IGCSE Maths / Circles, cylinders, cones and spheres

Circumference of a circle revision notes

Edexcel International GCSE Maths (4MA1), chapter 12: Circles, cylinders, cones and spheres, specification point 4.9e-f. Free lesson.

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The circumference is the distance all the way round a circle. You find it using the diameter and π, so it is important to use the full width across the circle and keep π unrounded until the end.

What the circumference formula means

The circumference is the distance all the way round the outside of a circle. It is the circle’s perimeter. The formula is on the formula sheet, so you can copy it rather than memorise it. C = πd C is the circumference, d is the diameter, and π is a number with no units. The diameter is the full width across the circle through its middle. The radius reaches only halfway across. Circumference is a length, so its units are cm or m, not squared.

How to find circumference from the radius

The formula needs the diameter. If you are given the radius, double it first because the radius is half the diameter. You can also use C = 2πr, which includes that doubling.

Worked example: radius 7 cm

The radius is 7 cm, so the diameter is 14 cm. Keep π in the calculation and give the circumference to 3 significant figures.

Why using the radius gives the wrong answer

Putting the radius straight into C = πd uses only half the required width. This makes the circumference exactly half as large as it should be. Using 7 instead of 14 gives C = π × 7 ≈ 22.0 cm. Using the diameter gives C = π × 14 ≈ 44.0 cm. If your answer seems too small, check whether you doubled the radius.

How circumference changes when a circle is enlarged

If you double the radius, you also double the diameter. Since circumference is π multiplied by the diameter, doubling the diameter doubles the circumference. Doubling the radius makes the circumference twice as large. This rule is about circumference. Area increases four times when the radius doubles.

How to find the diameter from circumference

You can rearrange the formula when the circumference is given and the diameter is needed. Since d is multiplied by π, divide by π to leave d on its own.