Area of a Circle
The area enclosed by a circle.
Formula
Variables
Example
r = 5 → A = 25π ≈ 78.54
How it works
A circle’s area depends on how far its edge is from the center, so the radius is the key measurement. The formula A = πr² comes from the fact that if you imagine a circle split into many thin slices and rearranged, those slices form a shape close to a rectangle with height r and width πr, giving area πr × r. That is why the area grows with the square of the radius: doubling the radius makes the area four times larger.
When to use it
Use this formula whenever you need the amount of flat space inside a circular shape, such as a round table top, pond, garden bed, or cross-section in physics and engineering. It is also used in geometry problems involving circles, disks, and sectors.
Worked example, step by step
Find the area of a circle with radius 8 cm. A = πr² A = π × 8² A = π × 64 A = 64π cm² A ≈ 201.06 cm²
Common mistakes to avoid
- Using the diameter instead of the radius
- Forgetting to square the radius before multiplying by π
- Leaving the answer in linear units instead of square units
Did You Know?
Archimedes proved the area of a circle by squeezing it between inscribed and circumscribed polygons — an early form of calculus.
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