About the triangle calculator
Enter any three values (sides, angles, the area, a height, a median, the inradius or the circumradius) and the triangle is solved completely. Classic cases (SSS, SAS, ASA, AAS) use the laws of sines and cosines directly. The ambiguous SSA case, where two different triangles fit the same data, is detected automatically and both solutions are offered.
Side a is opposite angle A, b is opposite B and c is opposite C. Hover or focus a field to highlight it on the diagram, heights, medians and the in- and circumcircle appear when you do.
Unusual combinations (say, perimeter plus two heights) have no neat closed-form answer, so the calculator solves them numerically and reports every triangle it finds.
Formulas
| Law of cosines | c² = a² + b² − 2ab·cos C |
| Law of sines | a/sin A = b/sin B = c/sin C = 2R |
| Angle sum | A + B + C = 180° |
| Area (SAS) | K = ½ab·sin C |
| Heron’s formula | K = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2 |
| Height | hₐ = 2K/a |
| Median | mₐ = ½√(2b² + 2c² − a²) |
| Inradius / circumradius | r = K/s, R = abc/(4K) |
Frequently asked questions
What is the ambiguous case (SSA)?
When you know two sides and an angle that is not between them, the law of sines can give two valid angles (θ and 180° − θ). Both can produce real triangles, so the calculator shows Solution 1 and Solution 2.
How do I find the area of a triangle with three sides?
Use Heron’s formula: with s = (a+b+c)/2, the area is √(s(s−a)(s−b)(s−c)).
Why does it say the sides can’t form a triangle?
The triangle inequality: each side must be shorter than the sum of the other two. Sides 2, 3 and 6 fail because 2 + 3 < 6.