How to use this calculator
Choose three sides (SSS), two sides with their included angle (SAS), or two angles with the side between them (ASA). Enter all lengths in one consistent unit. Angles are in degrees; side a is opposite angle A, and similarly for b and c.
The math behind it
A + B + C = 180° c² = a² + b² − 2ab cos(C) a / sin(A) = b / sin(B) = c / sin(C) s = (a + b + c) / 2 Area = √[s(s − a)(s − b)(s − c)] Height to c = 2 × area / c
A worked example
Sides 3, 4 and 5 give area 6 square units, perimeter 12 units and angles approximately 36.870°, 53.130° and 90°. The height to side c is 2.4 units.
Assumptions & precision
Flat Euclidean triangles only. This tool supports SSS, SAS and ASA; an SSA input can have two solutions and is not included. The two shorter sides must sum to more than the longest. Near-degenerate triangles are rejected to avoid unreliable floating-point results. Area uses a numerically stable rearrangement of Heron’s formula. Results show up to six decimals; intermediate values are not rounded.
A common question
Why is my triangle impossible?
A side cannot equal or exceed the sum of the other two. Two known angles must total less than 180°. Check that an SAS angle is actually between the two known sides.