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# 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 select what to compute.
show help ↓↓ examples ↓↓
I want to calculate:
Input one element of a circle
use letter r to input square root. Ex: $3\sqrt{2} = \text{3r2}$
type PI to input $\pi$
area $A$
=

circ. $C$
=
radius $r$
=

diam. $d$
=
working...
examples
example 1:ex 1:
Find the area of the circle with a diameter of $6cm$.
example 2:ex 2:
Find the area of the circle with a circumference of $C = 6 \pi$.
example 3:ex 3:
Find the diameter of the circle with area $A = \frac{9}{4} \pi$.

# 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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