About the triangle calculator
A triangle has six parts: three sides (a, b, c) and three angles (A, B, C), where each angle is opposite the side with the same letter. Knowing three of them, including at least one side, fixes the rest. Pick the tab that matches what you know.
SSS gives three sides, SAS gives two sides and the angle between them, ASA gives two angles and the side between them, AAS gives two angles and a side that is not between them, and SSA gives two sides and an angle that is not between them.
The SSA case can be ambiguous. Depending on the numbers there may be no triangle, exactly one, or two different triangles. When two exist, the calculator shows both solutions and draws both.
Along with sides and angles you get the area, perimeter, inradius, circumradius, medians and altitudes, and a labelled drawing. Impossible inputs, such as sides that break the triangle inequality or angles that add up to 180° or more, are rejected with an explanation.
Formula
- Law of cosines: c² = a² + b² − 2ab·cos C
- Law of sines: a ÷ sin A = b ÷ sin B = c ÷ sin C
- Angles: A + B + C = 180°
- Heron's formula: area = √(s(s−a)(s−b)(s−c)), s = (a + b + c) ÷ 2
- Inradius = area ÷ s; circumradius = abc ÷ (4 × area)
Example
With sides 3, 4 and 5 (SSS) the angles are 36.87°, 53.13° and 90°, the perimeter is 12 and the area is 6. It is a right triangle.