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Triangle Area (Heron) Calculator

How do I find the area of a triangle?

How it is calculated

Enter the three side lengths a, b and c in the same unit. The tool uses Heron's formula:

s = (a + b + c) / 2 and area = √(s(s − a)(s − b)(s − c))

The perimeter is a + b + c. Both results are rounded to two decimals; the area is in the square of your unit (cm² for cm) and the perimeter in the unit itself. All sides must be above zero. Before calculating, the tool checks the triangle inequality: each side must be strictly shorter than the sum of the other two. If not, it reports that these sides cannot form a triangle, which includes the flat case such as 1, 2, 3.

Worked example

Sides 7, 8 and 9. Half the perimeter is s = (7 + 8 + 9) / 2 = 12. Then s − a = 5, s − b = 4 and s − c = 3, so the product is 12 × 5 × 4 × 3 = 720. The square root of 720 is 26.83. The perimeter is 7 + 8 + 9 = 24.00. If the sides were in centimetres, the area is 26.83 cm².

Try this example →

Common mistakes

  • Mixing units, such as one side in metres and another in centimetres; convert all three first.
  • Entering a base and a height instead of three sides. This tool needs all three side lengths, not the height.
  • Reading the area as a length: it is in square units, while the perimeter is in plain units.
  • Entering sides that cannot close, such as 2, 3 and 10, then taking the message as a bug; the longest side must be shorter than the sum of the other two.
  • Rounding the sides heavily before entering them; for thin triangles the area is very sensitive to small changes in length.

About this calculator

This calculator finds a triangle's area using only its three side lengths, via Heron's formula, which avoids needing to know an angle or drop a height — useful because a triangle's area is normally taught as half of base times height, information that is not always available from a real-world measurement. It also returns the perimeter as a simple side-length sum.

It is used by students verifying geometry homework, by surveyors, carpenters and DIYers who measured three edges of a triangular plot, panel or piece of land and need the area without a protractor, and by anyone who just knows three side lengths and needs the enclosed area quickly.

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Comments (1)

  • Editorial team

    Heron's formula gives you a way to measure an odd four-sided plot with only a tape. Measure the four sides plus one diagonal, which splits the plot into two triangles, run each triangle here and add the areas. The result is only as good as the tape work, so measure the diagonal twice and keep the tape level over uneven ground. What shape of plot or panel are you measuring?

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