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# Circle calculator

Input the area, circumference, radius or diameter of a circle, then choose a missing value. The calculator provides a step-by-step explanation on how to find the missing value.

Circle Calculator
input value you know and select what to find
show help ↓↓ examples ↓↓
I want to find:
Enter one element of a circle.
Input the square root using the letter r. Ex: $3\sqrt{2} = \text{3r2}$
type PI to input π
area $A$
=

circ. $C$
=
radius $r$
=

diam. $d$
=
working...
examples
example 1:ex 1:
Find the area of the circle with a diameter of 6 cm.
example 2:ex 2:
Calculate the area of a circle whose circumference is C = 6π.
example 3:ex 3:
Calculate the diameter of a circle with an area of A = 9/4π.

# 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}
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