Circumference of a Circle: Complete Formula & Worked Examples

To calculate the circumference of a circle, use the formula C = 2πr (if you know the radius) or C = πd (if you know the diameter), where π ≈ 22/7 or 3.14. Example: a circle with a radius of 7 cm has a circumference of 2 × (22/7) × 7 = 44 cm. Choose π = 22/7 when r is a multiple of 7.

What Is the Circumference of a Circle?

The circumference of a circle is the distance all the way around the circle. The idea has been known since ancient Babylonia, around 1900 BC, when the earliest mathematicians first approximated π ≈ 3.125. Unlike straight-sided shapes, the circumference relies on the special constant π (pi) ≈ 3.14 or 22/7.

A circle has two key measurements:

• Radius (r): the distance from the centre to the edge of the circle
• Diameter (d): the distance from edge to edge through the centre = 2 × radius

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Formulas for the Circumference of a Circle

There are two formulas, depending on what you know:

Written out: C = 2 × π × r or C = π × d, where d = 2r and π ≈ 22/7 or 3.14

💡 Tip for Choosing π: Use π = 22/7 when the radius or diameter is a multiple of 7 (7, 14, 21, 28...) so the answer is a whole number. Use π = 3.14 for calculator work or problems with decimals.

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Worked Examples: Circumference of a Circle

Example 1: Radius Given

A round wall clock has a radius of 21 cm. Calculate its circumference.

Step 1: Given r = 21 cm. Since 21 is a multiple of 7, use π = 22/7.

Step 2: Substitute into C = 2πr:

Answer: The circumference of the clock is 132 cm.

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Example 2: Diameter Given

A bicycle wheel has a diameter of 56 cm. What is the circumference of the wheel?

Step 1: Given d = 56 cm. Use C = πd with π = 22/7:

Answer: The circumference of the wheel is 176 cm.

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Example 3: Finding the Radius from the Circumference

A circular Olympic-sized pool in Jakarta has a circumference of 88 m. What is its radius?

Step 1: Use C = 2πr and substitute C = 88:

Step 2: Solve:

Answer: The radius of the pool is 14 m.

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Common Mistakes When Calculating the Circumference

Many Year 5–6 pupils slip up in the same two ways. Spot them and avoid them:

Mistake 1: Mixing up radius and diameter If a problem gives diameter = 14 cm but you plug r = 14 into C = 2πr, the answer comes out twice as large. Remember: if you know the diameter, use C = πd; if you know the radius, use C = 2πr.

Mistake 2: Choosing the wrong value of π Using π = 3.14 when the radius is a multiple of 7 leaves you with unnecessary decimals. For example, r = 14 cm with π = 3.14 gives C = 87.92 cm, whereas π = 22/7 gives a tidy C = 88 cm. Pick π = 22/7 for multiples of 7.

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Circumference Table

💡 Quick Tip: Notice the pattern: every increase of 7 in r adds 44 cm to the circumference. So C(7) = 44, C(14) = 88, C(21) = 132... You can multiply straight away!

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Practice Problems: Circumference of a Circle

Problem 1: ⭐ A circular garden in Surabaya has a radius of 14 m. How long is the fence needed to go around it?

Problem 2: ⭐⭐ A circle has a diameter of 10 cm. Calculate its circumference (use π = 3.14).

Problem 3: ⭐⭐⭐ A rickshaw wheel covers 11 m in one full turn. What is the radius of the wheel? (π = 22/7)

Answer Key:

1. C = 2 × (22/7) × 14 = 2 × 44 = 88 m
2. C = 3.14 × 10 = 31.4 cm
3. 11 = 2 × (22/7) × r → r = (11 × 7) / 44 = 77/44 = 1.75 m

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Summary

1. The circumference of a circle is the distance all the way around it, calculated with C = 2πr (if you know the radius) or C = πd (if you know the diameter).
2. The value of π used: 22/7 for numbers that are multiples of 7, or 3.14 for other numbers.
3. The radius (r) is half the diameter: d = 2r.
4. To find the radius from the circumference, use r = C ÷ (2π).
5. The circumference appears all over real life: the length of a fence around a round garden, the distance a vehicle wheel rolls in one turn, and the design of round objects.

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