GCSE Maths / Edexcel

Circumference and area of circles

Choose between circumference and area formulae, convert diameter to radius when needed, and give accurate rounded circle answers.

Geometry and MeasuresFoundation and HigherGrades 4 to 6Skill

Curriculum path: GCSE Maths > Edexcel > Geometry and Measures > Circle circumference and area

Pearson Edexcel GCSE Maths geometry G9 and G16: know and use formulae for circumference and area of circles.

Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

The radius is the distance from the centre of a circle to the edge.

The diameter is the distance all the way across the circle through the centre. Diameter = 2 x radius.

Circumference is the distance around the circle. Circumference = πd or 2πr.

Area is the space inside the circle. Area = πr².

The most common mistake is using diameter in the area formula. Area uses radius, not diameter.

For calculator questions, use the π button unless the question tells you to use a rounded value.

If the question gives diameter and asks for area, halve the diameter first to get the radius.

Circumference answers use length units such as cm or m. Area answers use square units such as cm² or m².

Do not round too early. Keep the calculator value until the final answer, then round to the requested accuracy.

Key ruleCircumference = πd = 2πr; area = πr².

Diagram guide

diameterradiussectorcircumference = πd, area = πr²
Circle measuresUse diameter for circumference if given. Use radius squared for area.
rdiameter = 2rarea uses radius, then square itA = πr², not πd²
Area uses radiusThe area formula is πr². If you use the diameter instead of the radius, the answer is four times too large.
diameter 18 cmradius 9 cmhalve the diameter before area18 ÷ 2 = 9, so A = π x 9²
Diameter to radiusWhen area is asked and diameter is given, halve the diameter before substituting into πr².

Worked examples

Circumference from diameter

Find the circumference of a circle with diameter 10 cm.

diameterradiussectorcircumference = πd, area = πr²
Example: circumference from diameterCircumference uses the distance around the edge.
  1. Circumference = πd.
  2. C = 10π.

Answer: 10π cm, or 31.4 cm to 1 decimal place

Area from radius

Find the area of a circle with radius 6 cm.

rdiameter = 2rarea uses radius, then square itA = πr², not πd²
Example: area from radiusSquare the radius, not the diameter.
  1. Area = πr².
  2. A = π x 6² = 36π.

Answer: 36π cm², or 113.1 cm² to 1 decimal place

Radius from diameter

A circle has diameter 18 cm. Find its radius.

diameter 18 cmradius 9 cmhalve the diameter before area18 ÷ 2 = 9, so A = π x 9²
Example: halve the diameterRadius is half of diameter.
  1. Radius is half the diameter.
  2. 18 / 2 = 9.

Answer: 9 cm

Area from diameter

A circle has diameter 12 cm. Find its area in terms of π.

diameter 18 cmradius 9 cmhalve the diameter before area18 ÷ 2 = 9, so A = π x 9²
Example: area from diameterHalve first, then square the radius.
  1. Radius = 12 / 2 = 6 cm.
  2. Area = πr².
  3. Area = π x 6² = 36π.

Answer: 36π cm²

Common mistakes

  • Using diameter instead of radius in πr².
  • Forgetting to square the radius for area.
  • Using 2πr for area.
  • Rounding too early before the final answer.
  • Giving square units for circumference or length units for area.
  • Halving the diameter for circumference when πd could be used directly.

Quick exercise

Try these before moving to the exam-style questions.

  1. Find the circumference of a circle with diameter 8 cm.
    diameterradiussectorcircumference = πd, area = πr²
    Quick check: circumference from diameterUse C = πd.
  2. Find the circumference of a circle with radius 5 cm.
    diameterradiussectorcircumference = πd, area = πr²
    Quick check: circumference from radiusUse C = 2πr.
  3. Find the area of a circle with radius 4 cm.
    rdiameter = 2rarea uses radius, then square itA = πr², not πd²
    Quick check: area from radiusUse A = πr².
  4. A circle has diameter 14 cm. Find its radius.
    diameter 18 cmradius 9 cmhalve the diameter before area18 ÷ 2 = 9, so A = π x 9²
    Quick check: radiusRadius is half the diameter.
  5. Find the area of a circle with diameter 12 cm.
    diameter 18 cmradius 9 cmhalve the diameter before area18 ÷ 2 = 9, so A = π x 9²
    Quick check: area from diameterHalve the diameter before using πr².
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationCalculator2 marks

A circle has diameter 12 cm. Work out its circumference. Give your answer to 1 decimal place.

diameterradiussectorcircumference = πd, area = πr²
Question diagram: circumferenceThe diameter is given, so use C = πd.
circumferencediametercalculator geometry
Standard exam styleFoundation and HigherCalculator3 marks

A circle has radius 7 cm. Work out its area. Give your answer to 1 decimal place.

rdiameter = 2rarea uses radius, then square itA = πr², not πd²
Question diagram: area from radiusUse the radius in A = πr².
area of circleradiusmethod marks
ChallengeFoundation and HigherCalculator4 marks

A circular garden has diameter 9 m. Work out its area to 2 decimal places.

diameter 18 cmradius 9 cmhalve the diameter before area18 ÷ 2 = 9, so A = π x 9²
Question diagram: area from diameterArea needs radius, so halve the diameter first.
circle areadiameter to radiusrounding