Triangle Inradius
The incircle touches all three sides. Its radius is the area divided by half the perimeter, and since Heron’s formula gives the area from the sides alone, three sides are all you need.
Your numbers
Inradius
2cm
Area
24cm²
Perimeter
24cm
Formula
Inradius = Area ÷ (Perimeter ÷ 2)
If the sides cannot form a triangle — one longer than the other two combined — the area comes out as zero.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Side a (cm)The length of the first side. | 6 | 0 and up |
| Side b (cm)The length of the second side. | 8 | 0 and up |
| Side c (cm)The third side; it must be shorter than the other two combined. | 10 | 0 and up |
Step by step
Quick reference table
Results when only Side a (cm) changes and everything else stays put.
| Side a (cm) | Inradius (cm) | Area (cm²) | Perimeter (cm) |
|---|---|---|---|
| 3 | 0.945 | 9.922 | 21 |
| 4.5 | 1.561 | 17.564 | 22.5 |
| 6 | 2 | 24 | 24 |
| 9 | 2.533 | 34.197 | 27 |
| 12 | 2.646 | 39.686 | 30 |
What each result means
| Result | At default values |
|---|---|
| Inradius (cm)Radius of the circle touching all sides, sitting inside the shape. | 2 |
| Area (cm²)The space a shape covers — length squared. | 24 |
| Perimeter (cm)The total length around the outside of a shape. | 24 |
Common mistakes
If the sides cannot form a triangle — one longer than the other two combined — the area comes out as 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.
- Inradius
- Radius of the circle touching all sides, sitting inside the shape.
- Area
- The space a shape covers — length squared.
- Perimeter
- The total length around the outside of a shape.
Frequently asked questions
Q. How is Triangle Inradius calculated?
Inradius = Area ÷ (Perimeter ÷ 2) — The incircle touches all three sides. Its radius is the area divided by half the perimeter, and since Heron’s formula gives the area from the sides alone, three sides are all you need.
Q. Can you walk through an example?
With Side a 6cm, Side b 8cm, Side c 10cm, the answer is Inradius 2cm.
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) 3 → Inradius (cm) 0.945 and Side a (cm) 12 → Inradius (cm) 2.646. 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?
If the sides cannot form a triangle — one longer than the other two combined — the area comes out as zero.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.