Triangle Calculator
Enter three sides of a triangle to find the area, perimeter, angles and type (equilateral, isosceles, scalene).
Written by Rahman · Last reviewed
Quick answer
Three side lengths determine a triangle completely. Heron's formula gives the area as √(s(s−a)(s−b)(s−c)), where s is half the perimeter, and the law of cosines gives each angle. The sides must satisfy the triangle inequality (any two added together must exceed the third), or no such triangle exists.
Enter the three side lengths of a triangle.
Results are estimates for general guidance only. Double-check any figure you rely on for an important decision.
About the Triangle Calculator
Knowing the three sides of a triangle is enough to determine everything else about it: its perimeter, area, angles and shape category. This calculator uses Heron's formula for the area and the Law of Cosines for the angles.
The triangle inequality must hold for the inputs to form a valid triangle: each side must be less than the sum of the other two. If your inputs violate it, the calculator says so.
Heron's: Area = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2 Law of cosines: cos A = (b² + c² − a²) / (2bc)
Angles are in degrees. Triangle type is classified two ways: by sides (equilateral / isosceles / scalene) and by angles (acute / right / obtuse).
Frequently Asked Questions
What is the triangle inequality?
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A rule that says any side of a triangle must be shorter than the sum of the other two. If a + b ≤ c, the "triangle" cannot exist as a flat shape.
How do you know if a triangle is a right triangle?
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When one of the three angles is exactly 90°. Equivalently, when the three sides satisfy a² + b² = c² (Pythagoras' theorem) for some labelling of the sides.
What is Heron's formula?
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A way to find the area of a triangle from just the three side lengths, without needing to know any angles. It uses the semi-perimeter s = (a + b + c) / 2.
Can I use other inputs like two sides and an angle?
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This version supports three sides only (SSS). For other combinations you would use the Law of Sines or Cosines manually.