Think of the mirror as a slice of a large ball; the distance from the center of that ball to the edge is the radius, and the mirror's focus sits halfway between the center and the edge.

R is double F: Reach (R) for the Focus (F) and Double it.

A spherical mirror is essentially a part of a hollow sphere. The center of this sphere is called the Center of Curvature ($C$), and the distance from the pole of the mirror to $C$ is the radius of curvature ($R$). The focal point ($F$) is the midpoint between the pole and the center of curvature, establishing the geometric relationship $R = 2f$.

Always remember that for lenses, $f = \frac{R}{2}$ is also used for thin lenses, and sign conventions are critical in competitive exams to avoid errors with virtual vs. real images.