General-purpose triangle solver. Enter any valid combination of sides and angles (SSS, SAS, ASA, AAS, SSA) and compute all remaining sides, angles, area, perimeter, and more.
The **Triangle Side-Angle Calculator** is a comprehensive triangle solver. Given any valid combination of three known elements — sides and angles — it determines all remaining unknowns and reports the full set of triangle properties.
Five classic input combos are supported:
- **SSS** — three sides known. All angles can be found via the Law of Cosines. - **SAS** — two sides and the included angle. The third side comes from the Law of Cosines, then the remaining angles from the Law of Sines. - **ASA** — two angles and the included side. The third angle is 180° minus the other two, and the remaining sides follow from the Law of Sines. - **AAS** — two angles and a non-included side. Equivalent to ASA after computing the third angle. - **SSA** — two sides and a non-included angle (the ambiguous case). There may be zero, one, or two valid triangles.
Beyond just sides and angles, the calculator outputs the area, perimeter, inradius, circumradius, altitude from each vertex, and the type of triangle (acute, right, or obtuse). Visual bars show side and angle proportions at a glance, and a reference table explains when to use each input combination.
Whether you are a geometry student, a surveyor, an architect, or an engineer, this tool replaces tedious manual computation with instant, accurate results.
A general triangle solver is useful because real problems do not arrive in one neat format. One question gives you three sides, another gives two angles and a side, and the next introduces the ambiguous SSA case where there may be two valid answers. This calculator keeps those combinations separate and solves each one using the correct sequence of cosine and sine relationships.
It is especially helpful for checking whether a problem has a unique triangle or multiple solutions. Seeing the full solved triangle, along with area and radius values, makes it much easier to understand what a given side-angle combination actually determines.
Law of Cosines: c² = a² + b² − 2ab cos C. Law of Sines: a/sin A = b/sin B = c/sin C. Area = ½ ab sin C. Inradius r = Area / s. Circumradius R = a / (2 sin A).
Result: c ≈ 7.21, A ≈ 73.22°, B ≈ 46.78°, Area ≈ 20.78
SAS example: a = 8, b = 6, C = 60°. c = √(64 + 36 − 96·cos60°) = √(100 − 48) = √52 ≈ 7.211. A ≈ 73.22°, B ≈ 46.78°. Area = ½·8·6·sin60° ≈ 20.785.
A triangle can be determined by several combinations of sides and angles, but each combination has its own logic. SSS starts with shape from side lengths, SAS uses an included angle to lock in the third side, and ASA or AAS use the angle sum to unlock the missing side lengths through the Law of Sines. Treating all of those as the same kind of exercise hides the reasoning that makes triangle solving work.
SSA is the unusual case because the same data can describe zero, one, or two triangles. That happens because the Law of Sines determines a sine value, and the same sine can correspond to two different angles between 0° and 180°. If both resulting geometries satisfy the triangle conditions, both solutions are valid.
After a triangle is solved, do not stop at the missing numbers. Compare the side lengths to the opposite angles, check whether the triangle is acute, right, or obtuse, and see whether the perimeter and area agree with the overall scale you expected. A good solver should support interpretation, not just produce a list of values.
When you know two sides and an angle opposite one of them, the Law of Sines can yield 0, 1, or 2 valid triangles depending on relative sizes. Use this as a practical reminder before finalizing the result.
No. Three angles fix the shape but not the size. You need at least one side to determine a unique triangle.
The inradius r is the radius of the largest circle that fits inside the triangle. r = Area / s, where s is the semi-perimeter.
The circumradius R is the radius of the circle passing through all three vertices. R = a / (2 sin A).
Count your known sides (S) and angles (A). Common combos are SSS (3 sides), SAS (2 sides + included angle), ASA (2 angles + included side), AAS (2 angles + non-included side), and SSA (2 sides + non-included angle).
Computations use double-precision floating point (about 15 significant digits). Results are displayed rounded to your chosen precision.