Find the area from 3 sides instantly
This calculator uses Heron's formula to find the area of a triangle when all three side lengths are known. You don't need a height value and you don't need any angles. Just enter side a, side b, and side c, then click calculate.
It is useful for homework, construction estimates, surveying checks, CAD work, and quick geometry validation.
Formula used (Heron's Formula)
Given three sides:
- a = first side
- b = second side
- c = third side
First compute the semi-perimeter:
s = (a + b + c) / 2
Then area:
Area = √(s(s − a)(s − b)(s − c))
Example calculation
Suppose the three sides are 3, 4, and 5.
- s = (3 + 4 + 5) / 2 = 6
- Area = √(6 × (6−3) × (6−4) × (6−5))
- Area = √(6 × 3 × 2 × 1) = √36 = 6
So the area is 6 square units.
Triangle validity check
Not every set of 3 numbers can form a triangle. The sides must satisfy the triangle inequality:
- a + b > c
- a + c > b
- b + c > a
If these conditions fail, the calculator will show an error message instead of returning an area.
Common mistakes to avoid
1) Mixing units
If one side is in centimeters and another is in inches, your result will be wrong. Convert everything first.
2) Using zero or negative values
Side lengths must be positive numbers.
3) Assuming every 3 values make a triangle
Always check triangle inequality. This calculator does it for you automatically.
Where this calculator helps
- Geometry classes and exam prep
- Roofing, carpentry, and land layout
- Civil and mechanical drafting checks
- Quick sanity checks in spreadsheets and reports
Quick FAQ
Can I calculate area without height?
Yes. If you know all three sides, Heron's formula gives area directly.
What unit is the output in?
The output is in square units of your input. Example: if sides are in meters, area is in m².
Does this work for equilateral and isosceles triangles?
Yes. It works for any valid triangle.