Heron's Formula Calculator
Compute triangle area from three sides using Heron's formula with triangle inequality validation.
Inputs
Area
14.6969sq units
Semi-perimeter (s)
9.0000units
Step by step
Semi-perimeter
s = (5 + 6 + 7) / 2
= 9
Apply Heron's formula
A = √(9 × 4.0000 × 3.0000 × 2.0000)
= 14.696938456699069
How it works
Heron's formula computes the area of a triangle when you know all three sides. It first calculates the semi-perimeter, then uses it in a square root expression. The sides must satisfy the triangle inequality.
Formulas
Semi-perimeter
s = (a + b + c) / 2
- a
- Side a
- b
- Side b
- c
- Side c
Heron's Formula
A = √(s(s−a)(s−b)(s−c))
- s
- Semi-perimeter
- a
- Side a
- b
- Side b
- c
- Side c
Frequently Asked Questions
What happens if the sides don't form a valid triangle?
The calculator rejects the input with a clear error explaining the triangle inequality violation.
Is Heron's formula exact?
Yes — it gives the exact area for any valid triangle. Floating-point precision may introduce tiny rounding in extreme cases.