3 Sides Triangle Area Calculator

Enter the three side lengths of a triangle to find its area using Heron's formula, plus perimeter, semi-perimeter, and triangle classification.

Quick Facts

Heron's formula
Area = √(s(s−a)(s−b)(s−c))
s is the semi-perimeter, (a + b + c) / 2 — no height or angle needed.
Triangle inequality
Any two sides must outweigh the third
If a + b ≤ c (or any such pairing), the three lengths cannot form a triangle.

Your Results

Calculated
Area
-
Via Heron's formula, in square units
Perimeter
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a + b + c
Semi-perimeter (s)
-
Half the perimeter
Triangle type
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By side lengths and angles

Ready

Enter three side lengths and press Calculate.

Formula and method: triangle area from 3 sides

Heron's Formula:

s = (a + b + c) / 2

A = √(s(s−a)(s−b)(s−c))

s is the semi-perimeter (half the perimeter); a, b, c are the three side lengths.

Heron's formula computes a triangle's area directly from its three side lengths, without needing to know the height or any angle. It works by first finding the semi-perimeter s — half the sum of all three sides — and then taking the square root of s multiplied by the difference between s and each side in turn.

How the calculation works

Given sides a, b, and c, the calculator first checks the triangle inequality: the sum of any two sides must be strictly greater than the third, or no triangle can exist with those lengths. If the sides are valid, it computes the semi-perimeter s = (a + b + c) / 2, then the area A = √(s(s−a)(s−b)(s−c)). Perimeter is simply a + b + c. The triangle is also classified by its sides (equilateral, isosceles, or scalene) and, using the converse of the Pythagorean theorem, by its largest angle (right, acute, or obtuse).

Common mistakes

  • Ignoring the triangle inequality: lengths like 2, 3, and 10 cannot form a triangle because 2 + 3 is less than 10 — the calculator will flag this as invalid rather than return a number.
  • Units: area comes out in square units — if the sides are in feet, the area is in square feet (ft²), not feet. A degenerate or near-degenerate triangle (where a + b is only slightly more than c) has an area close to zero even though the sides themselves are sizable.
  • Mixing unit systems: enter all three sides in the same unit (all inches, all meters, etc.); mixing feet and centimeters in the same calculation produces a meaningless result.

Real-world applications

  • Land surveying and lot measurement, when boundary lengths are known but angles or a baseline height are not
  • Construction and carpentry, for triangular braces, roof sections, and gussets measured by their edges
  • Sailmaking, tarp, and fabric cutting, where panel area is estimated from edge lengths
  • Geometry and trigonometry coursework, as the standard method for area when only side lengths are given (SSS triangles)

Frequently Asked Questions

What is Heron's formula?
Heron's formula finds a triangle's area from its three side lengths alone, with no need for height or angles. First compute the semi-perimeter s = (a+b+c)/2, then the area is the square root of s(s-a)(s-b)(s-c). It works for any valid triangle, right or oblique.
Why does the calculator say the sides can't form a triangle?
Three lengths only form a triangle if the sum of any two sides is greater than the third side (the triangle inequality). If, for example, a + b is less than or equal to c, the sides are too short to meet and no triangle exists — check your measurements and try again.
What unit should I use for the sides?
Any consistent unit works — inches, feet, centimeters, meters — as long as all three sides use the same one. The area result will be in that unit squared (for example, entering feet gives an area in square feet).
How does the calculator classify the triangle?
By side lengths: equilateral if all three sides are equal, isosceles if exactly two are equal, and scalene if all three differ. By angles, it compares the square of the longest side to the sum of squares of the other two to report right, acute, or obtuse.

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