of sines for two angles plus a side (ASA or AAS).
What is the Law of Cosines?
For any triangle, c^2 = a^2 + b^2 - 2ab cos(C). It generalizes the Pythagorean theorem and lets you find a missing side when you know two sides and the angle between them, or a missing angle when you know all three sides.
What is the Law of Sines?
In any triangle, a / sin(A) = b / sin(B) = c / sin(C) = 2R (where R is the circumradius). It is the go-to formula when you know two angles and a side, since the third angle follows from 180 minus A minus B and the remaining sides come from ratios.
What is the difference between SSS, SAS, and ASA?
SSS means three sides are known. SAS means two sides and the angle between them. ASA means two angles and the side between them (AAS is two angles and a non-included side). All three cases produce one unique triangle.
Why does my SSA input sometimes return no result?
SSA (two sides plus an angle not between them) is the ambiguous case. Depending on the numbers it can yield zero, one, or two valid triangles. When two solutions exist this calculator returns nothing, since picking one would be arbitrary.