Heron's Formula Calculator
Find the area of any triangle when you know all three sides. Heron's formula uses the semi-perimeter s = (a + b + c) / 2, then area = sqrt(s(s - a)(s - b)(s - c)). Defaults show the classic 3-4-5 right triangle.
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How to find area with Heron's formula
- Enter the three side lengths a, b, and c in the same length unit.
- Confirm the sides can form a triangle: each pair sum must exceed the third side.
- Read area, semi-perimeter s, and perimeter in the result rows.
- Keep units consistent. Area comes back in that unit squared.
- Use the default 3, 4, 5 to verify you get area 6 before changing inputs.
Heron's formula
Triangle area from three sides
| Side a | First edge length |
|---|---|
| Side b | Second edge length |
| Side c | Third edge length |
| Semi-perimeter s | s = (a + b + c) / 2 |
| Area | sqrt(s(s - a)(s - b)(s - c)) |
| Triangle inequality | a + b > c, a + c > b, and b + c > a |
What Heron's formula computes
Heron's formula returns triangle area from SSS data alone. You do not need a height or an included angle. For sides 3, 4, and 5, s = 6 and the area is exactly 6.
Sides, semi-perimeter, and area
Sides are positive lengths. Semi-perimeter is half the perimeter. Area is the non-negative square root of the Heron product. Degenerate inputs that only touch equality fail the inequality check.
How this page applies Heron
The engine requires positive a, b, and c, rejects sides that break the triangle inequality, forms s, then evaluates sqrt(s(s - a)(s - b)(s - c)). Floating point rounding follows ordinary IEEE math in the browser.
When SSS area is the right tool
Survey sketches, plot plans, and homework problems often give three measured edges and ask for area. Heron avoids constructing an altitude first.
Limits
Sides must be positive and satisfy the triangle inequality. The page does not convert units for you. It is arithmetic only, not a CAD area takeoff. See the disclaimer.