Heron’s Formula Calculator

Heron’s formula gives a triangle’s area from its three sides alone, with no height or angle needed. It is part of the Class 9 syllabus.

Results update as you type.

Area

84

Semi-perimeter (s)
21
Perimeter
42
Type
scalene, acute

About this calculator

The calculator first checks the sides can form a triangle.

How to use it

  1. Enter the three sides.
  2. Read the area and type.

The formula

Area = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2
s
semi-perimeter

Worked example

Sides 13, 14 and 15

  1. s = 21.
  2. Area = √(21 × 8 × 7 × 6) = 84.

What the result means

Each side must be shorter than the other two added together.

Assumptions

  • All lengths in the same unit.

Limitations

  • Results are rounded to 10 significant figures.

Frequently asked questions

What is Heron’s formula?

Area = √(s(s − a)(s − b)(s − c)) with s the semi-perimeter.

Why does it fail for some sides?

They cannot form a triangle.

Does it work for right triangles?

Yes, for any triangle.

Last reviewed on 3 October 2026. Found a mistake? Tell us.