What is the formula for circumference?

C = πd, or C = 2πr. Both give the same answer, because the diameter is twice the radius. A circle with radius 4 cm has circumference 8π ≈ 25.13 cm.

What's the difference between circumference and area?

Circumference is the distance around the edge of the circle, measured in plain units like cm. Area is the space inside, measured in square units like cm². Circumference uses 2πr; area uses πr².

How do I find the diameter from the circumference?

Divide the circumference by π: d = C ÷ π. Halve that for the radius. If C = 50 cm, d = 50 ÷ π ≈ 15.92 cm and r ≈ 7.96 cm.

How do I find the perimeter of a semicircle?

Add half the circumference to the straight edge (the diameter): P = ½πd + d. For a diameter of 10 cm, P = 5π + 10 ≈ 25.71 cm.

What year level learns circumference?

In the Victorian Curriculum 2.0, Year 7 covers π and the relationship between the circumference, radius and diameter. Year 8 uses the formulas to solve problems, including composite shapes. Arc length is often taught in Year 9 or 10, depending on the school.

How to Find the Circumference of a Circle: Formula, Examples and Calculator (Years 7 to 10)

The circumference formula

C = \pi d = 2\pi r

$\pi$ is the number you get when you divide any circle's circumference by its diameter: about $3.14159$ . That's why $C = \pi d$ . Because the diameter is two radii, $C = 2\pi r$ is the same formula.

Given the diameter: multiply by $\pi$ .
Given the radius: multiply by $2$ , then by $\pi$ .

Circumference from the radius or diameter

Worked example: from the radius

Find the circumference of a circle with radius $4$ cm.

C = 2\pi r = 2 \times \pi \times 4 = 8\pi

C \approx 25.13 \text{ cm}

Worked example: from the diameter

Find the circumference of a circle with diameter $15$ m.

C = \pi d = \pi \times 15 = 15\pi

C \approx 47.12 \text{ m}

$8\pi$ cm is the exact answer; $25.13$ cm is rounded to 2 decimal places.

Circumference calculator (with working)

Enter the radius, diameter, circumference or area. You’ll get all four, with the exact answer in terms of π where it’s tidy and decimals rounded to 2 decimal places.

I know theValueUnits (optional)

Circumference = 10π ≈ 31.42 cm

Radius = 5 cm
Diameter = 10 cm
Circumference = 10π ≈ 31.42 cm
Area = 25π ≈ 78.54 cm²

Radius: $r = 5\text{ cm}$
Diameter: $d = 2r = 2 \times 5 = 10\text{ cm}$
Circumference: $C = 2\pi r = \pi d = \pi \times 10 = 10\pi \approx 31.42\text{ cm}$
Area: $A = \pi r^2 = \pi \times 5^2 = 25\pi \approx 78.54\text{ cm}^2$
Decimal answers are rounded to 2 decimal places using the π button. If your teacher says to use 3.14, your answer may be slightly different.

Pick what you know and enter it. Area units are squared (cm²), lengths are not.

Perimeter of a semicircle and a quarter circle

The perimeter is the whole way around the shape, so include the straight edges as well as the curved part.

\text{semicircle: } P = \frac{1}{2}\pi d + d

Worked example

Find the perimeter of a semicircle with diameter $10$ cm.

\text{curved part} = \frac{1}{2} \times \pi \times 10 = 5\pi

P = 5\pi + 10 \approx 25.71 \text{ cm}

Worked example: quarter circle

Find the perimeter of a quarter circle with radius $6$ cm.

\text{curved part} = \frac{1}{4} \times 2\pi \times 6 = 3\pi

P = 3\pi + 6 + 6 = 3\pi + 12 \approx 21.42 \text{ cm}

Arc length and the perimeter of a sector (Years 9 and 10)

An arc is part of the circumference. If the angle at the centre is $\theta$ degrees, the arc is $\dfrac{\theta}{360}$ of the whole circumference.

l = \frac{\theta}{360} \times 2\pi r

Worked example

A sector has radius $8$ cm and angle $45^\circ$ . Find the arc length and the perimeter of the sector.

l = \frac{45}{360} \times 2 \times \pi \times 8 = \frac{1}{8} \times 16\pi = 2\pi \approx 6.28 \text{ cm}

P = l + 2r = 2\pi + 16 \approx 22.28 \text{ cm}

The perimeter of a sector is the arc plus the two radii. Forgetting the radii is the most common mistake.

How to find the radius or diameter from the circumference

d = \frac{C}{\pi} \qquad r = \frac{C}{2\pi}

Worked example

A circle has a circumference of $50$ cm. Find its diameter and radius.

d = \frac{50}{\pi} \approx 15.92 \text{ cm}

r = \frac{50}{2\pi} \approx 7.96 \text{ cm}

Wheels and distance

Each full turn of a wheel moves it forward one circumference.

Worked example

A bike wheel has a diameter of $60$ cm. How far does the bike travel in $100$ full turns?

C = \pi \times 60 = 60\pi \text{ cm}

100 \times 60\pi = 6000\pi \approx 18\,849.56 \text{ cm}

That's about $188.50$ m.

Common mistakes

Using $\pi r$ instead of $2\pi r$ . With the radius you must double it (or use $\pi d$ ).
Doubling the diameter. $C = \pi d$ already uses the full width. Don't multiply by 2 again.
Mixing up circumference and area. Circumference is $2\pi r$ in cm. Area is $\pi r^2$ in cm².
Leaving out straight edges. The perimeter of a semicircle or sector includes the diameter or the two radii.

Practice questions with answers

Try each one before you open the answer. Decimal answers use the π button and are rounded to 2 decimal places.

Find the circumference of a circle with radius $7$ cm.
Show the answer
$C = 2 \times \pi \times 7 = 14\pi \approx 43.98$ cm
Find the circumference of a circle with diameter $20$ m.
Show the answer
$C = \pi \times 20 = 20\pi \approx 62.83$ m
Find the circumference of a circle with radius $3.5$ mm.
Show the answer
$C = 2 \times \pi \times 3.5 = 7\pi \approx 21.99$ mm
Find the perimeter of a semicircle with diameter $8$ cm.
Show the answer
Curved part: $\dfrac{1}{2} \times \pi \times 8 = 4\pi$ . Add the diameter: $P = 4\pi + 8 \approx 20.57$ cm
Find the arc length of a sector with radius $10$ cm and angle $90^\circ$ .
Show the answer
$l = \dfrac{90}{360} \times 2\pi \times 10 = 5\pi \approx 15.71$ cm
A circle has a circumference of $100$ cm. Find its diameter and radius.
Show the answer
$d = \dfrac{100}{\pi} \approx 31.83$ cm, so $r \approx 15.92$ cm
Find the perimeter of a sector with radius $12$ m and angle $60^\circ$ .
Show the answer
Arc: $\dfrac{60}{360} \times 2\pi \times 12 = 4\pi$ . Add the two radii: $P = 4\pi + 24 \approx 36.57$ m

Circumference by year level

Following the Victorian Curriculum 2.0. Schools sequence topics differently, so check your course.

Year 7

Circles

Radius, diameter, π, and the circumference from the radius or diameter.

Worksheets and topic test · Free PDF with answers

Year 8

Circles

Circumference and area problems, working back to the radius, and semicircles and quadrants.

Worksheets and topic test · Free PDF with answers

Year 8

Area and perimeter

Perimeter of composite shapes, including where some sides need calculating first.

Worksheets and topic test · Free PDF with answers

Year 9

Surface area and volume

The circumference inside the curved surface area of a cylinder, 2πrh.

Worksheets and topic test · Free PDF with answers

How to find the circumference of a circle

The circumference formula

Circumference from the radius or diameter

Circumference calculator (with working)

Perimeter of a semicircle and a quarter circle

Arc length and the perimeter of a sector (Years 9 and 10)

How to find the radius or diameter from the circumference

Wheels and distance

Common mistakes

Practice questions with answers

Circumference by year level

Circumference: common questions

More maths help, Years 7 to 10

Got a circle question wrong in homework?