Heron’s Formula Calculator

Enter the three sides of a triangle to calculate the area using Heron’s formula.

Solution:

Area T =  


How to use Heron’s Formula

Diagram showing how to use Heron's formula to solve the area of a triangle

Using Heron’s formula is an easy way to calculate the area of a triangle given the length of the sides. The interior angles of the triangle are not needed to find area using the formula.

For a triangle with three sides a, b, and c, Heron’s formula can be used to find the area.

T = s(s – a)(s – b)(s – c)

Thus, the area T of a triangle is equal to the square root of the semiperimeter s times s minus side a times s minus side b times s minus side c .

The semiperimeter s in Heron’s formula is half the perimeter, so the equation to find s is:

s = a + b + c2

After solving the semiperimeter, substitute s in Heron’s formula above.

Alternate Heron’s Formula Equations

Heron’s formula can be simplified or rewritten in a few different ways to solve for area. The following formulas are all derived from Heron’s formula using sides a, b, and c.

T = 14(a + b + c)(-a + b + c)(a – b + c)(a + b – c)
T = 142(a²b² + a²c² + b²c²) – (a⁴ + b⁴ + c⁴)
T = 14(a² + b² + c²)² – 2(a⁴ + b⁴ + c⁴)
T = 144(a²b² + a²c² + b²c²) – (a² + b² + c²)²
T = 144a²b² – (a² + b² – c²)²

Our triangle area calculator can also be used to solve for area.