Circle Area
A = π·r²P = 2·π·rThe area of a circle is π multiplied by the radius squared. The perimeter, called circumference, is 2 times π times the radius.
The radius is the distance from the centre to the edge. The diameter is twice the radius, and confusing the two is the most common mistake — using the diameter in place of the radius multiplies the area by four.
π is the ratio between the circumference and the diameter of any circle, roughly 3.14159. It is irrational, so every result is an approximation.
Area grows with the square of the linear dimension, not proportionally. Doubling the radius quadruples the area; tripling it multiplies by nine.
That is why a 16-inch pizza holds twice as much as an 11-inch one, rather than 45% more as the measurement difference suggests.
The same logic explains why two medium pizzas rarely beat one large, despite looking like more food.
- Area of a circular floor or flower bed, to calculate materials.
- Cross-section of a pipe or cable, used in flow and current calculations.
- Sprinkler irrigation coverage, which waters a circular area.
- Comparing the real size of round products sold by diameter.
Frequently asked questions
Divide the diameter by two. Using the diameter directly in the formula multiplies the result by four, and it is the most frequent error in this calculation.
Because area grows with the square of the radius. Going from 11 to 16 inches doubles the amount of pizza, even though the measurement rose only about 45%.
The language’s double precision constant, with about 15 significant digits. Far beyond what any practical application needs.
Use the circular sector calculator, which takes the angle into account alongside the radius.