Last updated October 10, 2026 · Report an error
Given the three side lengths of a triangle, Heron's formula finds its area without needing to know any angles or the height — a useful shortcut whenever only the sides are known.
This calculator also checks the triangle inequality, classifies the triangle by its sides, and detects right triangles.
How it works
Enter the three side lengths. The calculator first checks that a valid triangle can be formed, then finds the semi-perimeter and applies Heron's formula to compute the area.
- Enter side a.
- Enter side b.
- Enter side c.
- Click Calculate to see your results.
Examples
The classic 3-4-5 right triangle
Sides of 3, 4, and 5 give a perimeter of 12 and an area of 6 — and since 3² + 4² = 5², it's also a right triangle.
Who should use it
- Finding the area of a triangular plot of land or surface when only the side lengths are measured.
- Checking geometry homework involving Heron's formula.
Industry applications
- Geometry and mathematics education
- Surveying and construction
Advantages
- Works from side lengths alone — no angles or height needed.
- Classifies the triangle type and flags right triangles automatically.
Limitations
- Only supports the side-side-side (SSS) case — for angle-based inputs, a different method is needed.
Common mistakes to avoid
- Entering side lengths that don't satisfy the triangle inequality and expecting a valid result.
- Confusing the semi-perimeter (half the perimeter) with the full perimeter when applying Heron's formula by hand.
Best practices
- Double-check your three side lengths satisfy the triangle inequality before relying on the result — the calculator will flag it, but it's a good sanity check.
Tips
- If all three sides are equal, the triangle is equilateral and every angle is exactly 60°.
Frequently asked questions
Yes, with no signup and no limit on how many calculations you run.
For three lengths to form a valid triangle, the sum of any two sides must be greater than the third side. If this fails, the "triangle" would be degenerate (a flat line) or impossible.
Heron's formula calculates a triangle's area purely from its three side lengths, without needing an angle or height: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter.
It checks whether the Pythagorean theorem holds for the three sides (the square of the longest side equals the sum of the squares of the other two), allowing for tiny rounding differences.