Enter the three side lengths of a triangle to calculate all angles, area, perimeter, and classify the triangle type.
This tool calculates missing sides, angles, area, and perimeter of a triangle based on the values you already know, using trigonometric rules and geometric formulas. It's useful for geometry homework, construction layout, and any calculation involving triangular shapes.
Depending on the known values, the calculator applies the Law of Sines (a/sin A = b/sin B = c/sin C), the Law of Cosines (c² = a² + b² − 2ab·cos C), or basic angle sum rules (angles in a triangle always total 180°). Area is commonly calculated as ½ × base × height, or using Heron's formula when all three sides are known.
Enter the known sides and/or angles of your triangle (at least three values, including at least one side), and the calculator solves for the remaining sides, angles, area, and perimeter.
Example: A triangle with sides 5, 6, and 7 (all sides known) has an area of approximately 14.7 square units, calculated using Heron's formula.
Why do triangle angles always add up to 180 degrees? This is a fundamental property of Euclidean geometry — for any triangle on a flat plane, the sum of its three interior angles is always exactly 180 degrees.
What is the Law of Sines used for? It relates the sides and angles of any triangle (not just right triangles), useful when you know two angles and one side, or two sides and a non-included angle.
What is the Law of Cosines used for? It's used to find a missing side or angle when you know either all three sides, or two sides and the included angle between them — it generalizes the Pythagorean theorem to non-right triangles.
What is Heron's formula? It calculates a triangle's area directly from its three side lengths, without needing to know any angle, using the formula Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter.
Can any three values determine a unique triangle? Not always — knowing three angles only determines the triangle's shape, not its size, since infinitely many similar triangles share the same angles; at least one side length is needed to fully define a specific triangle.