Arithmetic Additive Identity Associative Property Averages Brackets Closure Property Commutative Property Conversion of Measurement Units Cube Root Decimal Distributivity of Multiplication over Addition Divisibility Principles Equality Exponents Factors Fractions Fundamental Operations H.C.F / G.C.D Integers L.C.M Multiples Multiplicative Identity Multiplicative Inverse Numbers Percentages Profit and Loss Ratio and Proportion Simple Interest Square Root Unitary Method
Algebra Algebraic Equation Algebraic Expression Order Relation Standard Identities & their applications Transpose Cartesian System Linear Equations Probability Polynomials
Geometry Circle Curves Angles Define Line, Line Segment and Rays NonCollinear Points Polygons and its Types Rectangle Rhombus Square Three dimensional object Trapezium Basic Geometrical Terms Parallelogram Triangle
Trigonometry Trigonometry Ratios
DataHandling Arithmetic Mean Graphs Median Mode Range Frequency Distribution Table 
Home >> Circle >> Circumference of circle >> Circumference of circle
Definition:The distance around a circular region is known as “Circumference of Circle”
Or, In other words, perimeter of circle is also referred to as “Circumference of Circle”
In the following figure.
Points A, B, C, D, E all fall on the circular region of circle i.e Circumference of Circle.
Formula for finding Circumference of Circle :
circumference of circle = 2 (𝜋) radius
or circumference of circle = (𝜋) diameter
In order to understand the relevance of this formula, consider following table :
Radius  Diameter  circumference  Ration of Circumference to Diameter  1  2  6  3.00  2  4  13  3.25  3  6  19  3.17  4  8  25  3.13  5  10  31  3.10  6  12  38  3.17  7  14  44  3.14  8  16  51  3.19  9  18  57  3.17  10  20  63  3.15 
From the above table you can make out that :
1. Circumference of Circle is always greater than three times of diameter.
2. Ratio of Circumference to Diameter falls between 3 and 3.3
Hence ratio of circumference to diameter is fixed at 3.14 or 22/7 and it is commonly denoted by ‘𝜋’
So formula become :
Circumference / Diameter = 𝜋
or Circumference = 𝜋 X diameter
or Circumference = 𝜋 X ( 2 X radius, as diameter is twice of radius) = 2 𝜋 r
Find circumference of circle when diameter of circle is given
Example 1: Find circumference of circle whose diameter is 14cm
Solution: As given in question:
Diameter (d) = 14 cm (given)
Apply formula of Circumference of Circle when diameter is given
Circumference of Circle = (𝜋) d
Put the value of diameter & 𝜋 and we get:
= (22/7)14
Solve the above expression and we get:
= 44 cm
Hence, circumference of circle = 44 cm
Find circumference of circle when radius of circle is given
Example 2: Find circumference of circle whose radius is 21 cm
Solution : As given in question:
Radius (r) = 21
Apply formula of Circumference of Circle when radius is given
Circumference of Circle = 2 (𝜋) r
Put the value of radius & 𝜋 and we get:
= 2 (22/7)21
Solve the above expression and we get:
= 132 cm
Hence, circumference of circle = 132 cm
Find diameter of circle when its circumference is given
Example 3: Find diameter of circle whose circumference is 22 cm
Solution: As given in question:
Circumference of Circle = 22 cm
Apply formula of Circumference of Circle when diameter is given
Circumference of Circle = (𝜋) d
Put the value of circumference & 𝜋 and we get:
22 = 22/7 d
Multiply both sides with 7/22 and we get:
7 = d
Hence, diameter of circle = 7 cm
Find radius of circle whose circumference is given
Example 4: Find radius of circle whose circumference is 22 cm
Solution: As given in question:
Circumference of Circle = 22 cm
Apply formula of Circumference of Circle when radius is given
Circumference of Circle = 2 (𝜋) r
Put the value of circumference & 𝜋 and we get:
22 = 2 (22/7) r
Divide both side by 2 and we get
11 = (22/7) r
Multiply both sides with 7/22 and we get:
7/2 = r
Convert the fraction into decimal and we get
3.5 = r
Hence, radius of circle = 3.5 cm
Find circumference of circle when area of circle is given
To understand this, you are advice to read:
How to find Area of Circle ?
Example 5: Find circumference of circle, if area of circle is 196 cm^{2}
Solution : As given in the question:
Area of Circle = 616 cm^{2}
This question is solved in two parts:
Part 1 : Find Radius of Circle
Part 2 : Find Circumference of Circle
Part 1 is explained in the following ways:
Apply formula of Area of circle:
Area of Circle = 𝜋 r ^{2}
Put the value of area of circle & 𝜋 and we get:
616 = 22/7 X r^{2}
Multiply both sides by 7/22 and we get:
196 = r^{2}
Take square root of both sides and we get:
r = 14
Therefore, Radius = 14 cm
Part 2 is explained in the following ways:
Apply formula of Circumference of Circle:
Circumference of Circle = 2 (𝜋) r
Put value of radius (from Part 1) & 𝜋 and we get:
=2 X 22/7 X 14
Solve the above expression and we get:
= 88 cm
Hence, circumference of circle = 88 cm


