For a spherical mirror under the paraxial approximation, the focal length $f$ and radius of curvature $R$ are related by 

Using the geometry of reflection for paraxial rays and the small-angle approximation, one obtains $\mathrm{FD}=\mathrm{CD}/2$. Since for paraxial rays $\mathrm{FD}=f$ and $\mathrm{CD}=R$, it follows that $f=R/2$.