The circumference is the distance around the edge of a circle.
In other words, it is the perimeter of a circle – however, the word perimeter is generally only used for shapes with straight edges.
Why is finding the circumference helpful?
Finding the circumference is a topic taught from Year 6 through to KS4. Not only is it one of the essential skills in geometry, but finding the circumference of a circle can also be used for many reasons in day-to-day life.
Think about circular everyday items – car wheels, cups and saucers, roundabouts, and even the Earth!
Architects find the circumference when looking at materials for their projects, and it’s also used a lot in farming for fencing and looking at crop yields.
Because the circumference measures the distance around something, it’s an invaluable tool for lots of work that involves area, shape, and measurement.
How To Calculate Circumference
Radius (r) and diameter (d) are two other essential measurements on a circle that is needed before you can calculate the circumference.
This picture shows the circumference, diameter, and radius of a circle:
Using these measurements, there are two different ways to calculate the circumference.
The radius(r) is the distance from any point on the circumference to the circle’s center. The diameter (d) is the distance from one side of the process to the other and is double the radius.
How To Calculate the Circumference Using the Diameter
The first step in working out the circumference is finding the correct formula. To find the circumference using the diameter, you will need to use the following formula:
C = πd
Let’s break this formula down. So, the ‘C’ in this formula stands for circumference, and the ‘d’ stands for diameter. This means that this formula essentially means:
Circumference of circle = π × diameter of the ring
*π or Pi is a mathematical constant equal to 3.14159. When you are using pi in maths, it can be simplified to 3.14.
So, now that we know the formula, we can start calculating the circle’s circumference.
This method of measuring the circumference assumes that we already know the circle’s diameter. So, we need to put it into our formula. For example, let’s say that the circle’s diameter is 10.
C = π10
C = π × 10
Put π × ten into your calculator, and you will get 31.4.
Answer: C = 31.4
Let’s look at a few more examples to solidify your understanding of circumference calculating.
Example 1: Find the circumference of a circle with a diameter of 93 cm.
C = πd
Let’s put our numbers into the formula.
C = π × 93
Answer: 292.2 cm.
Example 2: The Smith family has just bought a new dining table that is 13 feet wide. Find the circumference of this dining table.
Since we have not been given the diameter of this dining table, we must work it out with the information provided. We know that the diameter is half of the entire width of a circle, so we must divide our width by two.
Width ➗ 2
13 ➗ 2
Diameter = 6.5 feet
Now that we have the diameter, we can use our formula to calculate the circle’s circumference.
C = πd
C = π × 6.5
Answer: 20.4 feet.
How To Calculate the Circumference Using the Radius
To calculate the circumference of a circle using the radius, we need to use a different formula. The formula for finding the circumference with the radius is:
C = 2πr
Let’s break this formula down. So, the ‘C’ in this formula stands for circumference, as in the one above, and the ‘r’ stands for radius. This means that this formula essentially means:
Circumference of circle = 2 × π × radius
Again, as stated above, you can find π in your calculator, whose numeral value is approximately 3.14.
Because the radius is just half the diameter, the formula for calculating the circumference using the radius is similar to C = πd.
Let’s look at a few examples to solidify your understanding of how to calculate the circumference using the radius.
Example 1: Find the circumference of a circle with a radius of 6 m. The first step in solving this problem is to get the right formula, which we know is: C = 2πr.
The formula is
C = 2πr
Now, let’s put our numbers into the formula:
C = 2 × π × 6
This formula can be simplified as follows:
C = π × (2 × 6)
C = π × 12
C = 37.7
Answer: 37.7 m
Example: Holly’s favorite hobby is hula-hooping. Every day after school, she goes home and plays with her hula-hoop for hours in the garden. A few days ago, Holly broke her favorite hula-hoop, so now she has to look for a new one. Holly wants her new hula-hoop to be the same circumference as her last one. Her old hula-hoop had a diameter of 3 feet. What should the rim of Holly’s new hula-hoop be?
Step 1: In this maths problem, we have not been given the radius straight away, so we must work it out with the information given. We know that a circle’s radius is half its diameter, so we must divide three by 2.
Radius = diameter ➗ 2
Radius = 3 ➗ 2
Radius = 1.5
Step 2: Now that we have the radius, we can use our tried and true formula to calculate the circumference of the hula-hoop.
C = 2πr
Let’s put our numbers into the formula:
C = 2 × π × 1.5
C = π × (2 × 1.5)
C = π × (3)
C = 9.4
Answer: 9.4 feet.