# 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.

We can find the radius of a circle when the diameter, area, or circumference is known.

## Radius Formulas

**Radius Formula 1: **The radius is half the length of the diameter. If the diameter of a circle is known then the radius formula is expressed as:

Radius Formula = Diameter/2 or D/2 units

**Radius Formula 2: **The radius is the ratio of circumference to 2π. If the circumference of a circle is known then the radius formula is expressed as:

Radius Formula = Circumference/2π or C/2π units

**Radius Formula 3: **We can derive the radius formula using the area of circle formula which is Area = π(Radius)^{2}. If the area of a circle is known then the radius formula is expressed as:

Radius Formula = √(Area/π) units

Let us learn the radius formula with a few solved examples.

## Examples on Radius Formula

**Example 1: **Find the radius of a circle whose diameter is 24 inches long. (Hint: use radius formula when the diameter is known)

**Solution:** We will use the radius formula when the diameter of a circle is given. Which is expressed as.

Radius = Diameter/2

D = 24 inches

R = 24/2 = 12 inches

**Answer:** Radius of the given circle is 12 inches.

**Example2:** Find the radius of a circle whose circumference is 4π units. (Hint: use radius formula when the circumference of a circle is known)

**Solution:**

We will use the following radius formula to find the radius of the circle.

Radius = Circumference/2π

C = 4πunits

Radius = 4π/2π = 2 units

**Answer: **Radius of the given circle is 2 units.

**Example3:** Find the radius of a circle whose area is 4π units^{2}. (Hint: use radius formula when the area of a circle is known)

**Solution:**

We will use the following radius formula to find the radius of the circle.

Radius Formula = √(Area/π)

Area = 4π units^{2}

R = √(4π/π)

Radius = 2 units

**Answer: **Radius of the given circle is 2 units.

## FAQ's on Radius Formula

### What Is the Radius Formula When Area of a Circle Is Known?

If the area of a circle is given in square units then it is easy to derive the radius formula as given below:

Area = π(Radius)^{2}

The formula for Radius = √(Area/π) units

### What Is the Radius Formula When Diameter of a Circle Is Known?

If the diameter of a circle is given in 'x' units then it is easy to derive the radius formula as given below:

Diameter = 2r.

Radius Formula = Diameter/2 units

### What Is the Radius Formula When Circumference of a Circle Is Known?

If the circumference of a circle is given in 'x' units then it is easy to derive the radius formula as given below:

Circumference = 2πr.

The formula for radius = Circumference/2π units

### How To Find Circumference With Radius Formula?

If a radius of a circle is given then by substituting the given values in the following radius formula we can easily find the circumference of a circle.

The formula for radius = Circumference/2π.

C = 2πr units.

visual curriculum