Area of a circle formula: A = πr²

The area of a circle formula is A = πr² (circumference C = 2πr = πd).

\(\displaystyle A=\pi r^2\) \(\displaystyle C=2\pi r=\pi d\)

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 circular pond has circumference 18 m. Find its area.

\(2\pi r=18\), so \(r=\dfrac{9}{\pi}\)
\(A=\pi\left(\dfrac{9}{\pi}\right)^2=\dfrac{81}{\pi}\)

Answer: \(A=25.8\text{ m}^2\) (3 s.f.)

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
AA SL	In the IB formula booklet
AI SL	In the IB formula booklet
AA HL	In the IB formula booklet
AI HL	In the IB formula booklet

From our own IB Maths formula sheets, in our words. The IB gives its booklet to schools, so we checked against our own copy: your teacher has the official one. Official: IB DP Mathematics page.

Practise and revise

Practise AI SL volume and surface area questions
Revise 3D geometry (AI SL)
Print AA SL one-page formula sheet

Area of a circle formula card: A = πr² (circumference C = 2πr = πd). IB Math Revision — Area of a circle formula card. Download the card (PNG) to save or print it.

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?

AA SL: in the IB formula booklet. AI SL: in the IB formula booklet. AA HL: in the IB formula booklet. AI HL: in the IB formula booklet. This comes from our own IB 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 IB Math Revision. Not produced or endorsed by the International Baccalaureate Organization.