Missing Radius From Circumference

Find the radius from the circumference

When the circumference of a circle is given, you can work backward to find the radius. The key relationship is:

C = 2πr

Here, C is the circumference and r is the radius.

Steps

1. Write the formula with the given circumference.

2. Isolate the radius by dividing both sides by 2π:

   r = C / (2π)

3. Substitute the value of the circumference.

4. Simplify the result as much as possible. If possible, leave the answer in exact form using π.

Example method

If a circle has circumference 18π, then

r = 18π / (2π) = 9

So the radius is 9.

Check your answer

Use the radius you found and substitute it back into C = 2πr. If you get the original circumference, your answer is correct.

Common reminder

Be careful not to confuse radius and diameter. The radius is half the diameter, and the circumference formula uses the radius directly.