Radius  (of a circle)
From Latin: radius "staff, spoke of a wheel"
1. A line from the center of a circle to a point on the circle.
2. The distance from the center of a circle to a point on the circle.
Try this Drag the orange dot. The blue line will always remain a radius of the circle.

The radius of a circle is the length of the line from the center to any point on its edge. The plural form is radii (pronounced "ray-dee-eye"). In the figure above, drag the orange dot around and see that the radius is always constant at any point on the circle.

Sometimes the word 'radius' is used to refer to the line itself. In that sense you may see "draw a radius of the circle". In the more recent sense, it is the length of the line, and so is referred to as "the radius of the circle is 1.7 centimeters"

If you know the diameter

Given the diameter of a circle, the radius is simply half the diameter:
where:
D  is the diameter of the circle
 

If you know the circumference

If you know the circumference of a circle, the radius can be found using the formula
where:
C  is the circumference of the circle
π  is Pi, approximately 3.142
 


If you know the area

If you know the area of a circle, the radius can be found using the formula
where:
A  is the area of the circle
π  is Pi, approximately 3.142
 

Calculator

ENTER ANY ONE VALUE
Radius clear
Diameter clear
Area clear
Circumference clear
   
 

Use the calculator on the right to calculate the properties of a circle.

Enter any single value and the other three will be calculated. For example: enter the radius and press 'Calculate'. The area, diameter and circumference will be calculated.

Similarly, if you enter the area, the radius needed to get that area will be calculated, along with the diameter and circumference.

Related items

Diameter Which is the circle's 'width'. The diameter is two times the radius. See diameter of a circle

Circumference The circumference is the distance around the edge of the circle. See Circumference of a Circle for more.

Things to try

  1. In the figure above, click 'reset' and drag the orange dot. Notice that the radius is the same length at any point around the circle.
  2. Click on "show diameter". Drag either orange dot at the ends of the diameter line. Note how the radius is always half the diameter.
  3. Uncheck the "fixed size" box. Repeat the above and note how the radius is always half the diameter no matter what the size of the circle.

Other circle topics

General

Equations of a circle

Angles in a circle

Arcs

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