Using the radius
\(A = \pi r^2\)
Circle Area Calculator
Calculate circle area and circumference from radius or diameter
Explore how area depends on the radius
Drag the radius slider and watch the area change. Pick a preset to compare familiar circles.
Quick presets
3.00
0.1050.00
Predict what will happen
If you double the radius, what happens to the area?
Move the slider from r = 2 to r = 4 and read off the area.
Try this
Move the slider until the area is exactly 100. What value of r did you need? Compare it to √(100 / π).
Notice
The area grows much faster than the radius — small changes in r have a big effect on A.
Why it works
A = πr² because a circle of radius r can be unrolled into a triangle with base 2πr (the circumference) and height r, whose area is ½·2πr·r = πr².
Results
Final Answer
Area is \(A = 28.2743\)
Step-by-step Solution
- The formula for the area of a circle is \(A = \pi r^2\)
- Substitute the given value: \(A = \pi \times (3)^2\)
- Calculate the area: \(A = \pi \times 9 \approx 28.2743\)
Radius (r)
\(r = 3.00\)
Diameter
\(d = 6.00\)
Circumference
\(C = 18.8496\)
Circle Area Formula
The area of a circle is the space enclosed by its circumference.
Key points
- The radius is the distance from the center to any point on the circle.
- Doubling the radius quadruples the area, because area scales with r².
- Area is always in square units (cm², m², etc.).
- π (pi) is the same constant for every circle: roughly 3.14159.
\(A = \pi r^2\)
Worked Examples
Using the diameter
\(A = \pi \left(\frac{d}{2}\right)^2 = \frac{\pi d^2}{4}\)
Example: r = 5
\(A = \pi \times 5^2 = 25\pi \approx 78.54\)
Example: d = 10
\(r = 5, A = \pi \times 5^2 \approx 78.54\)
External educational resource
Build your own circles in GeoGebra
Open the GeoGebra geometry tool to construct circles, measure radius and area, and explore the relationship visually.
GeoGebra (geogebra.org)