OmniCalcsTriangle Area Calculator
Find the area of any triangle from three sides with Heron's formula.
How to Use This Triangle Area Calculator
Enter the three side lengths in any unit. The calculator checks that they form a triangle, then reports the area, perimeter and semi-perimeter.
- Triangle inequality — each side must be shorter than the sum of the other two.
- Any triangle — right, acute or obtuse; Heron's formula does not need an angle.
- Units — keep all sides in the same unit; area comes back in that unit squared.
Practical Example
The 3-4-5 right triangle:
- s = (3 + 4 + 5) / 2 = 6
- Area = √[6(6−3)(6−4)(6−5)] = √(6×3×2×1) = √36 = 6
- Perimeter = 3 + 4 + 5 = 12
That matches the right-triangle shortcut ½ × 3 × 4 = 6.
What Your Results Mean
- Area — the space inside the triangle, from Heron's formula.
- Perimeter — the sum of the three sides.
- Semi-perimeter — half the perimeter, the s in Heron's formula.
Frequently Asked Questions
What is Heron's formula?
A formula for the area of a triangle from its three sides alone: Area = √[s(s−a)(s−b)(s−c)], where s is the semi-perimeter.
When do three lengths not make a triangle?
When one side is longer than or equal to the sum of the other two. Those lengths cannot close into a triangle.
Does this work for a right triangle?
Yes. For a right triangle you can also use ½ab, but Heron's formula gives the same area without identifying the legs.
Do I need an angle?
Not for this tool. If you know two sides and the included angle, the SAS formula ½ab sin(C) is an alternative.
Can sides be decimals?
Yes. Enter any positive lengths; the formula does not require whole numbers.