Radius Formula
Before we begin with the radius formula, let us recall what is a radius. Radius is one of the important parts of a circle. Radius is the distance from the center of the circle to any point on its circumference, which means the straight line that connects the center of a circle to any point on its circumference is called the radius. Since there are infinite points on its circumference, this means that a circle has an infinite number of radii and each radius of the circle is equidistant from the center of the circle.
Let us learn the radius formula with a few solved examples.
Formula to Find Radius
We can find the radius of a circle when the diameter, area, or circumference is known.
Formula 1: The radius is half the length of the diameter.
\[\text{Radius} = \frac{\text{Diameter}}{2}\]
Formula 2: The radius is the ratio of circumference to \(2\pi\).
\[\text{Radius} = \frac{\text{Circumference}}{2\pi}\]
Formula 3: We can derive the radius formuls using the area formula which is \(\text{Area} = \pi (\text{Radius})^2\).
\[\text{Radius} = \sqrt{\frac{\text{Area}}{\pi}}\]
Solved Examples on Radius Formula

Example 1:
Find the radius of a circle whose diameter is 24 inches long.
Solution:
We will use the first formula to find the radius of the circle.
\(\begin{align}\text{Radius} &= \frac{\text{Diameter}}{2}\\&=\frac{24 \text{ inches}}{2}\\&=12 \text{ inches}\end{align}\)Answer: Radius of the given circle = 12 inches.

Example 2:
Find the radius of a circle whose circumference is \(4\pi\) units.
Solution:
We will use the second formula to find the radius of the circle.
\(\begin{align}\text{Radius} &= \frac{\text{Circumference}}{2\pi}\\&=\frac{4\pi \text{ units}}{2 \pi}\\&=2 \text{ units}\end{align}\)Answer: Radius of the given circle = 2 units.