GCSE MATHS • HIGHER TIER
Circumference Made Simple
Learn how to calculate the distance around a circle using radius, diameter and π, and solve reverse circumference problems.
Clear method
Exam practice
Worked proofs
circumference in Four Moves
1
Identify
Identify whether the radius or diameter is given.
2
Choose
Choose the correct circumference formula.
3
Substitute
Substitute the known measurement into the formula.
4
Calculate
Calculate using π and give the answer in exact or decimal form.
What You’ll Learn
Understand Circumference
Understand that circumference is the distance around the edge of a circle.
Use Circle Vocabulary
Recognise radius, diameter, circumference and π.
Apply Both Formulas
Use C = πd or C = 2πr depending on the information given.
Solve Reverse Problems
Find a missing diameter or radius from a known circumference.
Use Correct Units
Give circumference answers in linear units such as cm, m or km.
Key Rules
Using diameter
Circumference = π × Diameter
Using radius
Circumference = 2πr
Diameter and radius
Diameter = 2 × Radius
Exact answers
Leave the answer in terms of π when an exact value is required.
Units
Circumference is a length, so use linear units rather than square units.
Worked Proof: circumference
Step-by-Step Method
- 1. Identify whether the radius or diameter is given.
- 2. Choose the correct formula.
- 3. Substitute the values.
- 4. Calculate using π.
- 5. Give the answer in the required form, exact or decimal.
More Worked Examples
1
Question: A circle has a radius of 6 cm.
C = 2πr
C = 2 × π × 6
C = 12π cm
C ≈ 37.7 cm
C = 12π cm
C ≈ 37.7 cm
2
Question: A circle has a diameter of 14 cm.
C = π × 14
C = 14π cm
C ≈ 44.0 cm
C ≈ 44.0 cm
3
Question: A circle has a radius of 8 cm.
C = 2π × 8
C = 16π cm
C ≈ 50.3 cm
C ≈ 50.3 cm
4
Question: The circumference of a circle is 31.4 cm. Find the diameter.
d = C ÷ π
31.4 ÷ 3.14 = 10
- Common GCSE Mistakes
- Radius vs diameter: Check which measurement is given before choosing a formula.
- Missing factor of 2: Use 2πr when the radius is given.
- Wrong units: Circumference uses linear units, not square units.
- Early rounding: Keep full calculator accuracy until the final answer.
- Exam Tips
- Choose carefully: Use πd for diameter or 2πr for radius.
- Write the formula first: Show the correct formula before substituting.
- Keep π exact: Leave π when an exact answer is requested.
- Check reverse questions: Rearrange carefully to find radius or diameter.
- Check units: Use cm, m, km or the required linear unit.
Skills Used in circumference
Circle Area and Circumference
Circumference
Area of Circles
Area of a Sector
Geometry
Compound Shapes
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Circumference Tutorial
Step-by-step walkthroughs of Circumference with clear methods and exam tips.
Frequently Asked Questions
Circumference is the total distance around the edge of a circle.
Use C = πd when the diameter is known or C = 2πr when the radius is known.
The diameter is twice the radius, so d = 2r.
Divide the circumference by π.
Divide the circumference by 2π, or find the diameter first and halve it.
Use linear units such as centimetres, metres or kilometres.
