Circle Formulas

To calculate the missing value in a circle based on one known value, you need to remember just three formulas.

F1:	$$ A = r^2 \cdot \pi $$	A = area C = circumference r = radius d = diameter
F2:	$$ C = 2 \cdot r \cdot \pi $$
F3:	$$ d = 2 \cdot r $$

The diagram at the right shows when to use each of these formulas.

Example:

Find circumference of a circle if the area is 20.

Solution

To solve this problem we first need to find radius $r$, by using formula $ \color{blue}{A = r^2 \pi} $ (see the diagram).

$$ \begin{aligned} & \color{blue}{A = r^2 \pi} \\ & 20 = r^2 \pi \\ & r^2 = \frac{20}{\pi} \\ & r^2 = \frac{20}{3.14} \\ & r^2 = 6.37 \\ & r = \sqrt{6.37} \\ & r = 2.52 \end{aligned} $$

Now we will find circumference using the formula $\color{blue}{C = 2r\pi} $.

$$ \begin{aligned} & \color{blue}{C = 2 r \pi} \\ & C = 2 \cdot 2.52 \cdot 3.14 \\ & C = 15.82 \end{aligned} $$