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# 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 line segment 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 (plural form of radius). All the points on the circumference of the circle are equidistant from the center of the circle and hence all the radii have the same length.

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.

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