What is the formula for calculating the area of a circle?

The formula for calculating the area of a circle is represented as πr², where π (pi) is a constant approximately equal to 3.14, and r represents the radius of the circle. To understand this formula, think of the circle as being composed of many infinitesimally small triangles whose combined area forms the whole area of the circle.

The factor of π in the formula accounts for the ratio of the circumference of a circle to its diameter, and it emerges naturally when calculating the area based on the radius. The r² factor indicates that the area is proportional to the square of the radius, meaning if you double the radius, the area increases by a factor of four.

This concept is fundamental in geometry and is widely applied in various fields, including architecture, engineering, and physics. Notably, this formula precisely quantifies the space enclosed within a circular boundary.