Circle Calculator

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Radius $\hspace{0.2em} (r) = \hspace{0.2em}$

distance between two points - illustration

Please provide your input and click the calculate button

About the Circle Calculator

In this circle calculator, you can enter the value of a circle's radius, diameter, area, or circumference, and it will calculate the other three for you.

Also, the calculator will tell you not just the answers, but also you can calculate them.

Usage Guide

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i. Valid Inputs

Each of the inputs provided must be a non-negative real number. In other words, the input must be 0 or greater. Here are a few examples.

Whole numbers or decimals → $\hspace{0.2em} 2 \hspace{0.2em}$ , $\hspace{0.2em} 4.25 \hspace{0.2em}$ , $\hspace{0.2em} 0 \hspace{0.2em}$ , $\hspace{0.2em} 0.33 \hspace{0.2em}$
Fractions → $\hspace{0.2em} 2/3 \hspace{0.2em}$ , $\hspace{0.2em} 1/5 \hspace{0.2em}$
Mixed numbers → $\hspace{0.2em} 5 \hspace{0.4em} 1/4 \hspace{0.2em}$

ii. Example

If you would like to see an example of the calculator's working, just click the "example" button.

iii. Solutions

As mentioned earlier, the calculator won't just tell you the answer but also the steps you can follow to do the calculation yourself. The "show/hide solution" button would be available to you after the calculator has processed your input.

iv. Share

We would love to see you share our calculators with your family, friends, or anyone else who might find it useful.

By checking the "include calculation" checkbox, you can share your calculation as well.

Here's a quick overview of what a circle is and a few different concepts related to the shape.

Circle — The Basics

A circle is the set of all points in a plane that are at a fixed distance ( called radius and denoted by $\hspace{0.2em} r \hspace{0.2em}$ ) from a certain point, its center $\hspace{0.2em} (O) \hspace{0.2em}$ .

Now, a line segment from one point on the circle to another point on it that also passes through the center is known as a diameter $\hspace{0.2em} (d) \hspace{0.2em}$ of the circle.

Also, the length of the diameter is twice that of the radius.

d = 2r

Circumference and Area of a Circle

Cicumference refers to the perimeter (or the length of the boundary) of a circle. And here's the formula for the circumference of a circle in terms of its radius $\hspace{0.2em} r \hspace{0.2em}$ or diameter $\hspace{0.2em} d \hspace{0.2em}$ .

\begin{align*} C \hspace{0.25em} &= \hspace{0.25em} \pi d \\[1em] &= \hspace{0.25em} 2 \pi r \end{align*}

Finally, the area of a circle is given by

A = \pi r^2

Examples

Example

Find the circumference of a circle with a radius of $\hspace{0.2em} 4 \text{ cm} \hspace{0.2em}$ .

Solution

The formula for the circumference of a circle is

C \hspace{0.25em} = \hspace{0.25em} 2 \pi r

Substituting the value of $\hspace{0.2em} r \hspace{0.2em}$ into the formula, we have

\begin{align*} C \hspace{0.25em} &= \hspace{0.25em} 2 \pi \cdot 4 \\[1em] &= \hspace{0.25em} 25.13 \end{align*}

So the circumference of the circle is $\hspace{0.2em} 25.13 \text{ cm}^2 \hspace{0.2em}$

Example

The circumference of a circle is $\hspace{0.2em} 7 \pi \text{units} \hspace{0.2em}$ . Find its area.

Solution

The area of a circle is given by the formula

A \hspace{0.25em} = \hspace{0.25em} \pi r^2

As you can see, we need $\hspace{0.2em} r \hspace{0.2em}$ . And we can find it using the circumference (provided in the question) as follows.

\begin{align*} C \hspace{0.25em} = \hspace{0.25em} 2 \pi r \\[1em] 7 \pi \hspace{0.25em} = \hspace{0.25em} 2 \pi r \\[1em] r \hspace{0.25em} = \hspace{0.25em} 3.5 \end{align*}

Now, substituting the value of $\hspace{0.2em} r \hspace{0.2em}$ into the formula for area, we get —

\begin{align*} A \hspace{0.25em} &= \hspace{0.25em} \pi \times 3.5^2 \\[1em] &= \hspace{0.25em} 38.48 \end{align*}

So the area of the circle is $\hspace{0.2em} 38.48 \text{ sq. units} \hspace{0.2em}$ .