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.

(5-4)^2 + (0+3)^2 = r^2

1 +9 =r^2

√10 =radius (exact answer)

3.162 = radius (approximate answer)

- 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.

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 and two times radius times pi equals the circumference.

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.

Calculate the circumference of a circle with a diameter of 8 units and a radius of 4 units.

3.14*8=25.12 units

2 * 4 * 3.14 = 25.12 units

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r =4

Diameter =8

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

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

If you know the area of a circle you can find the radius using this formula:

If you know the circumference of a circle you can work backwards and find the diameter.

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)

15 = 3.14x

x = diameter

Divide each side by 3.14

15/3.14 = 3.14x/3.14

4.77 = diameter (x)