17.1 Circumference of a Circle 1

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: the parts of a circle, what π means, and working out the circumference. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

• Name the parts of a circle: centre, radius, diameter, circumference, chord, tangent, arc and sector
• Explain what π is and use π ≈ 3.14 when there is no calculator
• Work out the circumference using C = πd or C = 2πr
• Give answers rounded to a sensible accuracy or as an exact answer in terms of π

Key words

• Radius (r): A straight line from the centre to the edge of the circle. The plural is radii.
• Diameter (d): A straight line across the circle through the centre. d = 2r.
• Circumference: C for short. The distance all the way round a circle: the perimeter of the circle.
• Chord: A straight line joining two points on the circle. The longest chord is the diameter.
• Tangent: A straight line outside the circle that touches it at exactly one point.
• π (pi): The number you get when you divide any circumference by its diameter: 3.14159…

The parts of a circle

Every point on the edge of a circle is the same distance from the centre. That distance is the radius. The diameter goes right across, through the centre, so it is two radii long.

Key fact: d = 2 × r and r = d ÷ 2

Worked example: radius and diameter

(a) A circle has radius 7 cm. Diameter = 2 × 7 = 14 cm.
(b) A circular table mat has diameter 9.6 cm. Radius = 9.6 ÷ 2 = 4.8 cm.

Answer: (a) 14 cm (b) 4.8 cm

What is π?

Measure round any circle and divide by its diameter. You always get just over 3. This number is called π (the Greek letter “pi”). It never ends and never repeats: π = 3.141 592 65…

• Dinner plate; Diameter 26 cm; Circumference (measured) 81.7 cm; C ÷ d 3.14…
• Bike wheel; Diameter 62 cm; Circumference (measured) 194.8 cm; C ÷ d 3.14…
• Coin; Diameter 2.2 cm; Circumference (measured) 6.9 cm; C ÷ d 3.1… (hard to measure)

On a calculator paper, use the π key. On a non-calculator paper you are usually told to use π ≈ 3.14, or to leave π in the answer.

Worked example: without a calculator

A hoop has diameter 10 cm. Use π = 3.14 to estimate its circumference.
C = π × d = 3.14 × 10 = 31.4

Answer: 31.4 cm

Working out the circumference

Formulae: C = π × d or C = 2 × π × r

Both give the same answer, because 2r is the diameter. Pick the one that matches what you are given.

Worked example: given the diameter

C = π × 8 = 25.132 741…
Round to 1 decimal place.

Answer: 25.1 cm

Worked example: given the radius

C = 2 × π × 6.5 = 40.840 704…
Round to 1 decimal place.

Answer: 40.8 m

Exact answers and sensible rounding

If a question says “give your answer in terms of π”, do not multiply by π. Leave it as a number times π. This is the exact answer.

Worked example: in terms of π

(a) Radius 5 cm: C = 2 × π × 5 = 10π cm.
(b) Diameter 18 m: C = π × 18 = 18π m.

Answer: (a) 10π cm (b) 18π m

Otherwise, round only at the very end. Write down a few more digits than you need first, so the examiner can see your working, then round.

Worked example: a real-life circle

A circular flower bed has radius 2.3 m. How long is the edging needed to go round it?
C = 2 × π × 2.3 = 14.451 326… m
To the nearest 10 cm (1 decimal place of a metre):

Answer: 14.5 m

Common mistakes

• Using the radius in C = πd. If you are given r, either double it first or use C = 2πr.
• Mixing up the circumference formula with the area formula πr².
• Rounding too early, for example using π = 3 or rounding the radius first.
• Leaving out units, or writing cm² for a circumference. A length is in cm or m.
• Multiplying by π when the question asks for an answer “in terms of π”.

Revision questions

Try these, then check your answers below each one.

Question 1. A circle has radius 8.5 cm. What is its diameter?

Answer: 17 cm

Working: d = 2 × 8.5 = 17 cm.

Question 2. Work out the circumference of a circle with diameter 13 cm. Give your answer to 1 decimal place.

Answer: 40.8 cm

Working: C = π × 13 = 40.840… = 40.8 cm.

Question 3. Work out the circumference of a circle with radius 9 m. Give your answer to 1 decimal place.

Answer: 56.5 m

Working: C = 2 × π × 9 = 18π = 56.548… = 56.5 m.

Related lessons

• Previous lesson: 16.5 Solving Quadratic Equations Algebraically
• Next lesson: 17.2 Circumference of a Circle 2
• In this chapter: 17.3 Area of a Circle
• In this chapter: 17.4 Semicircles and Sectors
• In this chapter: 17.5 Composite 2D Shapes and Cylinders

Continue in the full course

This lesson is section 17.1 (EGCMF1701) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.