Area of a circle formula: A = πr²
The area of a circle formula is A = πr² (circumference C = 2πr = πd).
What each letter means
- \(A\) the area
- \(C\) the circumference: the distance round the circle
- \(r\) the radius
- \(d\) the diameter, d = 2r
When to use it
For the area inside a circle, or (with C = 2πr) the distance round it. Work backwards from an area or a circumference to find the radius first.
Worked example
A circle has diameter 9 cm. Find its area and its circumference, to 3 significant figures.
- \(r=4.5\)
- \(A=\pi(4.5)^2=20.25\pi\) and \(C=\pi\times9=9\pi\)
Answer: \(A=63.6\text{ cm}^2\), \(C=28.3\text{ cm}\)
Common mistake
Mixing up the two formulas: πr² is the area (square units) and 2πr is the circumference (length). And square only the radius: πr² is π × r², not (πr)².
On your course
| Course | In the exam |
|---|---|
| Edexcel 4MA1 (Higher) | Not given: learn it |
| Cambridge 0580 | On the list of formulas printed in the paper |
From our own IGCSE Maths formula sheets, in our words. Official: Pearson's 4MA1 specification (PDF, Appendix 5) · Cambridge's 0580 syllabus (PDF).
Practise and revise
Questions
What is the area of a circle formula?
The area of a circle formula is A = πr² (circumference C = 2πr = πd). A: the area; C: the circumference: the distance round the circle; r: the radius; d: the diameter, d = 2r.
Is the area of a circle given in the exam?
Edexcel 4MA1 (Higher): not given: learn it. Cambridge 0580: on the list of formulas printed in the paper. This comes from our own IGCSE Maths formula sheets; your teacher has the official booklet.
How do I find the radius from the circumference?
Rearrange C = 2πr to r = C ÷ 2π. Then use A = πr² if you need the area.
Our own wording, examples and card, checked by IGCSE Math Revision. Not produced or endorsed by Pearson Edexcel.