ABC Triangle Calculator
This ABC triangle calculator works out the perimeter and area of a triangle from its three side lengths a, b, and c. The perimeter is simply a + b + c, and the area comes from Heron's formula, A = √[s(s − a)(s − b)(s − c)], where s is the semi-perimeter (a + b + c) / 2. It is the quickest way to size up a triangle when you know its sides but not its height or angles.
Formula
Perimeter = a + b + c | Area = √[s(s-a)(s-b)(s-c)]
- The perimeter is the sum of the three sides: P = a + b + c.
- The area uses Heron's formula: first the semi-perimeter s = (a + b + c) / 2, then A = √[s(s − a)(s − b)(s − c)].
- Heron's formula needs only the side lengths - no height or angle is required.
- For a valid triangle the three sides must satisfy the triangle inequality: any two sides together must exceed the third.
- Enter all three sides in the same unit; the area is then in that unit squared.
Example Calculation
Inputs
- Side A: 3
- Side B: 4
- Side C: 5
For sides 3, 4, and 5 the perimeter is 3 + 4 + 5 = 12. The semi-perimeter is s = 6, so the area is √[6(6−3)(6−4)(6−5)] = √36 = 6 square units.
Frequently asked questions
How does this calculator find the area?
It uses Heron's formula, A = √[s(s − a)(s − b)(s − c)] with s = (a + b + c) / 2, which gives the area from the three side lengths alone.
When should I use it?
Use it when you know all three sides of a triangle and want its perimeter and area, but you do not know the height or any angle.
What if my sides do not form a triangle?
If any side is equal to or longer than the sum of the other two, the points are collinear and no triangle exists, so the area would be zero or undefined.
What unit is the area in?
The area is expressed in the square of the unit you use for the sides - for example, square metres if the sides are in metres.
Does Heron's formula work for any triangle?
Yes. It applies to acute, right, and obtuse triangles equally, as long as the three sides satisfy the triangle inequality.