Circumference to Diameter Formula

d = C ÷ π

Divide the distance around (the circumference) by pi, about 3.14, to get the distance straight across (the diameter).

The diameter formula and the circumference formula

The formula at the top of the page, d = C ÷ π, turns the circumference into the diameter. Here are two more: one turns the diameter back into the circumference, and one gives the radius.

C = π × d circumference from the diameter
r = C ÷ (2 × π) radius from the circumference: divide by 3.14, then halve

C is the circumference, the distance around. d is the diameter, the distance straight across through the middle. r is the radius, half the diameter. ÷ means divide and × means multiply.

π, written pi and said "pie", is the same for every circle: the distance around is always a little more than 3 times the distance across. Its exact value goes on forever (3.14159…), but 3.14 is close enough for homework and for a tape measure.

How to find diameter from circumference

Measure the distance around, then divide it by 3.14. Three everyday examples:

A string wrapped around a jar lid reads 9 in. 9 ÷ 3.14 = 2.87, so the lid is just under 3 in across.
A bike tire measures 207 cm around. 207 ÷ 3.14 = 65.9, so the wheel is about 66 cm across.
A tape around a tree trunk reads 60 in. 60 ÷ 3.14 = 19.1, so the trunk is about 19 in across. Tree experts measure trunks at about chest height so every tree is measured the same way; the tree diameter calculator works it out for any trunk.

To check your answer: the width across should be a bit less than a third of the distance around.

Circumference to diameter chart

Look for your distance around in the left column; the widths across are beside it. The numbers use the exact value of pi and are rounded to two digits after the point.

Circumference in inches

Circumference (in)	Diameter (in)	Diameter (cm)
1	0.32	0.81
2	0.64	1.62
3	0.95	2.43
4	1.27	3.23
5	1.59	4.04
6	1.91	4.85
7	2.23	5.66
8	2.55	6.47
9	2.86	7.28
10	3.18	8.09
12	3.82	9.70
15	4.77	12.13
18	5.73	14.55
24	7.64	19.40
36	11.46	29.11

Circumference in centimeters

Circumference (cm)	Diameter (cm)	Diameter (in)
5	1.59	0.63
10	3.18	1.25
15	4.77	1.88
20	6.37	2.51
25	7.96	3.13
30	9.55	3.76
40	12.73	5.01
50	15.92	6.27
60	19.10	7.52
70	22.28	8.77
80	25.46	10.03
90	28.65	11.28
100	31.83	12.53
150	47.75	18.80
200	63.66	25.06

How to find circumference from diameter

Measure straight across the circle, through the middle. That is the diameter.
Multiply it by 3.14.
The answer is the circumference, in the same unit. A plate 10 in across: 10 × 3.14 = 31.4 in around.

Circumference to radius

The radius is the distance from the middle of the circle to its edge, so it is half the diameter. Find the diameter first, then cut it in half.

A hoop 94.2 cm around is 94.2 ÷ 3.14 = 30 cm across, so its radius is 15 cm.

To get the distance around from a radius, first double the radius to get the diameter, then multiply that by 3.14. A radius of 4 in gives 8 in across, and 8 × 3.14 = 25.1 in around.

Circumference and diameter worksheet

Two printable versions, A and B, each with 16 problems and the answers (the answer key) on a separate page. Use 3.14 for pi and round each answer to one decimal place, one number after the point.

Preview the problems and answers

Version A

Circumference and diameter worksheet A

NameDate

Use π = 3.14 and round each answer to one decimal place.

Diameter from circumference

The circumference is 31.4 cm. Find the diameter.
The circumference is 47.1 in. Find the diameter.
The circumference is 25 cm. Find the diameter.
The circumference is 100 mm. Find the diameter.

Circumference from diameter

The diameter is 6 cm. Find the circumference.
The diameter is 12 in. Find the circumference.
The diameter is 2.4 m. Find the circumference.
The diameter is 45 mm. Find the circumference.

Radius

The circumference is 18.84 cm. Find the radius.
The radius is 5 in. Find the circumference.
The circumference is 50 cm. Find the radius.
The radius is 2.6 m. Find the circumference.

Word problems

A string wrapped once around a pipe measures 11 cm. How wide is the pipe across?
A bike wheel is 66 cm across. How far does it roll in one full turn?
A round cake pan is 9 in across. How long a strip of paper wraps once around its side?
A tape around a tree trunk reads 157 cm. What is the trunk's diameter?

Answer key A

Answers use π = 3.14, rounded to one decimal place.

10.0 cm
15.0 in
8.0 cm
31.8 mm
18.8 cm
37.7 in
7.5 m
141.3 mm
3.0 cm
31.4 in
8.0 cm
16.3 m
3.5 cm
207.2 cm
28.3 in
50.0 cm

Free to copy for classroom use with credit to girthtodiameter.com (CC BY 4.0).

Version B

Circumference and diameter worksheet B