Math
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 exactly three values, any mix of sides (a, b, c) and angles (A, B, C), and the calculator fills in the rest. It picks the method automatically: law of cosines for SSS or SAS, and law of sines for ASA or AAS. It also computes area, perimeter, inradius, circumradius, and triangle type.
What is the Law of Cosines?
The law of cosines states c^2 = a^2 + b^2 - 2ab x cos(C), where C is the angle opposite side c. It is the formula used for SSS (find a missing angle when all three sides are known) and SAS (find the third side when two sides and the included angle are known). For a right triangle with C = 90 degrees, cos(C) = 0, so it reduces to the Pythagorean theorem.
What is the Law of Sines?
The law of sines states a / sin(A) = b / sin(B) = c / sin(C). When you know two angles and one side, the third angle is simply 180 minus the other two, and the remaining sides follow from the ratios. The calculator uses this for ASA and AAS cases.
What is the difference between SSS, SAS, and ASA?
These abbreviations describe which three pieces of information you provide. SSS means all three sides. SAS means two sides with the angle between them. ASA means two angles with the side between them. AAS means two angles with a non-included side. Each of these combinations produces exactly one triangle, so the calculator always returns a result for valid inputs.
Why does my SSA input sometimes return no result?
SSA (two sides and an angle that is not between them) is the ambiguous case. Depending on the values, there may be zero, one, or two valid triangles. The calculator returns a result only when exactly one solution exists. If your input produces no result, try a SAS combination instead by providing the angle between your two known sides for an unambiguous solve.