Area of a circle formula
The area of a circle depends only on its radius. Multiply pi by the radius squared to get the space enclosed inside the circle. It is one of the most-used formulas in geometry and design.
What each symbol means
| Symbol | Meaning | Units |
|---|---|---|
| A | Area | square units |
| r | Radius (center to edge) | length unit |
| π | Pi, about 3.14159 | constant |
Rearranged forms
Worked example
A circle has a radius of 5 cm. Find its area.
- Start from A = π r².
- Square the radius: 5² = 25.
- Multiply by pi: A = π × 25.
Area comes out in square units of whatever length unit you use for the radius. If you have the diameter, halve it first. The circumference uses the same radius: C = 2 π r.
Have the radius or diameter?
Enter any one measurement and the Circle Calculator gives area, circumference, and diameter together.
How the formula works
Pi is the fixed ratio of a circle's circumference to its diameter. Squaring the radius and multiplying by pi totals the area enclosed. Because the radius is squared, doubling it quadruples the area — a circle twice as wide holds four times as much.
Where it is used
Circle area appears in pipe and duct sizing, tank and cylinder volumes, material estimates for round parts, land area, and countless design tasks. With circumference and diameter it covers most everyday circle math.
FAQ
What is the area of a circle formula?
A = π r², where r is the radius and pi is about 3.14159. The area comes out in square units.
How do I find area from the diameter?
Halve the diameter to get the radius, then use A = π r². Equivalently, A = π (d/2)².
Why is the radius squared?
Area is two-dimensional, so it scales with the square of a length. Doubling the radius multiplies the area by four, not two.