Triangle Area by Heron's Method Calculator

Triangle area from three sides (Heron's formula)

How it is calculated

The tool applies Heron's formula to the three side lengths a, b and c, all in the same length unit. First the semi-perimeter s = (a + b + c) / 2, then Area = √( s(s − a)(s − b)(s − c) ). It also reports the perimeter a + b + c. Both values are rounded to two decimals.

Every side must be positive and the sides must form a real triangle: the sum of any two sides has to be strictly greater than the third. If not (for example 1, 2, 3, which collapses into a line), the tool returns no result. The area comes out in the square of the unit you typed, while the perimeter stays in the unit itself.

Worked example

Take a triangle with sides 13, 14 and 15. The perimeter is 13 + 14 + 15 = 42, so s = 21. Then s − a = 8, s − b = 7 and s − c = 6. The product is 21 × 8 × 7 × 6 = 7056, and its square root is 84. The area is 84.00 square units, with a perimeter of 42.00.

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Common mistakes

  • Entering sides that cannot close into a triangle, such as 2, 3, 10; the tool gives no result because the triangle inequality fails.
  • Using the full perimeter in place of the semi-perimeter when doing the check by hand; s is half of a + b + c.
  • Mixing units, such as one side in metres and another in centimetres, which gives a meaningless area.
  • Reading the area as a length: if the sides are in metres, the area is in square metres, not metres.
  • Rounding the sides heavily before entering them; for a very flat triangle a small measuring error changes the area a lot.

About this calculator

Heron's formula finds a triangle's area from its three side lengths alone, no angles or height needed: first the semi-perimeter s = (a + b + c) / 2, then Area = √(s(s−a)(s−b)(s−c)).

It's the go-to method whenever you can measure all three sides but can't easily drop a perpendicular height — surveyors computing irregular plots, carpenters checking a triangular panel, and students working land-survey or trigonometry problems all rely on it, and it works for any triangle shape, not just right triangles.

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