Triangle Area by Sides
Find a triangle's area from the lengths of its three sides, using Heron's formula.
Area from sides alone
Usually finding a triangle's area needs a base and a height, but Heron's formula finds it from just the three side lengths, with no height required. This calculates the area that way, useful when you know the sides but not the height.
Enter the three side lengths to find the area.
Why Heron's formula is so handy
Heron's formula is genuinely useful because in the real world you can often measure the sides of a triangular region but not its height — a triangular plot of land, a sail, a truss. The usual area formula needs the perpendicular height, which is awkward to find, while the three sides are straightforward to measure. Heron's formula bridges that gap: it computes the area from the sides via the semi-perimeter, half the sum of the sides, and an elegant expression under a square root. It is an ancient result, attributed to Heron of Alexandria, and its cleverness is precisely that it needs no angle and no height. Whenever you have a triangle's three sides and want its area without the fuss of finding a height, this is the tool.
Triangle Area by Sides FAQ
What does Heron's formula need?
Only the three side lengths — no height and no angle — which is what makes it useful when you can measure the sides but not the height.
When is it more practical than the usual area formula?
When you can measure a triangle's sides but not its perpendicular height, as with a plot of land, a sail, or a truss.
Is anything uploaded?
No. The calculation happens in your browser.