How to Calculate Triangle Area from Three Sides (Heron's Formula): A Step-by-Step Guide
Calculates the triangle area from three sides (heron's formula) from the measurements you enter. Use any unit, as long as all inputs use the same one.
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.
What you need
- Side a
- Side b
- Side c
Step by step
- Enter the side a.
- Enter the side b.
- Enter the side c.
- The results update as you type, or press Calculate.
- Read the area first, then the supporting figures below it.
The formula
√(s(s−a)(s−b)(s−c)), s = (a+b+c)/2
Worked example
For example, with these inputs:
- Side a: 5
- Side b: 6
- Side c: 7
the calculator returns:
- Area: 14.6969
A second example
Now change the inputs to:
- Side a: 6.25
- Side b: 6
- Side c: 7
the calculator returns:
- Area: 17.5815
Practical tips
- Estimate the answer roughly first so you can spot a result that is clearly wrong.
- For exam work, show your method; marks are often given for working, not just the answer.
- Write down the formula before plugging numbers in; it prevents mixing up variables.
- Round only at the final step to avoid accumulated rounding errors.
Background
In everyday life the same maths shows up in discounts, recipe scaling, renovation measurements and comparing prices per unit. Being comfortable with it saves money and avoids costly measuring mistakes.
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.
A quick mental estimate before calculating is a powerful check. If a room's floor area comes out at 4,000 square metres or a percentage comes out above 100% when it should not, you know to look again.
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.
Want to skip the arithmetic? The free Triangle Area from Three Sides (Heron's Formula) does all of this instantly and updates as you type.
Run your own numbers: Triangle Area from Three Sides (Heron's Formula)