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

Side a(cm)Side b(cm)Side c(cm)

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

FormulaInradius = Area ÷ (Perimeter ÷ 2)

With the default numbersInradius = Area ÷ (Perimeter ÷ 2)

AnswerInradius = 2 cm

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

QHow 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.

QCan you walk through an example?

With Side a 6cm, Side b 8cm, Side c 10cm, the answer is Inradius 2cm.

QWhat 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.

QHow 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.

QHow 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.

QAnything 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

Circle Area CalculatorGet the area and circumference of a circle from its radius.Radius from CircumferenceMeasure around an object and work back to radius and area.Triangle Area CalculatorFind a triangle’s area from its base and height.Heron's Formula CalculatorFind a triangle’s area from three side lengths, without knowing the height.

Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.