Calculating your triangle area is straightforward once you know the Heron's Formula formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Heron's Formula Calculator.
What is Heron's Formula?
The Heron's Formula calculation tells you your triangle area from a few simple inputs. The figure you are solving for here is the triangle area.
The Heron's Formula formula
The core formula is:
Triangle area = √((Side a + Side b + Side c) ÷ 2 × ((Side a + Side b + Side c) ÷ 2 - Side a) × ((Side a + Side b + Side c) ÷ 2 - Side b) × ((Side a + Side b + Side c) ÷ 2 - Side c))Here is what each input means:
- Side a — a number. Example: 3.
- Side b — a number. Example: 4.
- Side c — a number. Example: 5.
How to calculate it step by step
- Write down the side a (for example, 3).
- Write down the side b (for example, 4).
- Write down the side c (for example, 5).
- Apply the formula above to get your triangle area.
- Double-check the result with the Heron's Formula Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Side a | 3 |
| Side b | 4 |
| Side c | 5 |
| Triangle area | 6.0000 |
| Perimeter | 12.00 |
With side a of 3, side b of 4 and side c of 5, the triangle area works out to 6.0000.
Example 2
With side a of 6, side b of 4 and side c of 5, the triangle area works out to 9.9216.
| Result | Value |
|---|---|
| Triangle area | 9.9216 |
| Perimeter | 15.00 |
Example 3
With side a of 1.5, side b of 4 and side c of 5, the triangle area works out to 2.4804.
| Result | Value |
|---|---|
| Triangle area | 2.4804 |
| Perimeter | 10.50 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Heron's Formula Calculator does it instantly, for free, with the formula and a worked example built in.
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