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Triangle Area from Three Sides Calculator.

Calculate a triangle's area from its three side lengths with Heron's formula.

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Results update as you type.

Result: Area 6.000000 square units · Perimeter 12.000000 units

Result

Area 6.000000 square units · Perimeter 12.000000 units

Use Cases

Geometry homework and exams

Quickly verify your manual calculations for triangle area when only side lengths are known, saving time and reducing errors.

Example: Check the area of a triangle with sides 5, 6, 7.

Construction and land measurement

Determine the area of a triangular plot or section when you can measure the three sides directly, without needing height.

Example: Find the area of a triangular garden with sides 30 ft, 40 ft, and 50 ft.

Frequently Asked Questions

How does the Triangle Area from Three Sides Calculator work?
It uses Heron's formula: first compute the semiperimeter s = (a+b+c)/2, then area = sqrt(s(s-a)(s-b)(s-c)). Enter the lengths of sides a, b, and c, and the calculator computes the area for you.
What if the side lengths do not form a valid triangle?
The calculator will not provide a valid area because Heron's formula requires that the sum of any two sides be greater than the third. If the input violates the triangle inequality, the result is undefined or imaginary.
Can I use this calculator for any triangle?
Yes, as long as you know all three side lengths. It works for scalene, isosceles, and equilateral triangles. The formula is universal for any triangle with given side lengths.

Tips & Common Mistakes

Tips

  • Ensure all side lengths are in the same unit (e.g., all in meters or all in feet) before entering them.
  • Double-check that the side lengths satisfy the triangle inequality: a+b > c, a+c > b, and b+c > a.
  • For an equilateral triangle, you can also use the formula (√3/4) * side², but Heron's formula works as well.
  • If you need the height, you can derive it from the area: height = (2 * area) / base.

Common Mistakes to Avoid

  • Entering side lengths in different units (e.g., one in meters and another in centimeters) without converting, leading to incorrect area.
  • Using side lengths that do not form a valid triangle, such as 1, 2, 3, which violates the triangle inequality.
  • Forgetting to take the square root in Heron's formula, resulting in the square of the area instead of the area.

Last updated: August 13, 2026