DfE statement G18 · Geometry and measures

Arc lengths and sector areas

Both tiersCalculator

Arc lengths and sector areas is content statement G18 of the DfE GCSE mathematics subject content, in the geometry area. It is on both tiers, and it is normally a calculator-paper question. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.

What the specification says

The DfE subject content for GCSE mathematics states, verbatim: "Calculate arc lengths, angles and areas of sectors of circles." (statement G18). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement G18

Tier

Both tiers. This statement is Foundation content, which means Higher students are examined on it too — Higher is Foundation plus more, never instead of it.

Calculator

This is calculator work, which places it on Papers 2 and 3. Know your own calculator before the exam, keep full accuracy through the working and round only at the end.

Common mistakes

Inverting the fraction of the circle: a 60° sector is 60/360 of the circle, not 360/60.
Giving the perimeter of a sector as the arc length alone, forgetting the two radii.
Using the sector formula with the angle in radians. GCSE works in degrees.

Formulae for this statement

Circumference of a circleC = 2πr = πdYou must know this Area of a circleA = πr²You must know this

Sample questions (10 of 30)

G18 · Arc lengths and sector areasQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Geometry and measures

G18

Beginner

A sector of a circle has radius 5 cm and angle 72°. Work out the arc length of the sector, in terms of π.

💡 Hints:

Foundation worksheet Higher worksheet Foundation geometry and measures practice Higher geometry and measures practice

Nearby statements

G1Geometric terms, notation and diagrams G2Ruler and compass constructions and loci G3Angle facts, parallel lines and polygons

Questions people ask

Is arc lengths and sector areas on Foundation or Higher?

Both. It is Foundation content, so it can be asked on either tier.

Can I use a calculator for arc lengths and sector areas?

Yes, on Papers 2 and 3, which are the calculator papers and where questions on this usually sit. Paper 1 is non-calculator.

What is the single most common mistake here?

Inverting the fraction of the circle: a 60° sector is 60/360 of the circle, not 360/60.

Are these past paper questions?

No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.

Back to Geometry and measures at Foundation or at Higher.