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Geometry & Measures · Foundation & Higher

Circle area & circumference

The two key circle formulas relate to its boundary (circumference) and enclosed area. Both use π (pi ≈ 3.14159...).

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Key facts to remember

  • 1Radius (r) = distance from centre to edge. Diameter (d) = 2r.
  • 2Circumference = distance around the outside of the circle.
  • 3Area = space inside the circle.
  • 4π ≈ 3.14159 (use the π button on your calculator).
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Formulas

Circumference
C = πd = 2πr
Area
A = πr²
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Worked examples

Example 1

Find the circumference and area of a circle with radius 5 cm. Give your answers to 1 d.p.

Working

  1. Circumference = 2 × π × 5 = 10π = 31.4 cm
  2. Area = π × 5² = 25π = 78.5 cm²
AnswerC = 31.4 cm, A = 78.5 cm²
Example 2

A circle has circumference 40 cm. Find its radius.

Working

  1. 2πr = 40
  2. r = 40 ÷ (2π) = 20/π ≈ 6.37 cm
Answerr ≈ 6.37 cm
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Common mistakes

✗Squaring the diameter instead of the radius in the area formula.
✗Confusing circumference and area formulas.
✗Forgetting to halve the diameter to get the radius.
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Exam tips

✓If the question gives the diameter, halve it before using the area formula.
✓Leave answers in terms of π (e.g. 25π cm²) if the question asks for an exact answer.

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