Circumference Of A Circle Calculator And Formula To Find It – Pi Day
Circumference Calculator
This calculator works much like the circle calculator in
that you can find the area, circumference and diameter of a circle.
A great feature of this calculator is that you an find the
diameter from circumference, the radius from circumference, convert from
circumference to area, area to circumference and so on.
Before using this calculator, it’s important to understand
some basics about the circumference of a circle.
What is the circumference of a circle?
If you move along an edge of a circle, the circumference is
the total length around the entire edge. Notice how this is the same thing as
perimeter with geometric figures that have many sides, as perimeter is the total
distance of all sides of the polygon.
There is a distinct relationship between the radius and
dimater of a circle to its circumference.
If you know the diameter (d), the circumference is C = πd.
Then since we know that the radius (r) is half the diameter. Therefore the
circumference in terms of the radius is C = 2πr. You can keep the circumference
in terms of π or you can calculate using the π feature on your calculator or
using 3.1415926 for π.
Next, let’s determine how to find the circumference using
the formula above. Very simply, suppose the radius is 10 cm. Then C = 2π(10) =
62.83 cm. Quite easily done!
We can also find the area of a circle simply by using the
formula A = πr^2. For the same radius of 10 cm, the area is A = 100π or
314.159 square cm.
So what if we have a scenario where you know the
circumference but what to find the diameter or the radius? Again, this is all
quite easy using the formula defined earlier.
Suppose the circumference is 100 cm.
Therefore, 100 = 2πr and r = 100/2π or approximately 15.92
cm. To find the diameter, simply double the radius to get 31.84 cm.
If you wish to avoid the manual calculations, give our
circumference calculator a try for results in a mere fraction of a second.
www.piday.org
Calculate the circumference of a circle
As seen in the the number pi, the formula for the circumference of a circle is
C = 2 × π × r or C = π × D
If either r or D is known, you can calculate the circumference by simply substituting the known value for r or D in the formula. Use 3.14 for π.
Examples #1
Calculate C if r = 2 inches
C = 2 × π × r = 2 × 3.14 × 2 = 12.56 inches
Examples #2
Calculate C if r = 4 inches
C = 2 × π × r = 2 × 3.14 × 4 = 25.12 inches
Examples #3
If D = 10 cm, calculate the circumference.
You have two choices. You can first find r and then replace its value
r is half the diameter, so r = 10 divided by 2
r = 5 cm
C = 2 × π × r = 2 × 3.14 × 5 = 31.4 cm
Otherwise, you can just use the formula C = π × D
C = 3.14 × 10 = 31.4 cm
Examples #4
The circumference of circle A is four times the circumference of circle B
The diameter of circle B is 7. What is the diameter of circle A?
Let C_{A} be the circumference of circle A
Let C_{B} be the circumference of circle B
Let D_{A} be the diameter of circle A
Let D_{B} be the diameter of circle B
Since the ratio of circumference to diameter is the same for all circles, you can use the following proportion to solve this problem
Things that we know:
C_{A} = 4 × C_{B}
D_{B} = 7
Replace these in the proportion
= 8 then, 2 × 20 = 5 × 8 |
= C_{B} then, 4 × C_{B} × 7 = D_{A} × C_{B} |
28 × C_{B} = D_{A} × C_{B}
D_{A} = 28 since 28 × C_{B} = 28 × C_{B} no matter what C_{B} is
Examples #5
If the circumference of a circle is 50.24 inches, calculate r.
Things that we know:
C_{A} = 4 × C_{B}
D_{B} = 7
Replace these in the proportion
= 8 then, 2 × 20 = 5 × 8 |
Then, 4 × C_{B} × 7 = D_{A} × C_{B}
28 × C_{B} = D_{A} × C_{B}
D_{A} = 28 since 28 × C_{B} = 28 × C_{B} no matter what C_{B} is
Examples #5
If the circumference of a circle is 50.24 inches, calculate r.
Circumference of a circle quiz. See how well you can calculate the circumference or perimeter of a circle.
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Circumference (perimeter) of a circle definition
Circumference, Perimeter of a circle
From Latin: circum «around» + ferre «to carry»
The distance around the edge of a circle. Also ‘periphery’ , ‘perimeter’.
Try this Drag the orange dots to move and resize the circle. The circumference is shown in blue.
Note the radius changes and the circumference is calculated for that radius.
You sometimes see the word ‘circumference’ to mean the curved line that goes around the circle.
Other times it means the length of that line, as in «the circumference is 2.11cm».
The word ‘perimeter’ is also sometimes used, although this usually refers to the distance around polygons,
figures made up of straight line segments.
If you know the radius
Given the radius of a circle,
the circumference can be calculated using the formula
where:
R is the radius of the circle
π is Pi, approximately 3.142
See also Derivation of circumference formula
If you know the diameter
If you know the diameter of a circle, the circumference can be found using the formula
where:
D is the diameter of the circle
π is Pi, approximately 3.142
See also Derivation of circumference formula
If you know the area
If you know the area of a circle, the circumference can be found using the formula
where:
A is the area of the circle
π is Pi, approximately 3.142
See also Derivation of circumference formula
Calculator
Use the calculator on the right to calculate the properties of a circle.
Enter any single value and the other three will be calculated.
For example: enter the radius and press ‘Calculate’. The area, diameter and circumference will be calculated.
Similarly, if you enter the area, the radius needed to get that area will be calculated, along with the diameter and circumference.
Related measures
- Radius
The radius is the distance from the center of the circle to any point on the perimeter.
See radius of a circle. - Diameter
The distance across the circle. See
Diameter of a Circle for more.
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Other circle topics
General
Equations of a circle
Angles in a circle
Arcs
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Circumference of a circle
CIRCUMFERENCE OF A CIRCLE
Another term of Perimeter of a circle is known as circumference of a circle.
This page is going to guide you how to find the perimeter of a circle.
Formula :
Circumference of circle = 2
Π r
Here the value of
Π is either 22/7 or 3.14 and «r» stands for radius of a circle.
Here the length of the red line is known as circumference of a circle. Now
let us see some example problems to understand this topic better.
Example 1:
Find the circumference of a circle whose radius is 14 cm.
Solution:
To find the circumference of circle we need to use the formula to find the
circumference of circle.
Circumference of circle = 2 Πr
= 2 ⋅ (22/7) ⋅ 14
= 2 ⋅ 22 ⋅ 2
= 4 ⋅ 22
= 8 cm
Example 2:
Find the diameter of circle whose circumference is 42 cm.
Solution:
Circumference of circle = 42 cm
2 Π r = 42
2 ⋅ (22/7) ⋅ r = 42
r = (42 ⋅ 7) / (2 ⋅ 22)
r = 294/44
r = 6.68 cm
Now we have to find the diameter for that we have to multiply the radius by
2.
Diameter = 2 r
= 2(6.68)
= 13.36 cm
Example 3:
A moon is about 384000 km away from the earth and its path around the earth is nearly circular. Find the distance traveled by moon every month.
Solution :
In one month, the moon describes a full circle about the earth.
Now the circumference = 2 Π r
= 2 ⋅ (22/7) ⋅ 384000 km
= 2413714 km
Hence the distance traveled by the moon = 2413714 km
Example 4 :
A copper wire is in the form of a circle with radius 35 cm. It is bent into a square. Determine the side of the square.
Solution :
Given: Radius of a circle, r = 35 cm.
Since the same wire is bent into the form of a square,
Perimeter of the circle = Perimeter of the square
Perimeter of the circle = 2Πr units
= 2 ⋅ (22/7) ⋅ 35
P = 220 cm
Let ‘a’ be the side of a square.
Perimeter of a square = 4a units
4a = 220
a = 55 cm
Side of the square = 55 cm.
After having gone through the stuff above, we hope that the students would have understood circumference of a circle.
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Math Made Easy—How to Find the Circumference of a Circle
Circumference of Circle
Understanding what the circumference of a circle is, as well as how to calculate the circumference of a circle is a relatively easy geometry principle. By following the circumference problems and solutions in the Geometry Help Online section below, you should easily be able grasp the concept of circumference.
By following along with the examples given and taking the online Math Made Easy! geometry quiz for circumference of a circle, you will be able to complete your geometry homework on this topic in a snap.
Circumference of Circle Formula
The circumference of a circle is merely the distance around a circle. Sometimes it is referred to as the perimeter, although the term perimeter is usually reserved for the measure of a distance around a polygon.
The equation for the circumference of a circle can be written in two ways:
Where: r represents the radius of the circle and d represents a circle’s diameter.
Recall that the radius is the distance from the center of the circle to a point on the edge of a circle and the diameter is the largest distance across a circle. The diameter is always twice the length of the radius.
When calculating the circumference with a known radius use the first version of the circumference formula shown; when the diameter is known use the second version of the circumference formula shown.
Modern Day Uses for Circumference
Did you know that the circumference of the Earth was first calculated more than 2200 years ago by the Greek mathematician, Eratosthenes?
Knowing how to calculate circumference is used in many fields of study, including:
- engineers
- architects
- carpenters
- artists
Math Made Easy! Tip
If you have trouble remembering geometry terms, it helps to think of other words from the same root with which you may be more familiar.
For example, the Latin root of the word circumference is circum, meaning around. Circum is now considered a prefix also meaning around or round about.
Here is a list of words that come from the root/prefix circum that can help you remember that circumference the distance of measure around a circle:
- Circus — (from the root circum) usually held in a circular arena
- Circle — (from the root circum) a round shape
- Circumvent — to go around or bypass; to avoid
- Circumstances — conditions surrounding and event
- Circumnavigate — to fly or sail around
Geometry Help Online: Circumference
Check out 4 common types of geometry homework problems and solutions involving the circumference of circles.
#1 Find the Circumference of a Circle Given the Radius
Problem: Find the circumference of a circle with a radius of 20 cm.
Solution: Plug in 20 for r in the formula C = 2 πr and solve.
- C = (2)(π)(20)
- C = 40π
- C = 125.6
Answer: A circle with a diameter of 20 cm. has a circumference of 125.6 cm.
#2 Find the Circumference of a Circle Given the Diameter
Problem: Find the circumference of a circle with a diameter of 36 in.
Solution: Simply plug in 36 for d in the formula C = πd and solve.
- C = (π)(36)
- C = (3.14)(36)
- C = 113
Answer: The circumference of a circle with a diameter of 36 in. is 113 in.
#3 Find the Radius of a Circle Given the Circumference
Problem: What is the radius of a circle with a circumference of 132 ft.?
Solution: Since we are trying to determine the radius, plug in the known circumference, 132, for C in the formula C = 2πr and solve.
- 132 = 2πr
- 66 = πr (divide both sides by 2)
- 66 = (3.14)r
- r = 21 (divide both sides by 3.14)
Answer: A circle with a circumference of 132 ft. has a radius of about 21 ft.
#4 Find the Circumference of a Circle Given the Area
Problem: Find the circumference of a circle that has an area of 78.5 m. squared.
Solution: This is a two-step problem. First, since we know the area of the circle we can figure out the radius of the circle by plugging in 78.5 for A in the area of a circle formula A = πr^{2} and solving:
- 78.5 = πr^{2}
- 78.5 = (3.14)r^{2}
- 25 = r^{2}(divide both sides by 3.14)
- r = 5 (take the square root of both sides)
Now that we know the radius is equal to 5 m. we can substitute 5 in for r in the formula C = 2πr and solve:
- C = 2π(5)
- C = (2)(3.14)(5)
- C = 31.4
Answer: A circle with an area of 78.5 m. squared has a circumference of 31.4 m.
Do you need more geometry help online?
If you still need help with other geometry problems about the circumference of a circle, please ask in the comment section below. I’ll be glad to help out and may even include circumference math problem in the problem/solution section above.
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Radius, Diameter, Circumference, and Area of Circles
- Education
- Math
- Trigonometry
- Radius, Diameter, Circumference, and Area of Circles
By Mary Jane Sterling
A circle is a geometric figure that needs only two parts to identify it and classify it: its center (or middle) and its radius (the distance from the center to any point on the circle). After you’ve chosen a point to be the center of a circle and know how far that point is from all the points that lie on the circle, you can draw a fairly decent picture.
With the measure of the radius, you can tell a lot about the circle: its diameter (the distance from one side to the other, passing through the center), its circumference (how far around it is), and its area (how many square inches, feet, yards, meters — what have you — fit into it).
Ancient mathematicians figured out that the circumference of a circle is always a little more than three times the diameter of a circle. Since then, they narrowed that “little more than three times” to a value called pi (pronounced “pie”), designated by the Greek letter π.
The decimal value of π isn’t exact — it goes on forever and ever, but most of the time, people refer to it as being approximately 3.14 or 22/7, whichever form works best in specific computations.
The formula for figuring out the circumference of a circle is tied to π and the diameter:
Circumference of a circle: C = πd = 2πr
The d represents the measure of the diameter, and r represents the measure of the radius. The diameter is always twice the radius, so either form of the equation works.
Similarly, the formula for the area of a circle is tied to π and the radius:
Area of a circle: A = πr^{2}
This formula reads, “Area equals pi are squared.”
Find the radius, circumference, and area of a circle if its diameter is equal to 10 feet in length.
If the diameter (d) is equal to 10, you write this value as d = 10. The radius is half the diameter, so the radius is 5 feet, or r = 5. You can find the circumference by using the formula
So, the circumference is about 31.5 feet around. You find the area by using the formula
so the area is about 78.5 square feet.
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Math Expression: Circumference of a Circle
Part 2
00:00:04.090
Let’s take a look at some examples, on using the formula for the circumference of a circle.
00:00:10.230
In these examples, we take pi as 3.14.
00:00:16.150
Find the circumference of this circle, with the radius of 3cm.
00:00:22.190
Now, we can start with the formula for the circumference of a circle, ‘C’ equals to, 2 pi r.
00:00:30.210
Since the radius is given as 3cm, we can substitute ‘r’ with 3..
00:00:38.100
Similarly, since pi is given as 3.14, we can substitute this with, 3.14.
00:00:47.000
Now, let’s calculate this.
00:00:50.140
3.14, multiply with 3, gives 9.42.
00:00:57.000
2, multiply with 9.42, gives 18.84.
00:01:03.190
Hence, we have ‘C’ equals to, 18.84.
00:01:09.160
Now, this number has no meaning unless we include the unit for it.
00:01:14.200
Since the radius of the circle is in centimeter, the circumference must also be in centimeter.
00:01:21.230
Hence, the circumference of the circle is, 18.84cm.
00:01:30.040
Next example. Find the diameter of this circle, when its circumference is 15.7ft.
00:01:39.080
Since we are finding the diameter, we can use the formula, ‘C’ equals to, pi ‘D’.
00:01:47.050
We can see that, the circumference, and pi are given. Hence, we can find the diameter of the circle, by solving the equation for ‘D’.
00:01:58.080
Here’s how. The circumference is given as 15.7. Hence, we can substitute ‘C’ with 15.7.
00:02:09.140
Next, since pi is given as 3.14. We can substitute this, with 3.14.
00:02:18.170
To find ‘D’, we need to remove 3.14.
00:02:24.020
We can do so, by dividing both sides of the equation with 3.14.
00:02:30.110
Hence, we get, 15.7 over 3.14 equals to ‘D’.
00:02:38.120
15.7, divided by 3.14, gives 5.
00:02:44.210
Now, we have ‘d’, equals to 5.
00:02:49.070
Let’s rewrite this equation so that it looks neater.
00:02:54.030
Now, let’s include the unit for this number. Since the circumference is given in ft, the diameter will also be in feet.
00:03:04.010
Hence, the diameter of the circle is 5 ft.
00:03:09.170
That is all. Try out the practice question to test your understanding.
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