Triangle calculator
Enter the three sides to solve the area, angles, and more.
Triangle
How the triangle is solved
Enter the three side lengths and the calculator finds the area, perimeter, all three interior angles, and the triangle type. It uses Heron's formula for the area and the law of cosines for the angles, then classifies the triangle by its sides and its largest angle.
The formulas
area = √(s(s−a)(s−b)(s−c))
cos A = (b² + c² − a²) / (2bc)
Worked example
A 3, 4, 5 triangle has a perimeter of 12 and an area of 6. Its angles are about 36.87°, 53.13°, and 90°, so it is a right scalene triangle, the classic Pythagorean triple.
Frequently asked questions
How do I find the area of a triangle from its three sides?
Use Heron's formula. Compute the semi-perimeter (half the perimeter), then take the square root of s times (s minus each side). The calculator does this automatically.
How are the angles calculated?
With the law of cosines, which relates each angle to the three side lengths. The three angles always add up to 180 degrees.
What makes three lengths a valid triangle?
The triangle inequality: each side must be shorter than the sum of the other two. If not, the sides cannot close into a triangle, and the calculator will say so.
What is the difference between acute, right, and obtuse triangles?
A right triangle has one 90-degree angle, an obtuse triangle has one angle over 90 degrees, and an acute triangle has all three angles under 90 degrees.
What are scalene, isosceles, and equilateral triangles?
Scalene has three different side lengths, isosceles has two equal sides, and equilateral has all three sides equal.