# How to Find the Radius from the Diameter (Mathematics Lesson)

# What Is the Radius in Terms of the Diameter?

The radius of a circle is half of the diameter.# How to Find the Radius from the Diameter

**Question:**What is the radius of the circle, with diameter d, below?

**Step 1:**Divide the diameter, d, by 2.

d ÷ 2 =

^{d}⁄

_{2}

This is the radius, r, of the circle.

# A Real Example of How to Find the Radius from the Diameter

**Question:**What is the radius of the circle, with diameter 10cm, below?

**Step 1:**Divide the diameter, 10cm, by 2.

10 ÷ 2 = 5cm

The radius of the circle is 5cm.

# Another Real Example of How to Find the Radius from the Diameter

The slider below shows another real example of how to find the radius of a circle from the diameter:##### Curriculum

##### Interactive Test

**show**

##### Note

**WHAT IS A CIRCLE?**

A circle is a shape containing a set of points that are all the same distance from the center. This distance is the radius.

**WHY IS KNOWING THE RADIUS IN TERMS OF THE DIAMETER USEFUL?**

Most of the properties of a circle - such as its circumference and area - can be expressed in terms of the radius or diameter.

Most students remember the area of a circle with a radius

**r**as:

But what if you are told the diameter

**d**instead? Divide it by 2 to find the radius.

If you substitute

**for**

^{r}⁄_{2}**r**, a formula for the area of a circle in terms of the diameter can be found:

Read more about how to find the area of a circle using the diameter