5.3 Circles, Arcs and Sectors

2026 Syllabus Objectives

By the end of this topic, you should be able to:

Calculate the circumference and area of a circle.
Calculate arc length and sector area when the sector angle is a factor of 360° (e.g. 90°, 60°, 45°).
Give answers in terms of π when asked, and use the given formulas correctly.
Calculate arc length and sector area for any angle, including minor and major sectors.

A circle is a perfectly round, flat shape. Every point on the edge of a circle is exactly the same distance from the centre.

Here are the key parts you need to know:

Centre — the middle point of the circle.
Radius (r) — the distance from the centre to the edge. Every radius in the same circle is the same length.
Diameter (d) — a straight line that goes from one side of the circle to the other, passing through the centre. The diameter is always twice the radius: d = 2r, or the other way around, r = d ÷ 2.
Circumference (C) — the distance all the way around the edge of the circle. Think of it as the "perimeter" of the circle.
π (pi) — a special number that never ends: 3.14159… It is the ratio (relationship) between the circumference and the diameter of any circle. On your calculator, there is a dedicated π button — use it for accuracy.

These formulas are provided in your exam's List of Formulas, but you should know them well enough to use them confidently.

Circumference of a circle:

C = 2\pi r \quad \text{or equivalently} \quad C = \pi d

Both versions mean the same thing. Use whichever one fits the information you are given.

Area of a circle:

$A = \pi r^2$

This means: multiply π by the radius squared (radius × radius).

Check whether you have the radius or the diameter.
- If you have the diameter, use C = πd directly.
- If you have the radius, use C = 2πr.
Substitute (plug in) the number.
Multiply and write your answer with the correct units (e.g. cm, m).

💡 Circumference is a length, so your answer will always be in single units like cm or m — never cm² or m².