# Radius of Inscribed Circle Calculator

An online calculator to calculate the radius R of an inscribed circle of a triangle of sides a, b and c.

This calculator takes the three sides of the triangle as inputs, and uses the formula for the radius R of the inscribed circle given below.

\[ R = \sqrt{\dfrac{(s-a)(s-b)(s-c)}{s}} \]

where \( s = \dfrac{a+b+c}{2} \)

## Use of Radius of Inscribed Circle Calculator

Enter the side lengths a, b and c of the triangle as positive real numbers and press "Calculate". The output is the radius R of the inscribed circle. If one of the sides of the triangle is negative or the sum of any two positive sides is smaller that the third one (i.e the triangle does not exist), there will be no solution.
__Example__

Use the formula given above to find the radius of the inscribed circle of the triangle with sides 6, 7 and 10 cm.

__Solution__

\( s = 0.5(a + b + c) = 0.5(6 + 7 + 10) = 11.5 \)

\( R = \sqrt{\dfrac{(s-a)(s-b)(s-c)}{s}} = \sqrt{\dfrac{(11.5-6)(11.5-7)(11.5-10)}{11.5}} = 1.796\)

Use the calculator to check the result of the above example.

## More References and Links

Incircle and excircles of a triangle.

Radius of Circumcircle.

Online Geometry Calculators and Solvers.