Triangle Calculator

You need at least 3 values with at least one being a side. Valid combinations: three sides (SSS), two sides and the included angle (SAS), two angles and a side (AAS/ASA), or two sides and a non-included angle (SSA, which may have two solutions). Three angles alone cannot determine side lengths.

The calculator uses the most appropriate formula: base x height / 2 (if height is known), Heron's formula (if three sides are known: area = sqrt(s(s-a)(s-b)(s-c)) where s is the semi-perimeter), or (1/2)ab*sin(C) if two sides and the included angle are known. All formulas give the same result.

Law of Sines: a/sin(A) = b/sin(B) = c/sin(C) — relates sides to opposite angles. Law of Cosines: c^2 = a^2 + b^2 - 2ab*cos(C) — a generalized Pythagorean theorem. The calculator automatically chooses the appropriate law based on your inputs and shows the formula used.

When given two sides and a non-included angle (SSA), there may be 0, 1, or 2 valid triangles. The calculator detects this ambiguous case and shows all valid solutions. It clearly labels each solution and explains why multiple triangles are possible.

Yes — the calculator works for all triangle types: right triangles (one 90-degree angle), isosceles (two equal sides), equilateral (all sides equal), scalene (all sides different), and obtuse (one angle > 90 degrees). It identifies the triangle type and uses optimized formulas when applicable.