Heron's Formula Calculator
Halve the perimeter to get s, multiply s by (s − each side), and take the square root. Surveyors use exactly this to measure plots of land.
Your numbers
Area
14.697cm²
Perimeter
18cm
Formula
Area = √(s(s−a)(s−b)(s−c)), s = (Side a+Side b+Side c) ÷ 2
Any two sides must sum to more than the third, otherwise no triangle exists and the area comes out zero.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Side a (cm)The length of the first side. | 5 | 0 and up |
| Side b (cm)The length of the second side. | 6 | 0 and up |
| Side c (cm)The third side; it must be shorter than the other two combined. | 7 | 0 and up |
Step by step
Quick reference table
Results when only Side a (cm) changes and everything else stays put.
| Side a (cm) | Area (cm²) | Perimeter (cm) |
|---|---|---|
| 2.5 | 7.308 | 15.5 |
| 3.75 | 11.247 | 16.75 |
| 5 | 14.697 | 18 |
| 7.5 | 19.732 | 20.5 |
| 10 | 20.662 | 23 |
What each result means
| Result | At default values |
|---|---|
| Area (cm²)The space a shape covers — length squared. | 14.697 |
| Perimeter (cm)The total length around the outside of a shape. | 18 |
Common mistakes
Any two sides must sum to more than the third, otherwise no triangle exists and the area comes out zero.
Glossary
- Side a
- The length of the first side.
- Side b
- The length of the second side.
- Side c
- The third side; it must be shorter than the other two combined.
- Area
- The space a shape covers — length squared.
- Perimeter
- The total length around the outside of a shape.
Frequently asked questions
Q. How is Heron's Formula Calculator calculated?
Area = √(s(s−a)(s−b)(s−c)), s = (Side a+Side b+Side c) ÷ 2 — Halve the perimeter to get s, multiply s by (s − each side), and take the square root. Surveyors use exactly this to measure plots of land.
Q. Can you walk through an example?
With Side a 5cm, Side b 6cm, Side c 7cm, the answer is Area 14.697cm².
Q. What do I need to enter?
Enter Side a, Side b, Side c. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Side a (cm) moves the answer to Side a (cm) 2.5 → Area (cm²) 7.308 and Side a (cm) 10 → Area (cm²) 20.662. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
Any two sides must sum to more than the third, otherwise no triangle exists and the area comes out zero.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.