
You Can Draw It Yourself
Put a pin in a board, put a loop of string around it, and insert a pencil into the loop. Keep the string stretched and draw the circle!
Try dragging the point to see how the radius and circumference change.
(See if you can keep a constant radius!)
 The Radius is the distance from the center outwards.
 The Diameter goes straight across the circle, through the center.
 The Circumference is the distance once around the circle.
 And here is the really cool thing:
When we divide the circumference by the diameter we get 3.141592654…
which is the number π (Pi)
So when the diameter is 1, the circumference is 3.141592654… 
We can say:
Circumference = π × Diameter
Distance walked = Circumference = π × 100m
= 314m (to the nearest m)
 Also note that the Diameter is twice the Radius:
 Diameter = 2 × Radius
 And so this is also true:
 Circumference = 2 × π × Radius
 In Summary:
Remembering
The length of the words may help you remember:
 Radius is the shortest word and shortest measure
 Diameter is longer
 Circumference is the longest
Definition
The circle is a plane shape (two dimensional), so: 
Area
 The area of a circle is π times the radius squared, which is written:
 A = π r2
 Where
 A is the Area
 r is the radius
To help you remember think “Pie Are Squared” (even though pies are usually round):
Area= πr2
= π × 1.22
= 3.14159… × (1.2 × 1.2)
= 4.52 (to 2 decimals)
Or, using the Diameter:
A = (π/4) × D2
Area Compared to a Square
A circle has about 80% of the area of a similarwidth square.
The actual value is (π/4) = 0.785398… = 78.5398…%
And something interesting for you:
See Circle Area by Lines
Names
 Because people have studied circles for thousands of years special names have come about.
 Nobody wants to say “that line that starts at one side of the circle, goes through the center and ends on the other side” when they can just say “Diameter”.
 So here are the most common special names:
Lines
 A line that “just touches” the circle as it passes by is called a Tangent.
 A line that cuts the circle at two points is called a Secant.
 A line segment that goes from one point to another on the circle's circumference is called a Chord.
 If it passes through the center it is called a Diameter.
 And a part of the circumference is called an Arc.
 There are two main “slices” of a circle.
 The “pizza” slice is called a Sector.
 And the slice made by a chord is called a Segment.
 The Quadrant and Semicircle are two special types of Sector:
 Quarter of a circle is called a Quadrant.
 Half a circle is called a Semicircle.
A circle has an inside and an outside (of course!).
But it also has an “on”, because we could be right on the circle.
Example: “A” is outside the circle, “B” is inside the circle and “C” is on the circle.
Ellipse
A circle is a “special case” of an ellipse.
Activity: Approximate Value For Pi
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Circumference of a Circle
A circle is a shape with all points the same distance from the center. It is named by the center. The circle to the left is called circle A since the center is at point A. If you measure the distance around a circle and divide it by the distance across the circle through the center, you will always come close to a particular value, depending upon the accuracy of your measurement. This value is approximately 3.14159265358979323846… We use the Greek letter (pronounced Pi) to represent this value. The number goes on forever. However, using computers, has been calculated to over 1 trillion digits past the decimal point.
The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter. is the ratio of the circumference of a circle to the diameter. Thus, for any circle, if you divide the circumference by the diameter, you get a value close to . This relationship is expressed in the following formula:
where is circumference and is diameter. You can test this formula at home with a round dinner plate. If you measure the circumference and the diameter of the plate and then divide by , your quotient should come close to . Another way to write this formula is: where · means multiply. This second formula for finding the circumference of a circle is commonly used in problems where the diameter is given and the circumference is not known (see the examples below).
The radius of a circle is the distance from the center of a circle to any point on the circle.
If you place two radii endtoend in a circle, you would have the same length as one diameter. Thus, the diameter of a circle is twice as long as the radius.
This relationship is expressed in the following circumference of a circle formula: , where is the diameter and is the radius.
Circumference, diameter and radii are measured in linear units, such as inches and centimeters. A circle has many different radii and many different diameters, each passing through the center. A reallife example of a radius is the spoke of a bicycle wheel.
A 9inch pizza is an example of a diameter: when one makes the first cut to slice a round pizza pie in half, this cut is the diameter of the pizza. So a 9inch pizza has a 9inch diameter. Let's look at some examples of finding the circumference of a circle.
In these examples, we will use = 3.14 to simplify our calculations.
Example 1: The radius of a circle is 2 inches. What is the diameter?
 Solution:
 = 2 · (2 in)
 = 4 in
Example 2: The diameter of a circle is 3 centimeters. What is the circumference?
 Solution:
 = *
 = 3.14 · (3 cm)
 = 9.42 cm
Example 3: The radius of a circle is 2 inches. What is the circumference?
 Solution:
 = 2 · (2 in)
 = 4 in
 = *
 = 3.14 · (4 in)
 = 12.56 in
Example 4: The circumference of a circle is 15.7 centimeters. What is the diameter?
Solution:
= *
15.7 cm = 3.14 ·
15.7 cm ÷ 3.14 =
= 15.7 cm ÷ 3.14
= 5 cm
Summary: The number is the ratio of the circumference of a circle to its diameter. The value of is approximately 3.14159265358979323846…The diameter of a circle is twice the radius.
Given the diameter or radius of a circle, we can find the circumference. We can also find the diameter (and radius) of a circle given the circumference. The formulas for diameter and circumference of a circle are listed below.
We round to 3.14 in order to simplify our calculations.
= *
Exercises
Circumference of a circle questions: Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR. Use = 3.14 to calculate your answers.
1.  The diameter of a nickel is 2 centimeters. What is the circumference? 
2.  The circumference of a bicycle wheel is 50.24 inches. What is the diameter? 
3.  The radius of a circular rug is 4 feet. What is the circumference? 
4.  The circumference of a compact disc is 28.26 centimeters. What is the radius? 
5.  The diameter of your bicycle wheel is 25 inches. How far will you move in one turn of your wheel? 
Circumference
Circumference (C in black) of a circle with diameter (D in cyan), radius (R in red), and centre (O in magenta). Circumference = π × diameter = 2 × π × radius.
Geometry GeometersProjecting a sphere to a plane.  


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In geometry, the circumference (from Latin circumferens, meaning “carrying around”) is the perimeter of a circle or ellipse.[1] That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment.[2] More generally, the perimeter is the curve length around any closed figure.
Circumference may also refer to the circle itself, that is, the locus corresponding to the edge of a disk.
Circle
The circumference of a circle is the distance around it, but if, as in many elementary treatments, distance is defined in terms of straight lines, this cannot be used as a definition.
Under these circumstances, the circumference of a circle may be defined as the limit of the perimeters of inscribed regular polygons as the number of sides increases without bound.
[3] The term circumference is used when measuring physical objects, as well as when considering abstract geometric forms.
When a circle's diameter is 1, its circumference is π.
When a circle's radius is 1—called a unit circle—its circumference is 2π.
Relationship with π
The circumference of a circle is related to one of the most important mathematical constants. This constant, pi, is represented by the Greek letter π. The first few decimal digits of the numerical value of π are 3.141592653589793 …[4] Pi is defined as the ratio of a circle's circumference C to its diameter d:
π
=
C
d
.
{displaystyle pi ={frac {C}{d}}.}
Or, equivalently, as the ratio of the circumference to twice the radius. The above formula can be rearranged to solve for the circumference:
C
=
π
⋅
d
=
2
π
⋅
r
.
{displaystyle {C}=pi cdot {d}=2pi cdot {r}.!}
The use of the mathematical constant π is ubiquitous in mathematics, engineering, and science.
In Measurement of a Circle written circa 250 BCE, Archimedes showed that this ratio (C/d, since he did not use the name π) was greater than 310/71 but less than 31/7 by calculating the perimeters of an inscribed and a circumscribed regular polygon of 96 sides.[5] This method for approximating π was used for centuries, obtaining more accuracy by using polygons of larger and larger number of sides. The last such calculation was performed in 1630 by Christoph Grienberger who used polygons with 1040 sides.
Ellipse
Main article: Ellipse § Circumference
Circumference is used by some authors to denote the perimeter of an ellipse.
There is no general formula for the circumference of an ellipse in terms of the semimajor and semiminor axes of the ellipse that uses only elementary functions.
However, there are approximate formulas in terms of these parameters. One such approximation, due to Euler (1773), for the canonical ellipse,
x
2
a
2
+
y
2
b
2
=
1
,
{displaystyle {frac {x^{2}}{a^{2}}}+{frac {y^{2}}{b^{2}}}=1,}
is
C
e
l
l
i
p
s
e
∼
π
2
(
a
2
+
b
2
)
.
{displaystyle C_{
m {ellipse}}sim pi {sqrt {2(a^{2}+b^{2})}}.}
Some lower and upper bounds on the circumference of the canonical ellipse with
a
≥
b
{displaystyle ageq b}
are[6]
2
π
b
≤
C
≤
2
π
a
,
{displaystyle 2pi bleq Cleq 2pi a,}
π
(
a
+
b
)
≤
C
≤
4
(
a
+
b
)
,
{displaystyle pi (a+b)leq Cleq 4(a+b),}
4
a
2
+
b
2
≤
C
≤
π
2
(
a
2
+
b
2
)
.
{displaystyle 4{sqrt {a^{2}+b^{2}}}leq Cleq pi {sqrt {2(a^{2}+b^{2})}}.}
Here the upper bound
2
π
a{displaystyle 2pi a}
is the circumference of a circumscribed concentric circle passing through the endpoints of the ellipse's major axis, and the lower bound
4
a
2
+
b
2
{displaystyle 4{sqrt {a^{2}+b^{2}}}}
is the perimeter of an inscribed rhombus with vertices at the endpoints of the major and minor axes.
The circumference of an ellipse can be expressed exactly in terms of the complete elliptic integral of the second kind.[7] More precisely, we have
C
e
l
l
i
p
s
e
=
4
a
∫
0
π
/
2
1
−
e
2
sin
2
θ
d
θ
,
{displaystyle C_{
m {ellipse}}=4aint _{0}^{pi /2}{sqrt {1e^{2}sin ^{2} heta }} d heta ,}
where again
a
{displaystyle a}
is the length of the semimajor axis and
e
{displaystyle e}
is the eccentricity
1
−
b
2
/
a
2
.
{displaystyle {sqrt {1b^{2}/a^{2}}}.}
Graph
In graph theory the circumference of a graph refers to the longest (simple) cycle contained in that graph.[8]
See also
 Arc length
 Area
 Isoperimetric inequality
References
 ^ San Diego State University (2004). “Perimeter, Area and Circumference” (PDF). AddisonWesley. Archived from the original (PDF) on 6 October 2014.
 ^ Bennett, Jeffrey; Briggs, William (2005), Using and Understanding Mathematics / A Quantitative Reasoning Approach (3rd ed.
), AddisonWesley, p. 580, ISBN 9780321227737
 ^ Jacobs, Harold R. (1974), Geometry, W. H. Freeman and Co., p. 565, ISBN 0716704560
 ^ Sloane, N. J. A. (ed.). “Sequence A000796”. The OnLine Encyclopedia of Integer Sequences. OEIS Foundation.
 ^ Katz, Victor J.
(1998), A History of Mathematics / An Introduction (2nd ed.), AddisonWesley Longman, p. 109, ISBN 9780321016188
 ^ Jameson, G.J.O. (2014). “Inequalities for the perimeter of an ellipse”. Mathematical Gazette. 98 (499): 227–234. doi:10.2307/3621497. JSTOR 3621497.
 ^ Almkvist, Gert; Berndt, Bruce (1988), “Gauss, Landen, Ramanujan, the arithmeticgeometric mean, ellipses, π, and the Ladies Diary”, American Mathematical Monthly, 95 (7): 585–608, doi:10.
2307/2323302, JSTOR 2323302, MR 0966232, S2CID 119810884
 ^ Harary, Frank (1969), Graph Theory, AddisonWesley, p. 13, ISBN 0201027879
External links
The Wikibook Geometry has a page on the topic of: Arcs 
Look up circumference in Wiktionary, the free dictionary. 
 Numericana – Circumference of an ellipse
Circumference of a Circle (Definition, Formula & Examples)
Circumference of the circle or perimeter of the circle is the measurement of the boundary across any twodimensional circular shape including circle. Whereas the area of circle, defines the region occupied by it. If we open a circle and make a straight line out of it, then its length is the circumference. It is usually measured in unit cm or unit m.
When we use the formula to calculate the circumference of the circle, then the radius of the circle is taken into account. Hence, we need to know the value of radius or the diameter to evaluate the perimeter of circle.
Circumference of a Circle Formula
 The Circumference (or) perimeter of a circle = 2πR
 where,
 R is the radius of the circle
 π is the mathematical constant with an approximate (up to two decimal points) value of 3.14
 Again,
 Pi (π) is a special mathematical constant, it is the ratio of circumference to diameter of any circle.
 where C = π D
 C is the circumference of the circle
 D is the diameter of the circle
 For example: If radius of the circle is 4cm then find its circumference.
 Given: Radius = 4cm
 Circumference = 2πr
 = 2 x 3.14 x 4
 = 25.12 cm
 Also, check:

Area of a Circle Formula
Area of any circle is the region enclosed by the circle itself or the space covered by the circle. The formula to find the area of the circle is;
A = πr2
Where r is the radius of the circle. This formula is applicable to all the circles with different radii.
Perimeter of SemiCircle
The semicircle is formed when we divide the circle into two equal parts. Therefore, the perimeter of the semicircle also becomes half.
Hence, Perimeter = 2πr/2 = πr
Area of SemiCircle
Area of the semicircle is the region occupied by a semicircle in a 2D plane. The area of the semicircle is equal to half of the area of a circle, whose radii are equal.
Therefore, Area = πr2/2
Summary
Circumference of Circle  2πr 
Area of circle  πr2 
Perimeter of semicircle  πr 
Area of semicircle  πr2/2 
Radius of a Circle
What Is the Circumference of a Circle?
Scientific American presents Math Dude by Quick & Dirty Tips. Scientific American and Quick & Dirty Tips are both Macmillan companies.
Throughout history, circles have symbolized many things: unity, protection, the Sun, infinity, and the Olympic Games, to name a few. Of course, philosophers and symbologists aren’t the only people to have taken an interest in circles. Mathematicians have spent millennia studying them, too.
Which is precisely why today’s article is all about circles.
In particular, after a quick refresher of circle basics, we’re going to figure out why the equation for the circumference of a circle that we all learned in school works, and we’re also going to learn how this equation is used to set up lots of Olympic track and field events.
What Is a Circle? My favorite way to define a circle is in terms of how to draw one. In the episode What Is Pi? we learned how to draw a circle artsandcrafts style. To do this, start by cutting a 3inch piece of string to serve as the radius of the circle. What’s the radius? It’s half the diameter.
Okay, but what’s the diameter? As you’ll soon be able to test with your finished drawing, it’s the greatest distance between any two points on the circle. Now, pin one end of the string down with your finger near the center of a normal sheet of binder paper, and then hold the loose end of the string up against the lead of your pencil.
Finally, pull the pencil so the string is taut and trace out your circle.
What does this all mean? Believe it or not, it means we’ve found a very good way to define a circle. Namely, a circle is the set of all points (that’s the curve you drew with your pencil) that are all the same distance from some common point (that’s the spot where you pinned the string down with your finger).
> Continue reading on QuickAndDirtyTips.com
Circumference (Perimeter) of a circle
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 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 above 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.
 Inscribed angle
 Central angle
 Central angle theorem
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