Free triangle calculator: enter three sides to instantly find the area, perimeter and all angles, and classify right, isosceles or equilateral shapes.
A triangle is fully determined by its three side lengths: once you know them, the area, perimeter and every angle follow. This calculator does all of it instantly — no trigonometry table needed.
Students use it to check geometry homework, builders and DIYers measure rafters and braces, and anyone working from three measurements can skip the long hand calculations.
Enter the three side lengths and the calculator validates the triangle first (the longest side must be shorter than the sum of the other two), then returns the area, perimeter, all three angles and the triangle type.
Start with the classic 3-4-5 right triangle to see how it works — area 6, angles 36.9°, 53.1° and 90°.
Use Heron's formula: s = (a+b+c)/2, then A = √(s(s−a)(s−b)(s−c)). For 3, 4, 5: s = 6, A = √(6×3×2×1) = 6.
Use the law of cosines: cos A = (b²+c²−a²)/(2bc), and repeat for B; the third angle is C = 180° − A − B.
The triangle inequality: the longest side must be shorter than the sum of the other two. Sides 1, 2, 10 cannot form a triangle.
Check the Pythagorean theorem: a² + b² = c² for the longest side c. 3-4-5 is the classic example and the calculator flags it automatically.