Radius-Circumference-Diameter

Circumference

  • The circumference of a circle is the distance around the circle.
  • It is calculated using the formula:

C = 2πr

  • where C is the circumference, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

Diameter

  • The diameter of a circle is the distance across the circle through its center.
  • It is calculated using the formula:

d = 2r

  • where d is the diameter and r is the radius of the circle.

Radius

  • The radius of a circle is the distance from the center of the circle to any point on the circle.
  • It is calculated using the formula:

r = C / (2π)

  • where r is the radius and C is the circumference of the circle.



The term radius is used often to describe spheres or circles. The radius is the distance from the center of the circle to any point on the surface.
 
The radius is half the length of the diameter.
Radius = Diameter/2
 
Circumference equals two times the radius times pi
C= 2r * π
radius
 
 
radius

7 Circumference Facts

  • The circumference, diameter, and radius can all be used to calculate one another.
  • The distance around a circle is the circumference. 
  • If you measure the distance around a square, or rectangle it is called perimeter, but with a circle it is labeled as its circumference. 
  • Is circumference squared? No, it is a one dimensional measurement, and therefore is not squared. 
  • In order to help understand radius, let’s review several properties of a circle. A circle can be named by its center point because all points of a circle are an equal distance from this center point. 
  • What is the circumference in terms of pi? Pi is calculated by dividing the circumference of a circle by the diameter of the same circle. It is approximately 3.14. 
  • The distance from the center of the circle to the edge of the circle is called radius. 
Circumference equals the distance around a circle.
circumference
Diameter is the distance across a circle passing through the center of the circle.
diameter
Radius equals the distance from the center of the circle to an edge of the circle.
radius
Radius equals 1/2 the diameter

 

The Geometry ratio of pi ( written using the Greek letter π)  is calculated when you take the circumference of a circle and divide by the diameter of the same circle. 

pi

π= Circumference /Diameter 

Calculate the Circumference of a Circle

Circumference = d ● π 
 
Circumference = 2 ● r ● π
 
d= Diameter of the Circle

r = radius 
 
π=pi which is 3.14159… but this is an approximation
 
Calculate the circumference of a circle with a diameter of 8 units and a radius of 4 units.
 
 
Method 1.  Circumference = pi * diameter
3.14*8=25.12 units  
 
 
Method 2. Circumference of circle = 2 * radius * p  
 2 * 4 * 3.14 = 25.12 units

Circumference to Diameter

If you know the circumference of a circle you can work backwards and find the diameter.
Circumference = π *diameter
 
Find the diameter of a circle with a circumference of 20 feet.
Let’s use 3.14 for pi
20= 3.14 x
Divide each side by 3.14
20/3.14 = 3.14x/3.14
6.369 = diameter (x)

Find the diameter of a circle with a circumference of 15 feet.
15 = 3.14x
x = diameter
Divide each side by 3.14
15/3.14 = 3.14x/3.14
4.77 = diameter (x)

Calculate the Radius of a Circle

The easiest method for finding radius from the circumference of a circle is to simply divide the circumference by pi, which equals the diameter. 
Next, divide the diameter by two for the radius.
 
For example. What is the radius of a circle with a circumference of 24 units?
 
Step 1. 24/π = 7.63 = diameter of the circle
Step 2. 7.63/2 = 3.81 units is the radius
 
What is the radius of a circle with a circumference of 314 units?
 
Step 1. 314/π = 99.94 = diameter of the circle.  
Step 2. 99.94/2 = 49.97 units is the radius

Calculate Radius from the Diameter of the Circle

To find the radius from diameter simply divide the diameter by two.

Radius= Diameter/2

Radius of the circle from the area

If you know the area of a circle you can find the radius using this formula:
 
Radius = √Area*π
 

Radius from equation of the circle and 1 point.

If you know one point and the equation of a circle, then the radius of this circle can be calculated.
 
Remember the general form of the equation of a circle equals,
 
(x-h)^2 +(y-k)^2
 
h and k are the x and y coordinates of the center of the circle.
 
Example problem radius from equation of a circle.
 
Find the radius of a circle with an equation of (x-4)^2 + (y+3)^2 and contains (5,0)

(5-4)^2 + (0+3)^2 = r^2
 
1 +9 =r^2

√10 =radius  (exact answer)
 
3.162 = radius (approximate answer)