Heron's Formula Calculator

Enter three side lengths to calculate a triangle's area using Heron's formula.

How to Use the Heron's Formula Calculator

Enter the three side lengths a, b, and c. The calculator shows the semi-perimeter first, then the three bracketed terms that feed into the final area — not just the answer on its own.

Heron's formula finds a triangle's area from its three sides alone, with no angle or height needed anywhere:

s = (a + b + c) ÷ 2
area = √(s × (s − a) × (s − b) × (s − c))

s is the semi-perimeter — half the total perimeter — and it's worth watching on its own, since each of the three bracketed terms (s − a, s − b, s − c) has to come out positive for a real triangle to exist. If any side is too long relative to the other two, one of those terms goes negative, the product under the square root turns negative, and there's no triangle left to measure — the same triangle-inequality check this calculator runs before it will show a result.

The formula is named for Heron of Alexandria, a Greek mathematician and engineer working around the 1st century AD, though some historians trace the idea back to Archimedes a few centuries earlier. Either way, it's the only common area formula that never needs an angle or an altitude — useful whenever three tape-measure readings are all there is to work with.