This triangle calculator solves any triangle from three sides (SSS) or from two sides and the angle between them (SAS). It returns every side and angle, the area, perimeter, height and the type of triangle.
Formulas used
Law of cosines: c² = a² + b² − 2ab cos C, used to find a missing side and every angle.
Heron’s formula: area = √(s(s − a)(s − b)(s − c)), where s = (a + b + c) ÷ 2.
The three sides must satisfy the triangle inequality: each side has to be shorter than the other two added together.
Worked example
A triangle with sides 5, 6 and 7 has s = 9 and an area of √(9 × 4 × 3 × 2) = √216 ≈ 14.6969. Its angles are about 44.42°, 57.12° and 78.46°, so it is a scalene, acute triangle.
Frequently asked questions
Can I use this for a right triangle?
Yes, but the Pythagorean theorem calculator is quicker when you know two sides of a right triangle.
Why can’t I solve from three angles?
Three angles fix the shape but not the size; infinitely many similar triangles share the same angles. You need at least one side.