Triangle Calculator
Calculate a triangle's area, perimeter and angles from its three sides.
Assumptions used in this calculation
- Valid triangle: Assumes the three side lengths satisfy the triangle inequality; inputs that can't form a triangle are rejected.
About this calculator
When you only know a triangle's three side lengths, not its height or any angle, finding its area or angles by hand requires two separate, less-common formulas (Heron's formula and the law of cosines) rather than the basic ½ × base × height most people default to. This calculator takes three side lengths and computes the area using Heron's formula (Area = √(s(s−a)(s−b)(s−c)), where s is the semi-perimeter (a+b+c)/2), the perimeter, all three interior angles using the law of cosines, and classifies the triangle by both side type (equilateral, isosceles, scalene) and angle type (acute, right, obtuse). Before computing anything, it checks the triangle inequality, that the sum of any two sides must exceed the third, since three lengths that fail this test can't form a real triangle at all. That covers what would otherwise require looking up and applying two separate formulas plus a validity check by hand.
Worked example
3-4-5 triangle
Result: Area = 6, right triangle
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