The formula for the area of a circle is given by the equation 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. To calculate the area, one must measure the radius (the distance from the center of the circle to its edge), square that measurement, and then multiply it by π. This formula is fundamental in geometry and is widely used in various fields such as engineering, architecture, and physics to solve problems involving circular shapes.