The formula for calculating the area of a circle is A = πr², where A represents the area, π (pi) is a constant approximately equal to 3.14159, and r is the radius of the circle. The radius is the distance from the center of the circle to any point on its edge. This formula helps in determining the space enclosed by a circle and is widely used in various fields of mathematics, physics, and engineering. Understanding how to apply this formula is essential for solving problems involving circular shapes.