3 Sides Triangle Area Calculator
This calculator finds the area of a triangle from the lengths of its three sides using Heron's formula. Enter sides a, b, and c, and it computes the semi-perimeter s = (a + b + c) / 2 and then the area A = √[s(s − a)(s − b)(s − c)]. It is the go-to method when you know all three sides but have no height or angle to work with.
Formula
Heron's Formula: Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2
- Heron's formula finds the area from the three side lengths alone, with no height or angle required.
- Step 1: compute the semi-perimeter s = (a + b + c) / 2.
- Step 2: the area is A = √[s(s − a)(s − b)(s − c)].
- The three sides must obey the triangle inequality (any two sides add up to more than the third); otherwise no triangle exists.
- Use a single length unit for all three sides; the area is reported in that unit squared.
Example Calculation
Inputs
- Side A: 3
- Side B: 4
- Side C: 5
For a 3-4-5 triangle, s = (3 + 4 + 5) / 2 = 6, so the area is √[6(6−3)(6−4)(6−5)] = √36 = 6 square units.
Frequently asked questions
What is Heron's formula?
It is a formula for the area of a triangle based only on its side lengths: A = √[s(s − a)(s − b)(s − c)], where s = (a + b + c) / 2 is the semi-perimeter.
When is this calculator useful?
Whenever you know the three sides of a triangle but not its height or angles - for example in surveying, construction, or geometry homework.
What if I get a 'NaN' or no result?
That usually means the sides cannot form a triangle. Make sure each side is shorter than the sum of the other two.
What unit is the area in?
The same length unit you enter, squared. Metres in give square metres out; feet in give square feet out.
Does it only work for right triangles?
No. Heron's formula works for any triangle, whether acute, right, or obtuse.