Triangle Calculator
Solve any triangle from any three pieces of information — using the Law of Sines, Law of Cosines or basic trigonometric identities.
Enter all three side lengths (SSS)
How to use the Triangle Calculator
- Enter your inputs into the Triangle Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
The triangle solver formulas
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C) · · · Law of Cosines: c² = a² + b² − 2ab·cos(C)
Given any 3 of the 6 elements (3 sides + 3 angles), at least one of these laws plus the angle sum (A + B + C = 180°) determines the rest. Special cases: SSS, SAS, ASA, AAS, SSA (ambiguous).
Worked example
Sides a = 5, b = 7, included angle C = 60°. By Law of Cosines: c² = 5² + 7² − 2·5·7·cos(60°) = 25 + 49 − 35 = 39, so c ≈ 6.24. Then by Law of Sines: A ≈ 43.9°, B ≈ 76.1°.
Frequently asked questions
What is the SSA ambiguous case?
Given two sides and an angle opposite one (not the included angle), there can be 0, 1 or 2 valid triangles. The calculator detects this and lists both solutions when applicable.
How do I find a triangle's area?
Area = ½·a·b·sin(C) using two sides and the included angle. Or Heron's formula: Area = √(s(s−a)(s−b)(s−c)) where s is the semi-perimeter.
Do the angles sum to 180°?
In Euclidean (flat) geometry, always. The angle-sum constraint plus any other 2 pieces uniquely determines the triangle.