Circle (with radius) - perimeter and area

A circle is a two-dimensional shape made up of all the points in a plane that lie at the same distance from a single fixed point called the center. That constant distance is the radius, and because every radius is equal in length, the circle is perfectly symmetric about its center. The straight line passing through the center from one side to the other is the diameter, which is exactly twice the radius, while the total distance around the edge is called the circumference. A circle also encloses a region whose size is its area, and both the circumference and the area depend only on the radius through the constant pi. The circle is one of the most fundamental shapes in geometry, prized for having the largest area of any figure with a given perimeter.

Circles appear almost everywhere in the real world, from wheels, gears, and coins to orbits, ripples on water, and the cross-sections of pipes. Engineers, architects, and designers rely on them to distribute forces evenly and to create smooth, efficient motion, which is why rotating machinery is built around circular parts. Knowing just the radius lets you determine every other measurement of the circle, making it a natural starting point for calculation.