Triangle Area from Three Sides (Heron's Formula) Formula Explained, With Examples
Every triangle area from three sides (heron's formula) result comes from one formula. Once you understand what goes into it, you can sanity-check any figure you are given, whether by an employer, a bank, a teacher or another website.
The formula
√(s(s−a)(s−b)(s−c)), s = (a+b+c)/2
What each input means
- Side a: the value you enter in the calculator.
- Side b: the value you enter in the calculator.
- Side c: the value you enter in the calculator.
Example
For example, with these inputs:
- Side a: 5
- Side b: 6
- Side c: 7
the calculator returns:
- Area: 14.6969
How the result changes
The table keeps the other inputs at their example values and changes side a.
| Side a | Area |
|---|---|
| 5 | 14.6969 |
| 2.5 | 7.3077 |
| 3.75 | 11.2469 |
| 6.25 | 17.5815 |
| 7.5 | 19.7317 |
Why it matters
These calculations come up in school, at work and in daily life, from PSLE and O-Level practice to measuring a room for new flooring. Doing them by hand builds understanding, and a calculator lets you check the answer instantly.
Each formula has assumptions built in. Area formulas assume flat shapes, volume formulas assume regular solids and statistical measures assume the data you enter is the data you want to describe. Knowing the assumptions helps you pick the right tool.
Rounding is a common source of small errors. Keep full precision during intermediate steps and round only the final answer to the number of decimal places or significant figures the question asks for.
These calculations appear throughout the Singapore syllabus, from primary school percentages and fractions to secondary school algebra and geometry. Understanding the formula makes problem sums easier because you can recognise which quantity is missing.
Related calculations
- Circumference of a Circle Calculator: Calculates the circumference of a circle from the measurements you enter.
- Perimeter of a Rectangle Calculator: Calculates the perimeter of a rectangle from the measurements you enter.
- Perimeter of a Square Calculator: Calculates the perimeter of a square from the measurements you enter.
- Perimeter of a Triangle Calculator: Calculates the perimeter of a triangle from the measurements you enter.
Use the Triangle Area from Three Sides (Heron's Formula) to plug in your own numbers.
Run your own numbers: Triangle Area from Three Sides (Heron's Formula)