Triangle Calculator
Enter the three side lengths of a triangle to calculate its perimeter, area, and interior angles.
Side lengths
How these triangle formulas work
Given three side lengths (a, b, c), this calculator uses Heron's formula to find the area: first compute the semi-perimeter s = (a + b + c) / 2, then area = √(s(s−a)(s−b)(s−c)).
The three interior angles are found with the law of cosines, which relates each angle to the lengths of the sides opposite and adjacent to it. The angles always add up to 180°.
Not every combination of three lengths forms a valid triangle — the triangle inequality requires that the sum of any two sides be greater than the third side.
Frequently asked questions
What is Heron's formula?
Heron's formula calculates a triangle's area directly from its three side lengths, without needing to know any angles: area = √(s(s−a)(s−b)(s−c)), where s is the semi-perimeter.
Why does my triangle show an error?
The three lengths you entered violate the triangle inequality — the sum of the two shorter sides must be greater than the longest side, or no triangle can be formed.
Do the three angles always add up to 180°?
Yes, for any triangle on a flat (Euclidean) plane, the interior angles always sum to exactly 180 degrees.