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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 =

circle
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.

circle diagram
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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