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
The circumference of a circle is 88 cm. Find its area. Use \(\pi=\tfrac{22}{7}\).
- \(2\times\tfrac{22}{7}\times r=88\), so \(r=14\)
- \(A=\tfrac{22}{7}\times14^2=22\times28\)
Answer: \(A=616\text{ cm}^2\)
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 |
|---|---|
| Class 10 | Learn it: CBSE gives no formula booklet |
From our own CBSE Maths formula sheets, in our words.
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?
Class 10: learn it: CBSE gives no formula booklet. This comes from our own CBSE 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 CBSE Math Revision. Not produced or endorsed by CBSE or NCERT.