This revision guide tells you everything you need to know about sectors for GCSE maths. We’ll show you: what a sector is; what the arc length is; and how to calculate the arc length and area. We’ve also set out a range of exam style questions at the end for you to practice. Before revising sectors, make sure you’ve learnt the basics about circles, including key terminology, area and circumference. Check out our revision guide on circles to see everything you need to know before starting your work on sectors.

What is a sector?

A sector is simply part of a circle defined by two radii and an arc length. The arc length is part of the circumference ‘cut out’ by the two radii. As with any shape, it’s easiest just to show you an example – you can see a sector in the diagram below.

Sector of a circle

Working out the arc length

For your GCSE maths exams you need to know how to work out the arc length created by any sector. An arc length is simply part of the circumference. You can calculate the arc length by using this formula:

Arc length formula

In this formula r is the radius and the strange looking symbol on the numerator is ‘theta’ (which is a greek letter we usually use to represent a missing angle) representing the interior angle at the centre of the sector. You can see both set out in the diagram below.


Working out the area of a sector

To work out the area of a sector there is another formula to remember. Here it is:

Area of a sector formula

Notice how the arc length and area formulas are based on the area and circumference formulas for a circle. Both are simply multiplied by the angle at the centre over 360 (this fraction ‘cuts out’ the part of the circle you’re working with).


Check out the example below. We’ve shown you how to use the formulas to calculate the arc length and the area of the sector shown.

Sector example

Sectors – practice questions

Now try the practice questions below. For each sector you need to work out both the arc length and the area of the sector.

Sector question 1
Sector question 2
Sector question 3

For the next question you are given the angle at the centre, 98 degrees, and the arc length, 10cm. You need to find the radius, marked x. To do this, write down the formula for the arc length, input the numbers you’ve been given and then solve the equation to find the value of x.

Sector question 4

Once you can do all four of the question above, then you’ll be ready to take on anything related to sectors in your GCSE maths exams. If you need any further help then why not book in a lesson with one of our online tutors? Contact us today and we’ll arrange a trial online lesson for you.

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