Definition
Area of a circle
The area of a circle is its inside space, found with A = πr².
What it means
The radius reaches from the centre to the edge. Make a square whose side is that radius; its area is r². The circle’s area is exactly π times the area of that radius square, so multiply r² by π.
Remember it
Radius, square it, then multiply by π: r → r² → πr².
Example
A circle has radius 3 cm. Squaring gives 3 × 3 = 9, so A = π × 9 = 9π cm², about 28.27 cm².
Watch for
The formula uses the radius, not the diameter. If 6 cm is the diameter, use radius 3 cm before squaring.
Common mix-up
Circumference measures distance around in linear units; area measures inside space in square units.
Exact meaning
For a circle of radius r, the area of its interior is A = πr², where π is the constant ratio of any circle’s circumference to its diameter. Circle area is expressed in square units.