⭕ Triangle Area from Inradius and Semiperimeter Calculator

Calculate triangle area from its inradius and semiperimeter using the standard area relationship A = r × s.

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Fill in the details and click Calculate to see your results.


Also available in our Android app, with charts and full breakdown tables.

📘 About the Inradius Area

The inradius is the radius of the circle tangent to all three sides of a triangle.

The semiperimeter is half the triangle perimeter.

This relationship is especially useful in advanced geometry and competitive mathematics.

🧮 Formula

Radius-based area formula
A = r × s
Semiperimeter definition
s = (a+b+c)/2

Where

  • r = inradius
  • s = semiperimeter
  • A = triangle area
Both inputs must use the same length unit.

✏️ Worked example

Inradius 4 cm and semiperimeter 15 cm

You enter
Inradius r4 cm
Semiperimeter s15 cm
You get
Triangle Area60
Valid Input1

The triangle area is 60 square centimetres.

Try this example →

🧭 How to use this calculator

What you enter

  • Inradius r (cm)
  • Semiperimeter s (cm)

What you get

  • Triangle Area
  • Valid Input

💡 Where this formula is useful

  • Advanced triangle geometry.
  • Problems involving an incircle and triangle perimeter.
  • Competitive examination questions where r and s are already known.

❓ Frequently asked questions

What is the formula for area using inradius?

Area equals the inradius multiplied by the semiperimeter.

What is the semiperimeter?

It is half the perimeter, or (a+b+c)/2.

What does the inradius represent?

It is the radius of the incircle, the circle tangent to all three sides.

Can I use different units for r and s?

No. Convert them to the same length unit before calculating.