Triangle Area Heron
Calculator
Results
- Area
- 26.832815
- Perimeter
- 24
- Semi-perimeter
- 12
Results
| Area | 26.832815 |
| Perimeter | 24 |
| Semi-perimeter | 12 |
formula-map diagram
- Area
- 26.832815
- Perimeter
- 24
- Semi-perimeter
- 12
Formula map
Formula
A = √(s × (s − a) × (s − b) × (s − c)), s = (a + b + c) ÷ 2= 26.832815729997
Note
Simplified model: these are exact results of the stated idealised formulas, assuming perfect shapes and exact inputs. Real measurements carry error, and the ellipse perimeter is a Ramanujan approximation. Verify independently before relying on these figures.
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See all →Frequently asked questions
What do I need to know about the triangle to use this?+
Just the three side lengths (a, b, c). No angles or height are needed — that is the whole point of Heron's formula.
How does Heron's formula work?+
First compute the semi-perimeter s = (a+b+c)/2, then the area is the square root of s(s-a)(s-b)(s-c). It lets you find area from sides alone, without knowing any angle.
Why did I get an error or an undefined result?+
The three lengths you entered do not form a valid triangle — one side is longer than or equal to the sum of the other two, violating the triangle inequality. Check your measurements.
Does it matter which side I call a, b, or c?+
No, Heron's formula is symmetric in the three sides, so you can enter them in any order and get the same area.
Is this more accurate than using base times height divided by two?+
Both are exact when you have the right inputs; Heron's formula is simply more convenient when you know all three sides but not the height, which is common when working from field or survey measurements.