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 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
/
20
then, 2 × 20 = 5 × 8


=
C_{B}
/
7
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.