Equilateral Triangle
Knowing one side fixes everything else. The height is √3÷2 of the side, the area is √3÷4 times the side squared, and the circumradius is exactly twice the inradius.
Your numbers
Area
43.301cm²
Height
8.66cm
Inradius
2.887cm
Circumradius
5.774cm
Formula
Area = √3 ÷ 4 × Side length ²
It is easy to assume the height is half the side. It is actually about 0.866 of it.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Side length (cm)One side of a regular polygon — they are all the same. | 10 | 0 and up |
Step by step
Quick reference table
Results when only Side length (cm) changes and everything else stays put.
| Side length (cm) | Area (cm²) | Height (cm) | Inradius (cm) |
|---|---|---|---|
| 5 | 10.825 | 4.33 | 1.443 |
| 7.5 | 24.357 | 6.495 | 2.165 |
| 10 | 43.301 | 8.66 | 2.887 |
| 15 | 97.428 | 12.99 | 4.33 |
| 20 | 173.205 | 17.321 | 5.774 |
What each result means
| Result | At default values |
|---|---|
| Area (cm²)The space a shape covers — length squared. | 43.301 |
| Height (cm)The perpendicular height from the base, not a slanted side. | 8.66 |
| Inradius (cm)Radius of the circle touching all sides, sitting inside the shape. | 2.887 |
| Circumradius (cm)Radius of the circle through every vertex, wrapping the shape. | 5.774 |
Common mistakes
It is easy to assume the height is half the side. It is actually about 0.866 of it.
Glossary
- Side length
- One side of a regular polygon — they are all the same.
- Area
- The space a shape covers — length squared.
- Height
- The perpendicular height from the base, not a slanted side.
- Inradius
- Radius of the circle touching all sides, sitting inside the shape.
- Circumradius
- Radius of the circle through every vertex, wrapping the shape.
Frequently asked questions
Q. How is Equilateral Triangle calculated?
Area = √3 ÷ 4 × Side length ² — Knowing one side fixes everything else. The height is √3÷2 of the side, the area is √3÷4 times the side squared, and the circumradius is exactly twice the inradius.
Q. Can you walk through an example?
With Side length 10cm, the answer is Area 43.301cm².
Q. What do I need to enter?
Enter Side length. 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 length (cm) moves the answer to Side length (cm) 5 → Area (cm²) 10.825 and Side length (cm) 20 → Area (cm²) 173.205. 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?
It is easy to assume the height is half the side. It is actually about 0.866 of it.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.