Circumference Calculator

What do we know?☝️

Radius

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

distance between two points - illustration

Please provide your input and click the calculate button

About the Circumference Calculator

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

The calculator will tell you not just the circumference, but also you can calculate it.

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 we mean by circumference and a few different formulas we can use to calculate it.

Circumference — An Overview

Circumference of a circle (usually denoted by $\hspace{0.2em} C \hspace{0.2em}$ ) refers to its perimeter (length of its boundary).

And here are the formulas for the circumference of a circle in terms of its —

1. radius $\hspace{0.2em} r \hspace{0.2em}$ ,

C \hspace{0.2em} = \hspace{0.2em} 2 \pi r

2. diameter $\hspace{0.2em} d \hspace{0.2em}$ ,

C \hspace{0.2em} = \hspace{0.2em} \pi d

3. area $\hspace{0.2em} A \hspace{0.2em}$ ,

C \hspace{0.2em} = \hspace{0.2em} 2 \sqrt{\pi \cdot A}

Circumference Calculations — Examples

Example

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

Solution

The circumference of a circle is given by the formula —

C \hspace{0.2em} = \hspace{0.2em} 2 \pi r

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

\begin{align*} C \hspace{0.2em} &= \hspace{0.2em} 2 \pi \cdot 4 \\[1em] &= \hspace{0.2em} 25.13 \end{align*}

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

Example

Calculate the circumference of a circle with an area of $\hspace{0.2em} 15 \text{ in}^2 \hspace{0.2em}$ .

Solution

Earlier I mentioned a formula that allows us to find the circumference using the area of a circle. Substituting the value of $\hspace{0.2em} A \hspace{0.2em}$ into the formula,

\begin{align*} C \hspace{0.2em} &= \hspace{0.2em} 2 \sqrt{\pi \cdot A} \\[1em] &= \hspace{0.2em} 2 \sqrt{\pi \cdot 15} \\[1em] &= \hspace{0.2em} 9.71 \end{align*}

The circumference of the circle is $\hspace{0.2em} 9.71 \text{ in} \hspace{0.2em}$ .

Note — Instead of using the direct formula as we did here, you can also find the radius using the relation between the area and radius of a circle. And then use the radius to calculate the circumference.