Triangle Solver Calculator
Enter 3 known values (sides or angles) to solve any triangle.
Solution Details
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Request a ToolHow to Use the Triangle Solver Calculator
This calculator solves any triangle when you provide at least 3 known values, with at least one side length included. Enter values for any combination of sides and angles, then leave the rest blank.
- Enter your known values. Fill in any 3 of the 6 fields: sides a, b, c and angles A, B, C. Angles are in degrees. Side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C.
- Read the results. The calculator instantly solves for all unknown sides and angles using the law of sines and law of cosines. It also shows the area and perimeter.
- Share or copy. Use the Share button to send a pre-filled link or Copy to grab the result.
The calculator handles SSS (three sides), SAS (two sides and included angle), ASA (two angles and included side), AAS (two angles and a non-included side), and SSA (two sides and non-included angle) configurations. All calculations run in your browser.
About Triangle Solving
Triangle solving uses two fundamental laws of trigonometry. The law of cosines generalizes the Pythagorean theorem to all triangles: c^2 = a^2 + b^2 - 2ab*cos(C). The law of sines relates sides to their opposite angles: a/sin(A) = b/sin(B) = c/sin(C). Together, these formulas can solve any triangle when enough information is given. The interior angles of every triangle always sum to exactly 180 degrees.
Frequently Asked Questions
What is the minimum information needed to solve a triangle?
You need at least 3 known values, and at least one must be a side length. Three angles alone cannot determine a unique triangle because infinitely many similar triangles share the same angles. Common combinations include SSS (three sides), SAS (two sides and the included angle), and AAS (two angles and one side).
What is the ambiguous case (SSA)?
When you know two sides and a non-included angle, there may be zero, one, or two valid triangles. This calculator finds one valid solution if it exists. If no valid triangle can be formed, you will see an error message explaining why.
How is the area calculated?
Once all three sides are known, the area is calculated using Heron's formula: Area = sqrt(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (a+b+c)/2. This formula works for any triangle and only requires the three side lengths.