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.

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 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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