Fiducia TogetherCircle geometry: arcs and sectors
Parts of a circle, and the fractions that give their size.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
An arc is part of the circumference; a sector is a slice bounded by two radii; a segment is cut off by a chord.
Where it applies
Both tiers; segments are higher tier.
How it works
Arc length and sector area are fractions of the whole circle, the fraction being the angle over 360.
Surface areas and volumes of cones, spheres and frustums build on the same idea.
How to use it in your work
Write the fraction explicitly before calculating — it earns a method mark and prevents the usual error of using the wrong formula.
Leave answers in terms of π when asked for an exact value.
Check whether the question wants the perimeter of a sector, which includes the two radii as well as the arc.
Where to get help
Your teacher and your board's specification and mark scheme.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.