What is the formula to calculate the area of a circle?

The formula for calculating the area of a circle is represented as A = πr², where A stands for area and r represents the radius of the circle. This formula originates from the concept that the area of a circle can be derived by considering the relationship between the radius and the properties of circles.

In this formula, π (pi) is a mathematical constant approximately equal to 3.14159, which relates to the ratio of a circle's circumference to its diameter. By squaring the radius (r²) and multiplying by π, we obtain a precise measurement of the space contained within the circle.

This concept is fundamental in geometry and is widely used in various applications involving circles, such as architecture, engineering, and even in everyday problem-solving situations. It’s important to distinguish this formula from those for circumference and surface area, which address different measurements of a circle and its 3-dimensional counterpart, respectively.