The circumference is the distance around the circle, and is thus the same as its perimeter. The formula is C=2π⋅r{\displaystyle C=2\pi \cdot r}, where C{\displaystyle C} equals the circumference and r{\displaystyle r} equals the radius. Since the radius is half the diameter, you can use the formula C=π(d){\displaystyle C=\pi (d)} if you have the diameter instead of the radius., Make sure you substitute for the variable r{\displaystyle r}. If you are using the diameter formula, substitute for d{\displaystyle d}. The length of the radius or diameter should be given, or you should be able to measure it. If you do not have this information, you can’t use these formulas.

For example, if the radius of the circle is 6 cm, your formula will look like this:C=2π⋅6{\displaystyle C=2\pi \cdot 6}.
 You can use 3.14 for π{\displaystyle \pi }, but if you are using a calculator you can use the π{\displaystyle \pi } key for a more precise answer. The product of these three values is equal to the circumference, or perimeter, of the circle.

For example: C=2π⋅6=37.7{\displaystyle C=2\pi \cdot 6=37.7}. So the circumference of the circle is 37.7 cm.
 The area of a circle is given by the formula A=π⋅r2{\displaystyle A=\pi \cdot r^{2}}. So, if you plug the area into the formula, you can solve for r{\displaystyle r}. Once you have r{\displaystyle r}, you can use the circumference formula to find the circumference.For example, if you are told that the area of a circle is 64 square centimeters, you would set up the formula 64=π⋅r2{\displaystyle 64=\pi \cdot r^{2}}. Then, use the  rules of algebra to solve for r{\displaystyle r}:64=π⋅r2{\displaystyle 64=\pi \cdot r^{2}}64π=π⋅r2π{\displaystyle {\frac {64}{\pi }}={\frac {\pi \cdot r^{2}}{\pi }}}20.37=r2{\displaystyle 20.37=r^{2}}20.37=r2{\displaystyle {\sqrt {20.37}}={\sqrt {r^{2}}}}4.51=r{\displaystyle 4.51=r}So, the radius of the circle is about 4.51 cm. Now you can plug this value into the perimeter formula and solve.
Set up the formula for finding the circumference of a circle.
Plug the length of the radius into the formula.
Multiply the radius by 2π{\displaystyle 2\pi }.
Find the perimeter given the area.
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