What is Heron's formula?

It calculates a triangle's area purely from its three side lengths (a, b, c): first find the semi-perimeter s = (a+b+c)/2, then area = √(s(s−a)(s−b)(s−c)).

Why does it say my sides can't form a triangle?

Any two sides of a triangle must add up to more than the third side (the triangle inequality) — if that's not true for your three numbers, no actual triangle can be formed.

Does this work for right triangles too?

Yes — Heron's formula works for any triangle type, including right triangles, though for a right triangle you could also just use half the product of the two legs if you already know which sides are the legs.

What units does the result use?

The area is given in whatever squared unit matches your side-length input — for example, entering side lengths in meters gives an area in square meters.

Can I use this for a triangle drawn on a map or blueprint?

Yes, as long as you can measure or determine the three side lengths at the same scale, the formula applies the same way regardless of the triangle's real-world size.

Math & Statistics Cluster

Triangle Area Calculator

Calculate triangle area from 3 sides using Heron's formula.

TL;DR: Triangle Area Calculator is a free, browser-based tool that lets you calculate triangle area from 3 sides using Heron's formula.

Side a

Side b

Side c

Understanding the Triangle Area Calculator

The Triangle Area Calculator solves mathematical equations, statistical distributions, and numerical relationships with step-by-step arithmetic breakdowns and high-precision calculations.

How It Works

Enter your known values, dataset numbers, or mathematical coefficients.
Select your preferred precision decimal places or calculation mode.
Click to compute and review the step-by-step derivation steps.
Copy the solved numerical answer or explore related mathematical proofs.

Mathematical Formula & Methodology

Here is the standard mathematical equation used to calculate this result accurately:

A = \frac{1}{2} b h = \sqrt{s(s-a)(s-b)(s-c)} \quad (\text{Heron's Formula})

Formula Variables Explained:
Calculates triangular area using base/height or side lengths $a, b, c$ where semi-perimeter $s = (a+b+c)/2$ .

Step-by-Step Worked Example

For a triangle with sides $a = 6, b = 8, c = 10$ ( $s = 12$ ): $A = \sqrt{12(12-6)(12-8)(12-10)} = \sqrt{12 \times 6 \times 4 \times 2} = \sqrt{576} = 24$

How to Get the Best Results

Sample vs Population Data: In statistical variance and standard deviation, use sample formulas (Bessel's correction $n-1$) when analyzing subset samples.
Order of Operations: Computations strictly adhere to standard mathematical PEMDAS / BODMAS operational precedence.
High Precision Arithmetic: Internal calculations use 64-bit IEEE floating-point arithmetic for extreme numerical accuracy.

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Frequently Asked Questions

: It calculates a triangle's area purely from its three side lengths (a, b, c): first find the semi-perimeter s = (a+b+c)/2, then area = √(s(s−a)(s−b)(s−c)).
: Any two sides of a triangle must add up to more than the third side (the triangle inequality) — if that's not true for your three numbers, no actual triangle can be formed.
: Yes — Heron's formula works for any triangle type, including right triangles, though for a right triangle you could also just use half the product of the two legs if you already know which sides are the legs.
: The area is given in whatever squared unit matches your side-length input — for example, entering side lengths in meters gives an area in square meters.
: Yes, as long as you can measure or determine the three side lengths at the same scale, the formula applies the same way regardless of the triangle's real-world size.

Cite This Tool

Referencing this tool in a paper, article, or bibliography? Copy a ready-made citation below.

NexLove.org. (2026). Triangle Area Calculator [Software]. https://nexlove.org/tools/triangle-area-calculator.html

“Triangle Area Calculator.” NexLove.org, 2026, nexlove.org/tools/triangle-area-calculator.html.

NexLove.org (2026) Triangle Area Calculator. Available at: https://nexlove.org/tools/triangle-area-calculator.html (Accessed: 2026).

@misc{nexlove_triangle_area_calculator,
  title = {Triangle Area Calculator},
  author = {{NexLove.org}},
  year = {2026},
  url = {https://nexlove.org/tools/triangle-area-calculator.html}
}

Embed This Tool

Add the live Triangle Area Calculator tool to your own website with this snippet — it loads the real, working tool in an iframe, not a static screenshot.

<iframe src="https://nexlove.org/embed/triangle-area-calculator.html" width="100%" height="600" style="border:1px solid #e2e8f0;border-radius:12px" title="Triangle Area Calculator — NexLove.org" loading="lazy"></iframe>

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