One-quarter of a circle is called a quadrant. According to Reference.com, it is also a 90 degree arc. "Quad" is a prefix that means "fourth."
There are 360 degrees in a circle. Half of a circle is called a semicircle, and it contains 180 degrees. Whereas there are four quadrants in every circle, there are two semicircles.
The diameter of a circle is a straight line passing through the circle's center and touching the circle at each end. A circle with a horizontal line of diameter and a vertical line of diameter drawn is divided into quadrants. With only one diameter drawn, the circle is divided into semicircles.