Heron's Formula Calculator

How to calculate Heron's Formula Area Calculator?

Compute a triangle's area using the lengths of its three sides by first finding the semiperimeter and then applying Heron's formula.

Key formula: Area = sqrt(s(s - a)(s - b)(s - c)), where s = (a + b + c) / 2

Using the Heron's Formula Area Calculator calculator: an example

Example with side lengths a = 7, b = 8, and c = 5.

Step-by-step calculation:

1. Compute the semiperimeter: s = (7 + 8 + 5) / 2 = 10.
2. Find the differences: s - a = 3, s - b = 2, s - c = 5.
3. Multiply the factors: 10 × 3 × 2 × 5 = 300.
4. Take the square root: Area = sqrt(300) ≈ 17.32 (square units).

Frequently Asked Questions

What if the three sides cannot form a triangle?

If the side lengths violate the triangle inequality, the expression under the square root becomes non-positive and the triangle is invalid; the calculator should indicate an error.

Which units does the area use?

The area is reported in square units corresponding to the side length units you enter (for example, meters → m², centimeters → cm²).

Can I use decimal side lengths?

Yes. Enter positive decimal values directly; the calculator accepts real numbers for side lengths.

Is Heron's formula accurate for very large or very small values?

For extreme magnitudes, floating-point rounding can affect precision. If needed, rescale units or use higher-precision arithmetic to improve accuracy.