Instant area, perimeter, and angles for any triangle
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Formulas Used
Area = ½ × base × height
The perpendicular height from the base to the opposite vertex.
Use this free triangle calculator to find the area and perimeter of any triangle instantly. Enter a base and height for the classic formula, or input all three side lengths to apply Heron's formula — which also reveals every interior angle and classifies the triangle by side type (equilateral, isosceles, scalene) and angle type (acute, right, obtuse). No sign-up needed.
Heron's formula calculates a triangle's area from its three side lengths alone. First compute the semi-perimeter s = (a + b + c) / 2, then Area = √(s · (s−a) · (s−b) · (s−c)). It works for any triangle without needing a height measurement.
The formula is Area = ½ × base × height, where height is the perpendicular distance from the base to the opposite vertex. This is the most direct method when the base and corresponding height are known.
The triangle inequality requires that the sum of any two sides must be greater than the third side. For example, sides 1, 2, and 10 fail because 1 + 2 = 3, which is not greater than 10. The calculator will warn you if your inputs violate this rule.
The calculator uses the Law of Cosines: cos(A) = (b² + c² − a²) / (2bc), solving for the angle opposite each side. All three angles are then computed, and they should always sum to exactly 180°.