➗
Triangle Area (Heron's Formula) Calculator
Find the area of a triangle from its three side lengths using Heron’s formula.
Side a
Side b
Side c
Loading calculator…
How it works
Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c) ÷ 2
Heron’s formula finds a triangle’s area from its three sides alone — no height needed. First compute the semi-perimeter s, then take the square root of the product shown.
Worked example
Sides 5, 6, 7 give s = 9 and area = √(9·4·3·2) = √216 ≈ 14.70.
Frequently asked questions
What if the sides can’t form a triangle?
If any side is longer than the sum of the other two, no triangle exists and the area is undefined.
Do I need an angle?
No — that is the point of Heron’s formula. Three side lengths are enough.
Related calculators
Triangle Area Calculator
Find a triangle’s area from its three side lengths with Heron’s formula — no height needed.
Pythagorean Theorem Calculator
Find the missing side of a right triangle — hypotenuse or either leg — using a² + b² = c².
Law of Cosines Calculator
Solve a triangle with the law of cosines: find the third side from two sides and the included angle (SAS), or all three angles from three sides (SSS), with area, perimeter, heights, medians, inradius, circumradius, triangle type and the worked steps.
This calculator is for educational purposes. Double-check important results before acting on them.