The circumference is the distance around a circle.
Place a piece of string round the
circle and then open it out flat:
diameter
Measure the length of the line:
Measure the diameter of the circle.
What is the connection between the diameter
and the circumference?
Measure the distance around the outside of each circle. Measure
the diameter of each circle and complete the table.
Circle Circumference
A
B
C
D
Diameter
Circle D
Circle B
Circle A
Circl
eC
The circumference is the distance around a
circle.
1
2
diameter
circumference
3
0.1
Circumference is equal to roughly 3 x
diameter…….and this works or every
circle!
It’s not easy to use a ruler to measure the
distance around a circle.
A formula for the circumference makes finding it
easy.
A formula for the connection
between the circumference
and the diameter is
d
C  d
The symbol, , (pi) is said as
pie, and is 3.14 (to 2 dp). This
is how accurate we need to be
on the GCSE calculator paper.
How to find circumference given the diameter of a circle
Find the circumference of the circle below:
If you have the diameter: multiply the diameter
by 3.14 ().
State the formula
C  d
10 c
m
Substitute the values for 
and d.
C  3.14  10
C  31.4 cm
Questions: Given diameter, find the
circumference
How to find circumference given the radius
Find the circumference of the circle below:
If you have the radius: multiply this by 2 first to
get the diameter. Then multiply the diameter by
3.14 ().
State the formula
C  d
3m
Substitute the values for 
and d.
d  23  6
C  3.14  6
C  18.84 m
Questions:Given radius, calculate the
circumference
Review
Answers
A
B
C
D
E
r = 3 cm r = 5 cm d = 3 cm r = 7 cm d = 4 cm d
F
= 2.5 cm
1
2
3
4
5
6
12.6
18.8
9.4
7.9
31.4
44.0
6
18.84955592
A2
10
31.41592654
B5
3
9.424777961
C3
14
43.98229715
D6
4
12.56637061
E1
2.5
7.853981634
F4
cm
cm
cm
cm
cm
cm
What’s the formula?
Calculate the missing numbers in the table
below using the circumference formula below.
C  d
Use 3.14 as an approximation for .
r (cm)
5
3.4
2.15
d (cm)
C (cm)
10
6.8
31.4
21.352
13.502
4.3
Plenary
• You should know the words used in a circle
to include the diameter, radius, circumference
and .
• Know that  is roughly 3.14.
• Know and use the formula for the
circumference of a circle. C   d or C  2 r
Find the circumference of each circle below.
12 c
m
C  d
C  3.14  12
C  37.68 cm
8 cm
C  d
d  2  8  16
C  3.14  16
C  50.24 cm