**Circumference Calculator**

### Circumference Calculation Explained

Understanding what a **circumference **of a circle is and how to calculate it is crucial as you move to higher level math. In this article you will learn the answers to the following questions.

- What is the circumference of a circle?
- How can you calculate the circumference of a circle?

**What is the circumference of a circle?**

The **circumference** of a circle is the distance around the outside of the circle. It is like the **perimeter** of other shapes like squares. You can think of it as the line that defines the shape. For shapes made of straight edges this line is called the **perimeter** but for circles this defining line is called the **circumference.**

This diagram shows the circumference of a circle.

There are two other important distances on a circle, the **radius (r) **and the **diameter****(d). **The radius, the diameter, and the circumference are the three defining aspects of every circle. Given the radius or diameter and pi you can calculate the circumference. The diameter is the distance from one side of the circle to the other at its widest points. The diameter will always pass through the center of the circle. The radius is half of this distance. You can also think of the radius as the distance between the center of the circle and its edge.

This diagram shows the circumference, diameter, center, and radius on a circle.

**How can you calculate the circumference of a circle?**

If you know the diameter or radius of a circle, you can work out the circumference. To begin with, remember that pi is an irrational number written with the symbol π. π is roughly equal to 3.14.

The formula for working out the circumference of a circle is:

**Circumference of circle = ****π x Diameter of circle**

This is typically written as C = πd. This tells us that the circumference of the circle is three “and a bit” times as long as the diameter. We can see this on the graphic below:

You can also work out the circumference of a circle if you know its radius. Remember that the diameter is double the length of the radius. We already know that C = πd. If r is the radius of the circle, then d = 2r. So, C = 2πr.

**Example 1**

If a circle has a diameter of 10cm, what is its circumference?

**Answer**

We know that C = πd. Since the diameter is 10cm, we know that C = π x 10cm = 31.42cm (to 2 decimal places).

**Example 2**

If a circle has a radius of 3m, what is its circumference?

**Answer**

We know that C = 2πr. Since the radius is 3m, we know that C = π x 6m = C= 18.84m (to 2 decimal places).

**Example 3**

Find the missing length (marked with a ?) on the diagram below:

**Answer**

The missing length is the circumference. Using the knowledge that the diameter is 4.3m on the diagram and knowing that C = πd, we can calculate the circumference. With a little thinking we can easily figure out that, C = π x 4.3m = 13.51m (to 2 decimal places). The missing length is 13.51m.

**How to calculate the circumference of the Earth**

Have you ever wondered how big the earth is? Well, using pi it’s possible to work out the circumference of the Earth! Scientists have discovered that the diameter of the Earth is 12,742km. Given this information, what is the circumference of the Earth? Get out a piece of paper and a calculator and see if you can work it out on your own.

Again, we know that C = πd, and that the diameter of the earth is 12,742km. Using this information we can calculate the circumference of the Earth as C = π x 12,742km = 40,030km.

**Formula for the Circumference and Area of a Circle**

## How To: Calculate the circumference of a circle

This video shows how to calculate the circumference of a given circle. The video first describes the circumference or perimeter of a circle as the distance around the outside of a circle. To find the circumference we need either the radius or the diameter of the circle. When you know the diameter of the circle, the formula to find the circumference denoted by 'C' is 'pi' times the diameter, where 'd' is the diameter and 'pi' is a constant, the approximate value being 3.14. And when you are given the radius, the formula for circumference is pi times 2 times r where 'r' is the radius. The speaker says both the formulas are the same because 2 times radius is equal to the diameter. He then explains an example where the diameter is given as 10 meters and you are asked to find the exact circumference. You can calculate the circumference as C=pi times d. The value is 10pi meters. He says that when you are asked to find the exact circumference, then you are supposed to leave pi as it is and not substitute pi with its approximate value 3.14 while finding the answer. Then he explains another example asking you to find the exact circumference. Here, the radius of the circle is given as 4 miles. He asks you to calculate the circumference using the formula C=pi times 2 times r. The value then becomes 2 times pi times 4 which is 8pi. The circumference of this circle, he says, is 8pi miles. Another example asks you to calculate the approximate circumference of the given circle. Here, the radius is given as 15.3 mm and you are asked to use pi=3.14 in the solution. So he asks you to use the formula C=pi times 2 times radius which is 2 times 15.3 times 3.14. The value works out to be 96.084 with the approximate circumference of this circle being 96mm. He then finally signs off saying that if you want to learn more about circumference of other different circles, there is video part two available.

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## Circumference Calculator

### Use our Circumference Calculator to determine the circumference of a circle.

Does calculating circumference have you running in circles? Our circumference calculator is an easy way for you to find the circumference of any circular object. Simply enter the radius of the circle and hit “calculate.” You can click the “reset” button if you need to clear the circumference calculator in order to find the answer for another circle.

### Try our *Circumference Calculator* now!

And if you're not sure what the radius is or how to find it, we'll walk you through some of the basics of finding a circle's circumference below.

### What is the Circumference of a Circle?

The circumference of a circle is the measurement around a circle's edge. It can be compared to finding the perimeter of a shape (although the word perimeter is reserved specifically for polygons). If you were to cut a circle and lay the outline flat, the length of the line it created would be its circumference. The circumference can be measured in any unit or system that traditionally measures length - imperial (inches, feet, etc.) or metric (centimeters, meters, etc.). Whichever unit the radius is measured in will also be the unit the circumference is calculated in.

The equation used to find circumference is C = 2Πr, where C stands for circumference, R stands for radius, and Π is Pi, a mathematical constant equivalent to approximately 3.14 (see more below).

You can also calculate the circumference of a circle using the diameter, with the equation C = Π * d. If you only have the diameter of a circle and would still like to use this calculator, you can find the radius by dividing the diameter in half.

We suggest working out some problems on your own and using the calculator to check your answer, as it provides you with a solution for each problem but will not show you the work that goes with it.

### Parts of a Circle

**Circumference:**The distance once around the circle. It can also be understood as the circle's perimeter.**Radius**: The distance from the center of the circle to its edge. No matter which direction you measure in, the radius will be the same from any point on the edge of the circle.**Diameter:**A straight line across the circle that intersects through the center point. This measurement is always equal to**twice the radius**(2r).

### The Value of **Pi **

**Pi (**Π) is a non-terminating number, which means it goes on forever and has no end. Its value is about **3.1415926535897... **Pi is also a constant, which means it is always equal to the same value.

The Greek letter **p** (pronounced as "pie") is used to describe this number. It stands for the ratio between the circumference of any circle and its diameter, and it's true for all circles. This means that any circle’s circumference will be about 3.14 times the length of its diameter.

### Circumference Equation Example

What is the circumference of a circle whose radius is 24 inches?

**Circumference = 2×Π×r**

C = 2 × 3.14 × 24

C = 150.79 inches

When you enter the radius of 24 into our calculator, it provides you with an answer of 150.79644737231007, which is a more precise answer. This is because it uses a more accurate number for Pi, rather than rounding to 3.14.

Our circumference calculator provides circumference of a circle by entering its radius. Our circumference calculator is free to use any time you want to determine the circumference of a circle!

We also have a fun instructional video on diameter, radius and circumference of a circle right here: Circumference of a Circle Video .

Other Calculators

## How do you find the approximate circumference of a circle?

**circumference of a circle**can be found by multiplying pi ( π = 3.14 ) by the diameter of the

**circle**. If a

**circle**has a diameter of 4, its

**circumference**is 3.14*4=12.56. If you know the radius, the diameter is twice as large.

Click to see full answer.

Considering this, how do you find the approximate circumference?

The **circumference** = π x the diameter of the circle (Pi multiplied by the diameter of the circle). Simply divide the **circumference** by π and you will have the length of the diameter. The diameter is just the radius times two, so divide the diameter by two and you will have the radius of the circle!

Likewise, what is the circumference of a 12 inch circle? Circumference & Areas

Size in Inches | Circumference Inches | Area in Square Inches |
---|---|---|

12 | 37.700 | 144.000 |

12 1/4 | 38.480 | 150.060 |

12 1/2 | 39.270 | 156.250 |

12 3/4 | 40.060 | 162.560 |

Just so, how do you calculate the length of a circle?

A **circle** is 360° all the way around; therefore, if you divide an arc's degree **measure** by 360°, you find the fraction of the **circle's** circumference that the arc makes up. Then, if you multiply the **length** all the way around the **circle** (the **circle's** circumference) by that fraction, you get the **length** along the arc.

What is the formula for area?

The most basic **area formula** is the **formula** for the **area** of a rectangle. Given a rectangle with length l and width w, the **formula** for the **area** is: A = lw (rectangle). That is, the **area** of the rectangle is the length multiplied by the width.

## Approximate circumference to find how

## How to Calculate the Circumference of a Circle

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