Triangle Calculator
Solve a triangle's remaining sides, angles, and area from three known values.
Try an example
36.9°
53.1°
90°
6
12
About this calculator
How This Triangle Calculator Works
Enter the lengths of all three sides, and the calculator returns each angle and the triangle's area — solving what's known as the SSS (side-side-side) case.
Worked Example
For a 3-4-5 triangle: the angles are 36.87°, 53.13°, and 90° (a right triangle), and the area is 6 square units.
The Formulas
Each angle is found with the Law of Cosines, rearranged to solve for angle: cos(C) = (a² + b² − c²) ÷ (2ab), applied once per angle using the side opposite it. Area uses Heron's formula: Area = √[s(s−a)(s−b)(s−c)], where s is the semi-perimeter, (a + b + c) ÷ 2.
The Triangle Inequality
Not every three lengths can form a triangle — each side must be shorter than the sum of the other two (a + b > c, and so on for every pairing). If this fails, the "triangle" would require one side to fold flat past the other two, which is why the calculator rejects such inputs rather than returning a nonsensical result.
Worked example
A 3-4-5 triangle (a classic right triangle) has angles of 90°, 53.13°, and 36.87°, an area of 6, and a perimeter of 12.
Frequently asked questions
What if the three lengths I enter can't form a triangle?
The calculator checks the triangle inequality — each side must be shorter than the sum of the other two. If it fails, no valid triangle exists with those lengths, and no result is shown.
Can this solve a triangle from angles instead of sides?
Not currently — this calculator specifically solves for angles and area given three side lengths (the SSS case).
What's Heron's formula?
A way to find a triangle's area purely from its three side lengths, without needing to know any angle or height directly: Area = √(s(s−a)(s−b)(s−c)), where s is half the perimeter.