# Radius of a circle

## Radius of a circle

The **radius of a circle** is a line segment with one end at the center of the circle, and the other end on the circle itself. The radius is identified with a lower-case, italic **r.**

## Radius of a circle formula

The formula you use depends on what is known about the circle. Below are three different formulas you can use to find the radius, *r*, of a circle.

If given circumference (

**C**), then the formula is: $r=\frac{C}{2\pi }$If given area (

**A**), then the formula is: $r=\sqrt{\frac{A}{\pi }}$If given diameter (

**d**), then the formula is: $r=\frac{d}{2}$

The relationship between radius and diameter is an important one to know when learning to how to calculate the radius.

Since the radius is a line segment from the center to the circle, and the diameter, **d**, is a line segment from on side of a circle through the center of a circle and out to the other side of the circle, it follows that a radius is $\frac{1}{2}$ a diameter.

## How to find the radius of a circle

To find the radius of a circle, plug the given information into the correct formula. You can find the radius of any circle if you are given the circumference, area, or diameter.

### How to find radius from circumference

No matter the size of the circle, the relationship of the radius to the circumference, **C**, is a constant, giving us the formula to find radius from circumference:

You can also calculate the circumference of a circle with a given radius by using algebra to isolate the **C** in our formula.

The radius to circumference formula is: $C=2\pi r$

### Radius of circle from area

You can use the area to find the radius and the radius to find the area of a circle. The **area **of a circle is the space it occupies, measured in square units.

Given the area, **A**, of a circle, its radius is the square root of the area divided by pi:

The formula for radius to area is: $A=\pi {r}^{2}$

### How to find radius from diameter

If you know the diameter of a circle, you can find its radius by dividing the diameter by **2**:

This is the simplest formula you can use to get the radius.

If you need to go from radius to diameter, multiply radius times** 2**: **d = 2r**

## Radius of a circle examples

A circle has a diameter of

**6 inches**. What is its radius?A circle has a radius of

**98 feet**. What is its diameter?A circle with a circumference of

**365 meters**will have a radius of how many meters?A circle with a radius of

**11 inches**will have a circumference of how many inches?With a radius of

**41 mm**, a circle will have an area equal to, what?

We don't like to talk in circles, but make sure you work these out before checking the answers below!

The radius of a 6 inch circle is

**3 inches**.A circle has a radius of 98 feet, so its diameter must be

**196 feet**.A circle with a circumference of 365 meters will have a radius of

**58.4 meters**.A circle with a radius of 11 inches will have a circumference of

**69.12 inches.**With a radius of 41 mm, a circle will have an area of roughly

**5,281 square millimeters**.