# Circumference Calculator

This circumference calculator will find the area, circumference and diameter of a circle. Please enter the radius of the circle, and then hit Calculate.

Whenever you are learning about circumferences at school, you absolutely need to try out our Circumference Calculator. After all, by simply inserting the radius in inches in our Circumference Calculator, you will be able to get the diameter in inches, the area in in2, and the circumference in inches.

## #1: Definition Of Circumference:

One of the things that we find extremely important is that besides the fact that you can simply use a Circumference Calculator and get all these values, is to know how they are calculated manually. So, with this in mind, we believe that it is important to clarify some definitions.

Before we define the circumference, it is important to define the circle. So, simply put, a circle is a geometric form where every point on the outside of the circle is the same exact distance away from the center of the same circle. In what concerns to the circumference, it is simply the distance around the edge of the circle.

One interesting fact is that no matter which circle you are looking at, in case you decide to divide the circumference by the diameter, you will always get pi which is usually rounded to 3.14.

Make sure that you check out the most useful geometry calculators.

## #2: The Formula Of The Circumference:

The truth is that even though you can use our Circumference Calculator to immediately discover the diameter, area, or circumference of any circle with the simple addition of the radius, it’s important that you know how to calculate each one of these parameters by hand.

So, the formula of a circumference is: C = 2πR

where C = circumference;

π = pi = 3.14;

R = radius of the circle.

However, if you are trying to determine the area of a circle as well as its radius, you should use the following formula:

A = π * R^2

where A = area of the circle;

π = pi = 3.14;

R = radius of the circle.

## #3: Determining The Circumference Of A Circle Manually:

As we already stated, nevertheless you can use a simple Circumference Calculator, you should always have in mind the formulas to calculate the circumference of any given circle.

The truth is that this won’t only serve you to get a good math grade. It will also have a positive impact on your future life. For example, you may need to put fencing around your hot tub. So, you’ll need to perform these calculations.

The truth is that there are tew different methods to determine the circumference of a circle. Let’s take a closer look at each one of these methods:

**Method #1: Using The Diameter: **

When you only have the diameter of the circle available and you want to determine the circumference, you just need to use the following formula:

C = πd, where:

– C = circumference of the circle

– π = pi = 3.14

– d = diameter

So, let’s say that you have a circle tub that has a diameter of 8 feet. Your goal is to build a fence that is able to create a 6-foot wide space around the tub. So, how can you calculate the circumference of the fence?

The first thing you need to do is to calculate the diameter of the tub and the fence together. So, according to the example provided, the diameter will be equal to 8 feet + 6 feet + 6 feet = 20 feet.

Now just take the formula of the circumference we showed you above and replace the letters by values:

C = πd

C = π x 20

C = 62.8 feet

**Method #2: Using The Radius:**

When you already have the radius of the circle and you want to determine circumference of the circle, you just need to use the same formula. Nevertheless, you need to know that the radius is half as long as the diameter. So, this means that you can think of the diameter as: 2 x r.

Let’s check a quick practical example so we can apply it. Let’s say that you just baked a cake and you want to cut out a decorative strip of paper to wrap around it. So, you already know the radius which is 5 inches.

So, in order to determine the circumference, you need to use its formula:

C = 2πr

Replacing with the radius value that is 5 inches, and the pi which is 3.14, you get:

C = 2 x 3.14 x 5 = 31.4 inches.

## Knowing More About The Variables

If you take a closer look at both the perimeter and the area of the circumference, you can easily see that we are basically using the same variables on both formulas. However, the way they are related to each other varies.

So, we believe that it is important that you know a bit more about these variables:

**π –** Pi, as it is also known, is always a constant. The truth is that the value of π is approximately 3.14159265358979323846. As a rule of thumb, whenever you need to use π, you should consider it as 3.14.

**Radius –** The radius of a circle is the distance between the center of a circle and any point on the circle. If you place two different radius from an end to end circle, you will get the diameter of the circle. So, this means that you can say that the diameter is twice as long as the radius. The radius is usually referred to as the letter r.

**Diameter –** The diameter is the distance across a circle through the center. As we just stated above, the diameter is twice the radius and it is usually referred to as d.

## Why Do You Need To Know So Much About Circumferences?

If you are a math student and you are now learning the circumference and the circle, you are probably wondering why you are spending so much time around this subject.

The truth is that circumferences have been being studied for thousands of years by mathematicians. They actually observed that there was a special relationship between the diameter of a circle and the circumference. And this relationship is given by Pi or π.

The reason why this is so important is that due to this relationship, mathematicians discovered that they can apply it to circles as well. Why? All you need to do is to look around you and look for circular shapes. Just look at your car wheels or at the court floor where you play basketball. How could you have ever defined such a diameter or radius for the floor if mathematicians haven’t been studying this topic for such a long time? If you are a girl who likes candles, someone had to define their diameter or radius. Or think of hats and crowns that were used many centuries ago by Kings and Queens. Someone had to measure the King and Queen’s heads and then build them their crowns. However, there was the need for the crown to have adornments as well. And again, you need to know about circumferences and circles.

As you can see, there were and still are many uses for the formulas that you are now learning. So, if you were thinking that you wouldn’t use these formulas anymore, you’re really wrong.

## Real World Examples

Now that you not only know what a circumference is and how you can determine the circumference of a circle (or perimeter) as well as the area of a circle, it is now the time to see some real world examples so that you can confirm you are not learning all these formulas just for your tests and exams.

### Example #1:

Let’s imagine that you have a construction company and that you have a constructor named Robert who is building a house. As you probably already know, the first step to do this is to drill holes so that you can then fill them with concrete.

Robert tells you that he will need to drill holes that are 0.4 m wide and 1 m deep. So, based on his information, you will need to determine how much concrete you need to order so that Robert can fill the holes. To make things a bit simpler, let’s do the math for just one hole.

You know that the holes that Robert needs to drill are circular because he is using an auger.

Based on the data provided, you know that the diameter (d) = 0.4 m.

Using the area of the circle formula:

A = π * R^2

And replacing it with the data that you have:

A = 3.14 x R^2

Knowing that:

d = 2 x r

r = d / 2

So:

A = 3.14 x (0.4 / 2)^2

A = 0.126 m^2

So, now you already determined the area of the circle. However, you also know that the holes are 1 m deep. So, you will need to use the volume formula as well:

Volume = 0,126 m2 × 1 m = 0.126 m^3

So, know you know that you will need to order 0.126 m^3 of concrete to fill each hole that Robert needs to drill to build the home.

### Example #2:

Let’s say that you have a bicycle and that its wheels have a radius of 27.5 cm. So, you just measured your way to school and you established that there are 3500 cm separating your home and school. So, you want to determine how many full rotations does your wheel needs to make from home to school.

The first thing that you need to determine is what you need to calculate. Since you want to know the number of full rotations, you want to calculate the perimeter or the circumference of a circle.

As you already know, the formula of the perimeter of a circle (or circumference of a circle) is:

C = πd

Where,

C = circumference of the circle

π = pi = 3.14

d = the diameter of the circle

So, replacing the values for the variables that are provided:

C = 3.14 x 27.5

C = 86.35 cm

So, you know know that in one full rotation, the wheel travels 86.35 cm. Since you want to determine the total number of rotations during 3500 cm:

3500 / 86.35 = 40.53

Since you want to know the number of full rotations, your answer will be 40 rotations.

## Conclusion

As you can see, determining both the circumference of a circle (or perimeter) as well as the area of a circle can be very useful in your daily life.