Circumference Calculator: Calculate Circle

The Circumference Calculator is a free online tool that calculates the circumference of a circle using either a radius or diameter. Whether it is for school work in maths or for a home improvement project, knowing the circumference of a circle will help you work out how long something is around a circular object.

What is Circumference?

Circumference is the length of the perimeter of a circle. Unlike square and rectangular shapes, circles have a curved edge. The circumference depends on how big the radius or diameter is.

How to Use the Circumference Calculator

Our Circumference Calculator allows you to quickly work out what the circumference of a circle is. Simply type in the radius or diameter.
To use it simply:

Choose whether you want to calculate it using the radius or diameter.

Type in the radius or diameter that you know.

Select your measurement type, e.g. inches, feet, centimetres or metres.

Click the calculate button.

Your circumference will show up.

If you have a circle with a radius of 5 inches then type in 5 into the radius box and choose inches. The calculator will automatically work out the circumference for you.

You won’t have to work out Pi manually.

Calculating the Circumference

There are two common formulas for working out the circumference of a circle. Depending on if you know the radius or diameter you can use one of the following:

Circumference using Radius

The formula is:

C = 2 x π x r

Where:

C = Circumference

π (Pi) = 3.14159

r = Radius

The radius is the distance from the centre of a circle to the outside.

Circumference using Diameter

The formula is:

C = π x d

Where:

C = Circumference

π (Pi) = 3.14159

d = Diameter

The diameter is the straight line distance across the circle.

As the diameter is double the radius both formulas give the same result.

d = 2r

\\(C = 2\\pi r\\)

\\(C=2\\pi r=2\\pi(\\text{3.00})=\\text{18.85}\\)

\\(r\\)

Circumferenced = 6.00r = 3.00

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Example

Let’s look at an example of how to work out the circumference.

Example 1 – Using Radius

You have a circular table with a radius of 10 inches. You want to know the distance all the way around the outside.

Radius (r) = 10 inches

Pi (π) = 3.14159

Formula:

C = 2 x π x r

Plug in the values:

C = 2 x 3.14159 x 10

C = 62.8318

Answer:

Circumference = 62.83 inches

So the distance around the circular table is 62.83 inches.

Example 2 – Using Diameter

You have a circular garden with a diameter of 12 feet.

Diameter (d) = 12 feet

Pi (π) = 3.14159

Formula:

C = π x d

C = 3.14159 x 12

C = 37.69908

Answer: 37.70 feet

So the distance around the garden is 37.70 feet.

Understanding your results

Once you’ve typed in your measurements the calculator will give you the total distance around the circle.

Understanding how it works will help you use it.

Some key things to note:

• Circumference – This is the total distance around the outside of a circle.
• Radius – Distance from the centre to the edge.
• Diameter – Distance across the circle.
• Measurement – The results will be in the same measurement as you typed in.
• Decimal numbers – Your results can be in decimal numbers as Pi is an irrational number.

If you get a result of 31.42 inches this means the circumference is 31.42 inches.

This can help you work out how much material you will need to cover the outside or add some decoration.

Remember that circumference is the distance around.

Factors that affect the result

There are a few factors that affect how big the circumference will be.

Radius

The bigger the radius the bigger the circumference. If you double the radius you’ll double the circumference.

Diameter

The diameter is directly proportional to the circumference. So if you increase the diameter then the circumference will increase by the same amount.

Pi

Pi is a mathematical constant and is used in all circumference calculations.

The commonly used value for Pi is 3.14159.

If you use more decimals then your result will be more accurate.

Measurement

The measurement you choose will affect how your result is shown. If you type in inches for the radius your result will be in inches. If you use metres your result will be in metres.

Accuracy

If you don’t measure the radius or diameter accurately this can affect your result. Even a small mistake can be noticeable with larger circular objects.

Advantages of using a Circumference Calculator

There are many advantages to using a Circumference Calculator.

Saves time

You can work out the circumference in seconds.

No errors

You won’t make any common errors as the calculator will apply the correct formula.

Helps with learning maths

Students can use this to learn about the relationship between radius, diameter, Pi and circumference.

Useful for building projects

Building professionals can use this to work out how much material they might need to go around a circular object, column, pipe or garden.

Home improvements

Home owners can work out the circumference of round tables, round rugs, garden beds, pools etc.

Engineering

Engineers can use this in their work with wheels, circular parts, pipes etc.

Everyday use

You can work out how long something is around circular objects like plates, pots, lids, tree trunks and round decorations.

Accuracy, Assumptions and Limitations

If you type in the correct radius or diameter the calculator will give you an accurate result.

However, there are a few assumptions and limitations.

Assumes perfect circle – Assumes that the object you’re measuring is a perfect circle.

Measurements – Must measure them accurately.

• Pi – Not using the full value of Pi can mean there is a very slight difference in your answer due to rounding.
• Measurements – Always use the correct measurement.
• 2D – Circumference gives you the distance around the outside of a circle it will not give you the area, volume or surface area.
• Not for irregular shapes – This formula isn’t suitable for working out the perimeter of an irregular or oval shape. You would need to use more maths.

If you’re using this for a real life scenario make sure you’re using the correct measuring tool and use the most accurate measurement you can. If you need a very accurate result for an engineering purpose then you could use more decimals for Pi and try to avoid rounding until the end.

FAQs

What is a circumference calculator?

A Circumference Calculator is an online tool that calculates the total distance around a circle. It uses the circumference formula and will give you the result in your chosen measurement.

How do you work out circumference?

If you know the radius use the formula C = 2πr. If you know the diameter use C = πd. Multiply the radius by 2 x Pi or the diameter by Pi.

What is the difference between circumference and diameter?

Circumference is the total distance around the outside of a circle. Diameter is the straight line distance across. The circumference is roughly 3.14159 times bigger than the diameter.

Can I work out circumference using just radius?

Yes! You can work out circumference using just the radius. Use the formula \\(C = 2\\pi r\\)0__. You won’t need to know the diameter as the calculator will work it out for you.

Does circumference use inches, feet or metres?

Yes! You can use any standard measurement for circumference. Inches, feet, yards, millimetres, centimetres and metres. The result will be in the same measurement you’ve used.