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# Calculators :: Plane Geometry :: Circle Calculator

Enter one known value of a circle and calculate the area, circumference, radius or diameter. You will get solution with step-by-step explanation.

## Circle Calculator

Input value you know and the value you want to find. You can enter either integers (10), decimal numbers(10.12) or FRACTIONS(10/3). To enter $\pi$ type PI.

0 1 2 3 4 5 6 7 8 9 / . π del
 Enter known values: area A = circumference C = radius r = diameter d =

 Select value to find: Area A Circumference C Radius r Diameter d
Show me an explanation.

# Circle Formulas

To calculate missing value in 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 when 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}

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