How to use the triangle calculator
Enter the lengths of all three sides. The calculator uses the Law of Cosines to find each angle (in degrees), Heron's formula for the area, and simple addition for the perimeter. The triangle inequality (a + b > c for all combinations) is checked first — if the sides don't form a valid triangle, an error is shown.
Triangle formulas reference
Law of Cosines: cos(A) = (b² + c² − a²) / (2bc). Heron's formula: s = (a+b+c)/2, area = √(s(s−a)(s−b)(s−c)). Perimeter = a + b + c. Sum of angles = 180°. For a right triangle (c is hypotenuse): c² = a² + b².
FAQ
What is the triangle inequality?
The triangle inequality states that the sum of any two sides must be greater than the third side. For sides a, b, c: a+b>c, b+c>a, and a+c>b must all be true. If any condition fails, the three lengths cannot form a triangle.
Can I calculate a triangle with angles instead of sides?
This calculator requires three side lengths (SSS). For other combinations (SAS, ASA, AAS), you would need a different input mode. However, given three sides, all angles are fully determined.