How to Find the Radius of a Circle

Because all circles have the same shape, their different measurements are related by a set of simple equations. If you know the radius, diameter, area or circumference of a circle, it is fairly easy to find any of the other measurements.

Instructions

1. Learn the formulas relating radius to circumference, area and diameter. If pi is a constant, area = a, circumference = c, diameter = d and radius = r, the formulas are:

   c =2 pi r

   a = pi r^2

   d = 2 r

2. Notice what you already know about the circle. If you are expected to find the radius, you will already know the diameter, area or circumference. Choose the equation from step 1 that relates radius to the quantity you already know.

3. Divide the diameter by 2 to get r if you know the diameter. For example, if your circle has a diameter of 4, the radius is 4/2 = 2.

4. Divide the circumference by 2 pi to find the radius if you know c. it's impossible to write the exact value of pi, but for most problems 3.14 is a good enough approximation. So, if your circumference is 618, you would get

   r = 618 / 2 pi

   r = 618 / 2 x 3.14

   r = 618 / 6.18

   r = 100

5. Plug in the area to find the radius if you know the area. If a = pi r^2 then r = the square root (sqrt) of the area divided by pi, or to put it in mathematical script, sqrt(a/pi).

   So, if the area is 3.14, we get:

   r = sqrt(3.14 / 3.14)

   r = sqrt(1)

   r = 1

References

• Circle Formulas