Triangle Calculator
Calculate triangle area, perimeter, and all three angles from the three side lengths using Heron's formula and the law of cosines.
Area
—
Perimeter —
Angle A (degrees) —
Angle B (degrees) —
Angle C (degrees) —
Triangle Type —
How to Use This Calculator
Enter all three side lengths (a, b, c). The calculator uses Heron's formula for area, the Law of Cosines for angles, and classifies the triangle type.
Formula
Area = √(s(s−a)(s−b)(s−c)), s=(a+b+c)/2 • cos A = (b²+c²−a²)/(2bc)
Example
a=3, b=4, c=5 → Area=6, Perimeter=12, Angles: 36.87°, 53.13°, 90° (Right Triangle)
Frequently Asked Questions
- Use Heron's formula: Area = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2.
- Use the Law of Cosines: cos A = (b²+c²−a²)/(2bc). Once you have two angles, the third is 180−A−B.
- For a valid triangle, the sum of any two sides must be greater than the third side. If not, the calculator will report an invalid triangle.
- All triangle types: equilateral (all sides equal), isosceles (two equal sides), scalene (all different), right, acute, and obtuse.
- A triangle with one 90-degree angle. It satisfies a²+b²=c² (Pythagorean theorem).