Enter three sides, or two sides with an angle. Leave others blank.
Optional: Enter angles in degrees.
Uses the Law of Cosines to solve SSS and SAS cases, and Heron's formula for area: s = (a+b+c)/2, area = √(s(s−a)(s−b)(s−c)). Classifies the triangle as equilateral, isosceles, or scalene — and flags right triangles via the Pythagorean check. Related: Pythagorean theorem, area.
You enter at least three measurements — three sides, or two sides with the included angle. The tool applies the Law of Cosines to find unknown sides or angles, then uses Heron's formula for area. It validates the triangle inequality (any two sides must sum to more than the third) and checks for a right angle via the Pythagorean theorem.
The Law of Cosines generalizes the Pythagorean theorem to any triangle: c² = a² + b² − 2ab·cos(C). It lets you find an unknown side from two sides and the included angle, or find an angle from all three sides.
Heron's formula calculates a triangle's area from its three side lengths without needing a height measurement. First compute the semi-perimeter s = (a+b+c)/2, then area = √(s(s−a)(s−b)(s−c)).
No — angles alone define the shape but not the size of a triangle. You need at least one side length combined with angles to determine a unique triangle with computable area and perimeter.
A valid triangle requires that the sum of any two sides exceeds the third side. If your inputs violate this rule, no real triangle can be formed and the calculator displays an error.
Yes. The Law of Cosines works for all triangle types — acute, right, and obtuse. The calculator correctly identifies the type and returns accurate results regardless of angle size.
Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.