Hero or Heron's formula Calculator area of a triangle | Calculator camp


Heron's formula

A=\sqrt{  s(s - a) (s- b) (s - c) },
where s is the semi-perimeter:
s = \frac{a+b+c}{2}
The formula is named after Hero of Alexandria or Heron of Alexandria, who was a Greek mathematician and engineer and lived in the ancient city of Alexandria, in Roman Egypt, around 10AD - 70AD. He proved his formula in his book Metrica, written around 60AD.

Heron's formula usage example

Problem: Given the sides of a triangle, a = 4, b = 13, c = 15 find the area of a triangle.

  1. Find the semi-perimeter: s = (a+b+c)/2 = (4+13+15)/2=16
  2. Find the area as square root of 16*(16-4)*(16-13)*(16-15) = 16*12*3*1 = 576. The square root of 576 is 24.

Here is how you should enter the example into the calculator above: Area of a triangle using Heron's formula