Heron’s formula finds a triangle’s area using only its three side lengths — no angle or height measurement needed.
How it works
Half the perimeter (the “semi-perimeter”) is combined with each side length in a square root expression that yields the exact area.
What this does not include
This does not include the base-and-height method — for that simpler approach when a perpendicular height is already known, use this site’s triangle area calculator instead.
How to use this calculator
- Enter the three side lengths of the triangle.
A worked example
A triangle with sides 3, 4, 5 (a right triangle): using Heron’s formula, area = 6.
Sides 7, 8, 9: area = 26.8328.
What the variables mean
| Variable | Meaning |
|---|---|
| a, b, c | The triangle’s three side lengths |
Edge cases worth knowing
Not every set of three lengths forms a real triangle. Sides 1, 1, and 5 fail the triangle inequality (the two shorter sides can’t reach each other across the longest side), so the calculator correctly declines to show an area.
This works without knowing any angles — Heron’s formula finds area from side lengths alone, unlike the more familiar ½ × base × height approach.
Frequently asked questions
Why doesn’t this need a height measurement?
Heron’s formula derives the area purely from the geometry of the three sides, without needing to identify or measure a perpendicular height separately.
What if the three lengths can’t form a triangle?
If one side is longer than or equal to the sum of the other two, no triangle can close, and the calculator declines to return a result.
Does this work for any type of triangle?
Yes — Heron’s formula works for any valid triangle, whether it’s right, acute, obtuse, or scalene.
