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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 = d2

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:
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Geometry Lessons
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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 r2 for 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