Heron's Formula Calculator
Compute triangle area from three sides using Heron's formula with triangle inequality validation.
About Heron's Formula Calculator
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
Worked example
With the default values below, Heron's Formula Calculator returns Area of 14.6969. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Side aminimum 0 units
- 5 units
- Side bminimum 0 units
- 6 units
- Side cminimum 0 units
- 7 units
Results
- Area
- 14.6969 sq units
- Semi-perimeter (s)
- 9.0000 units
Step by step
- 1Semi-perimeter= 9
- 2Apply Heron's formula= 14.696938456699069
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.